Description
IIPM
“A Report On Pricing and Technical Analysis of Derivatives”
THE INDIAN INSTITUTE OF PLANNING AND MANAGEMENT
EXECUTIVE SUMMARY
The emergence of Derivatives market especially Futures and Options can be traced back to the willingness of the risk adverse economic agents to guard against themselves against the fluctuations in the price of Underlying asset. Derivatives, whose price is determined by the price of underlying asset, generally do not cause any fluctuations in the price of underlying asset. But impact of any change in the price of underlying asset may cause swift change in the price of Derivatives instrument. This project concerns one of the core issues in DerivativesPricing of Derivatives and impact of change in price of underlying to the price of Futures and Option through scenario analysis , valuation of Option and Futures through appropriate mathematical models and comparison of actual market price with theoretical price and exploiting arbitrage opportunities when even there are any deviations in the pricing , past trend of Options and Futures market and daily movements in Nifty Spot , Nifty Futures and Options for the past three months.
Another important issue in Derivatives is the appropriate position to choose from plethora of series of Call options and Put Options on a single day and permutations and combinations of strategies along with various option positions can be daunting task. This project seeks to answer some of the questions regarding appropriate strategy to choose in order to maximize total payoff through technical analysis of the parameters of Option.
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TABLE OF CONTENTS DERIVATIVES:....................................................................................................................... 6 FORWARD CONTRACT:...................................................................................................... 6 FUTURES CONTRACT: ........................................................................................................ 6
PAYOFFS FROM THE FORWARD CONTRACT: ........................................................................................................6
BASIS: ..................................................................................................................................... 16 BASIS RISK: .......................................................................................................................... 16 PRICING OF FUTURES: ..................................................................................................... 27
FUTURES PRICE CALCULATOR ................................................................................................................. 28
STRATEGY USING FUTURES: ......................................................................................... 30
ARBITRAGE OPPORTUNITIES:...................................................................................................................30 HAVE FUNDS- LEND THEM TO THE MARKET: .....................................................................................................30 HAVE SECURITIES –LEND THEM TO THE MARKET. .............................................................................................30
HEDGING: ............................................................................................................................. 31
SHORT HEDGE...............................................................................................................................................31 LONG HEDGE:................................................................................................................................................31 OPTIMAL HEDGE RATIO:....................................................................................................................................31
HEDGING USING INDEX FUTURES: .............................................................................. 32
LONG SECURITY/PORTFOLIO - SHORT FUTURES: ................................................................................................32 SHORT SECURITY –LONG FUTURES: ...................................................................................................................32
HEDGING STATERGIES:................................................................................................... 32
LONG PORTFOLIO - SHORT FUTURES ................................................................................................................33 SHORT PORTFOLIO- LONG FUTURES ..................................................................................................................34
LOSS ON FUTURES ............................................................................................................. 34 GAIN ON SPOT RANSACTION ......................................................................................... 34 RISK FREE INTEREST ....................................................................................................... 34 NET POSITION ..................................................................................................................... 34 VALUE OF PORTFOLIO .................................................................................................... 34 SPECULATION ..................................................................................................................... 35
BEARISH- SHORT FUTURES ................................................................................................................................35
PROFIT FORM FUTURES .................................................................................................. 35 FUTURE PRICE-SPOT PRICE * NUMBER OF CONTRACTS..................................... 35
BULLISH- LONG FUTURES .................................................................................................................................35
OPTIONS................................................................................................................................ 36
CALL OPTION : ..................................................................................................................................................36 PUT OPTION : ....................................................................................................................................................36 AMERICAN OPTION :..........................................................................................................................................36 EUROPEAN OPTION :..........................................................................................................................................36 POSITION IN OPTION: .........................................................................................................................................36 PAY OFF FROM OPTION:.....................................................................................................................................36
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ADJUSTING OPTIONS TO SHARE SPLIT AND STOCK DIVIDENDS:..................... 36
SHARE SPLIT:.....................................................................................................................................................37 STOCK DIVIDENDS: ............................................................................................................................................37
TERMINOLOGY: ................................................................................................................. 37
PREMIUM : .........................................................................................................................................................37 INTRINSIC VALUE: .............................................................................................................................................37 TIME VALUE:.....................................................................................................................................................38 IN THE MONEY: ..................................................................................................................................................38 AT THE MONEY:.................................................................................................................................................38 OUT OF THE MONEY:..........................................................................................................................................38
FACTORS AFFECTING THE OPTION PRICES: ........................................................... 39
CALL OPTION:....................................................................................................................................................39 PUT OPTION: ......................................................................................................................................................39 TIME TO EXPIRATION .........................................................................................................................................39 VOLATILITY OF THE STOCK PRICE ......................................................................................................................39 RISK FREE RATE OF INTEREST ............................................................................................................................40 DIVIDENDS EXPECTED DURING THE LIFE OF ASSET ............................................................................................40
SCENARIO ANALYSIS........................................................................................................ 42
CHANGE IN DELTA TO CHANGE IN STOCK PRICE ...............................................................................................46 CHANGE IN GAMMA TO CHANGE IN STOCK PRICE .............................................................................................47 CHANGE IN RHO TO CHANGE IN STOCK PRICE ...................................................................................................48 CHANGE IN OPTION PRICE TO CHANGE IN VOLATILITY .....................................................................................50
LIMITS ON UPPER AND LOWER BOUND FOR OPTIONS: ....................................... 55
INTRINSIC VALUE OF AN OPTION:......................................................................................................................55
PUT CALL PARITY: ............................................................................................................ 56 PROPERTY DISTRIBUTION OF A STOCK PRICE: ..................................................... 58 PRICING OF OPTIONS ....................................................................................................... 60
BLACK SCHOLES MODEL:......................................................................................................................... 60 Value of Call Option: ...................................................................................................................................60 Value of Put : ...............................................................................................................................................61 BLACK SCHOLES MODEL ...........................................................................................................................61
TECHNICAL ANALYSIS OF OPTION PARAMETERS ................................................ 65
DELTA ...............................................................................................................................................................65 Hedge Ratio .................................................................................................................................................66 DELTA HEDGING STRATEGIES: ..........................................................................................................................73
GAMMA ................................................................................................................................. 75
MAKING PORTFOLIO GAMMA NEUTRAL ............................................................................................................75
ANALYSIS OF OPTION PARAMETERS: ........................................................................ 79
METHODOLOGY:................................................................................................................................................79 DELTA AND GAMMA:.........................................................................................................................................79
THETA :.................................................................................................................................. 80
VEGA (?) : .........................................................................................................................................................81 ANALYSIS OF VEGA OF CALL AND PUT OPTIONS ...............................................................................................84
RHO : ...................................................................................................................................... 85 ELASTICITY:........................................................................................................................ 85
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COMPARISON OF THEORETICAL AND ACTUAL PRICE OF OPTION:................ 86
THEORETICAL EDGE FOR CALL................................................................................................................ 87
RELATIVE STRENGTH INDEX (RSI).............................................................................. 93
METHODOLOGY FOR RSI CALCULATION ...........................................................................................................99 INTERPRETATION ...............................................................................................................................................99
IMPLICATIONS FOR OPTION TRADERS...................................................................... 99 TRADING STRATEGY USING OPTIONS: .................................................................... 101
USING SINGLE OPTION AND THE STOCK: ......................................................................................................... 101 BULL SPREAD:................................................................................................................................................. 101 Bull Spread with Calls: .............................................................................................................................. 102 Bull spreads with Puts: .............................................................................................................................. 102 Bull spread with put ................................................................................................................................... 102 BULL SPREAD WITH CALL ..................................................................................................................... 104 BEAR SPREAD : ................................................................................................................................................ 106 Bear spread with Call : .............................................................................................................................. 106 Bear Spread with Put :............................................................................................................................... 106 VOLATILITY SPREAD: ...................................................................................................................................... 106 Back spread: .............................................................................................................................................. 107 Ratio Vertical Spread: ............................................................................................................................... 107 BUTTERFLY SPREAD: ....................................................................................................................................... 109 Long Butterfly : .......................................................................................................................................... 109 Short Butterfly:........................................................................................................................................... 109 STRADDLE : ..................................................................................................................................................... 109 STRANGLE: ...................................................................................................................................................... 110 CALENDAR SPREAD: ........................................................................................................................................ 112 DIAGONAL SPREAD :........................................................................................................................................ 112 STRAP : ............................................................................................................................................................ 112 STRIPS: ............................................................................................................................................................ 112 LONG STRANGLE ............................................................................................................................................. 112 SHORT STRANGLE............................................................................................................................................ 115 LONG STRANGLE ............................................................................................................................................. 116 SHORT STRADDLE............................................................................................................................................ 118
VOLATILITY ...................................................................................................................... 121 CALCULATION OF HISTORICAL VOLATILITY: ..................................................... 125 OBJECTIVE BEHIND THE RESEARCH: ...................................................................... 128 INVESTMENT DECISION MAKING FACTORS IN STOCK & DERIVATIVE FORM OF INVESTMENT:.................................................................................................................... 128
EXECUTIVE SUMMARY:............................................................................................................................ 129
ADVANCE STATISTICAL METHODS: ......................................................................... 129
PARAMETERS REFLECTING ON INDEX OR STOCK MOVEMENT.......................................................................... 130
MARKET AND MOTIVE FOR INVESTMENT : ........................................................... 140 IMPORTANT FACTORS DETERMINATION WHILE CHOOSING A STOCK ..... 141
FACTOR ANALYSIS .................................................................................................................................... 141
FACTORS DETERMINING INVESTORS INVESTMENT DECISION...................... 144 CLUSTER ANALYSIS:....................................................................................................... 148
THE RESPONDENT’S CHARACTERISTICS FOR THE CLUSTERS:....................................................... 150
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PERCEPUAL MAPPING: .................................................................................................. 152 CONJOINT ANALYSIS: .................................................................................................... 157 CONJOINT RESULT.......................................................................................................... 159
CONJOINT ANALYSIS: WHEN MARKET IS BEARISH ................................................................................... 162 INTERPRETATION OF THE RESULTS :................................................................................................................. 165
ANNEXURE ......................................................................................................................... 166 BIBLIOGRAPHY ................................................................................................................ 173
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Derivatives: Derivative is a financial instrument whose value depends upon the underlying instrument. Forward Contract: A Forward contract is an agreement between two parties to buy or sell an asset at a certain future time for certain price. In this, one of the parties assumes a Long Position and agrees to buy the underlying asset at certain specified future date and the other party assumes Short Position and agrees to see the asset on the same date for the same price. A forward contract is settled at Maturity and the holder of short position delivers the asset to the holder of the long position in return for a cash amount equal to the Delivery Price. Futures contract: Like a Forward Contract, a Futures Contract is an agreement between two parties to buy or sell an asset at certain future date price but Futures Contract unlike forward contract are traded on the exchange and are standardized. Contango: Where the price of a more distant delivery is greater than the price of the near month. Backwardation: Markets where near by delivery is trading at the premium to the more distinct months are said to be in Backwardation. Payoffs from the Forward Contract: Payoff from a Long Position in the Forward Contract: St-k Payoff from a Short Position in the Forward Contract: K- St K: Delivery Price. St : Spot Price.
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Table: 1. FUTURE AND SPOT PRICES OF NIFTY S&P CNX NIFTY FUTURE DATE 2-Jan-06 3-Jan-06 4-Jan-06 5-Jan-06 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 13-Jan-06 16-Jan-06 17-Jan-06 18-Jan-06 19-Jan-06 20-Jan-06 23-Jan-06 24-Jan-06 SPOT 2835.95 2883.35 2904.40 2899.85 2914.00 2910.10 2870.80 2850.70 2850.55 2833.10 2829.10 2809.20 2870.85 2900.95 2884.05 2908.00 1 MONTH 2819.70 2868.85 2890.10 2883.90 2895.65 2893.45 2857.30 2831.40 2823.65 2821.15 2801.85 2797.00 2869.25 2897.55 2881.65 2906.25 2 MONTH 2813.70 2859.50 2882.40 2873.80 2886.85 2885.20 2849.50 2822.95 2812.40 2809.65 2794.55 2787.75 2858.55 2888.35 2866.35 2898.90 3 MONTH 2803.70 2849.00 2873.95 2867.25 2877.20 2878.50 2841.50 2815.20 2807.40 2801.65 2786.85 2783.90 2850.10 2882.00 2858.00 2891.75
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25-Jan-06 27-Jan-06 30-Jan-06 31-Jan-06 1-Feb-06 2-Feb-06 3-Feb-06 6-Feb-06 7-Feb-06 8-Feb-06 10-Feb-06 13-Feb-06 14-Feb-06 15-Feb-06 16-Feb-06 17-Feb-06 20-Feb-06 21-Feb-06 22-Feb-06
2940.35 2982.75 2974.50 3001.10 2971.55 2967.45 2940.60 3000.45 3020.10 3008.95 3027.55 3041.15 3017.55 3022.20 3021.60 2981.50 3005.85 3035.50 3050.80
2941.95 2959.75 2957.25 2984.75 2963.05 2956.45 2921.80 2991.55 3004.15 2992.95 3021.10 3028.20 3009.15 3017.15 3013.85 2978.40 3010.10 3039.45 3056.85
2922.25 2978.55 2972.35 3002.25 2952.45 2947.70 2913.15 2981.35 2994.90 2983.10 3011.60 3018.40 3000.15 3007.60 3003.80 2968.55 2998.50 3033.60 3048.55
2913.05 2969.05 2963.80 2992.35 2950.45 2942.90 2906.10 2976.60 2988.90 2976.25 3001.95 3012.60 2993.80 2999.70 2995.65 2963.70 2990.30 3024.30 3039.85
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23-Feb-06 24-Feb-06 27-Feb-06 28-Feb-06 1-Mar-06 2-Mar-06 3-Mar-06 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 13-Mar-06 14-Mar-06 16-Mar-06 17-Mar-06 20-Mar-06 21-Mar-06 22-Mar-06
3062.10 3050.05 3067.45 3074.70 3123.10 3150.70 3147.35 3190.40 3182.80 3116.70 3129.10 3183.90 3202.65 3195.35 3226.60 3234.05 3265.65 3262.30 3240.15
3064.40 3033.00 3039.30 3057.55 3101.75 3134.55 3137.60 3185.45 3167.35 3082.65 3113.85 3166.45 3180.85 3171.90 3205.00 3213.95 3251.70 3241.95 3227.25
3054.20 3044.10 3055.15 3071.05 3094.50 3131.25 3131.90 3179.50 3162.25 3081.95 3107.60 3160.90 3176.70 3167.40 3198.30 3208.85 3243.15 3234.45 3215.90
3046.20 3035.10 3047.30 3064.35 3085.15 3126.40 3124.00 3171.25 3153.75 3071.35 3100.35 3147.30 3168.90 3159.00 3188.10 3202.85 3238.05 3232.05 3212.85
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23-Mar-06 24-Mar-06 27-Mar-06 28-Mar-06 29-Mar-06 30-Mar-06 31-Mar-06 3-Apr-06 4-Apr-06 5-Apr-06 7-Apr-06 10-Apr-06 12-Apr-06 13-Apr-06 17-Apr-06 18-Apr-06 19-Apr-06 20-Apr-06 21-Apr-06
3247.15 3279.80 3321.65 3325.00 3354.20 3418.95 3402.55 3473.30 3483.15 3510.90 3454.80 3478.45 3380.00 3345.50 3425.15 3518.10 3535.85 3573.50 3573.05
3239.25 3279.90 3326.45 3332.40 3364.90 3412.75 3392.40 3474.00 3489.70 3510.20 3458.15 3488.55 3387.00 3348.50 3424.65 3524.05 3546.65 3581.80 3583.90
3231.50 3271.35 3317.35 3324.45 3353.05 3394.05 3403.60 3463.15 3482.35 3503.90 3455.30 3477.50 3384.35 3343.30 3413.50 3518.45 3540.80 3574.75 3576.80
3229.90 3262.50 3310.65 3309.70 3344.30 3386.65 3396.85 3457.60 3475.05 3495.85 3452.80 3472.35 3383.95 3341.45 3411.80 3512.05 3536.80 3568.10 3571.75
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24-Apr-06 25-Apr-06 26-Apr-06 27-Apr-06 28-Apr-06 29-Apr-06 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06
3548.90 3462.65 3555.75 3508.10 3508.35 3557.60 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90
3556.50 3465.50 3579.45 3508.80 3492.60 3523.70 3595.00 3612.40 3627.40 3644.10 3685.85 3712.95 3745.40 3692.90 3633.00 3462.05 3520.30 3641.25 3363.85
3549.75 3454.05 3562.50 3502.05 3497.60 3545.40 3585.80 3605.10 3620.35 3633.90 3676.80 3702.80 3729.50 3681.80 3620.90 3448.90 3509.15 3628.75 3350.95
3547.45 3451.25 3556.85 3493.25 3491.55 3533.75 3580.20 3595.05 3610.00 3624.35 3669.20 3692.10 3723.60 3677.25 3615.35 3440.05 3500.20 3619.85 3349.00
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19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06
3246.90 3081.35 3199.35 3115.55 3177.70 3209.60 3214.90 3185.30 3071.05 2962.25 3091.35 3016.65 2937.30 2860.45 2724.35 2866.30 2776.85 2663.30 2632.80
3224.35 3020.90 3190.50 3087.25 3180.15 3171.95 3154.05 3097.00 3001.85 2889.90 3061.55 2957.30 2902.80 2838.05 2705.60 2831.25 2716.00 2629.15 2618.25
3209.40 2994.50 3155.10 3030.50 3112.65 3179.15 3175.00 3125.35 3032.40 2869.20 3039.60 2934.85 2868.25 2805.70 2673.65 2811.70 2686.45 2599.40 2594.80
3225.05 2973.25 3143.15 3024.80 3097.20 3164.85 3158.95 3108.60 3011.80 2864.90 3018.55 2914.20 2858.30 2790.20 2658.70 2782.20 2663.55 2585.05 2586.75
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15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06
2798.80 2890.35 2916.90 2861.30 2923.45 2994.75 3042.70 3050.30 2943.20 2982.45 2981.10 2997.90 3128.20 3150.95 3138.65 3197.10 3156.40 3075.85 3142.00
2786.70 2880.75 2909.40 2839.35 2912.10 2982.25 3042.25 3043.90 2930.60 2981.10 2983.50 3003.00 3058.00 3130.30 3114.20 3170.10 3132.45 3039.45 3124.35
2760.40 2858.90 2886.05 2829.50 2891.15 2963.10 3017.25 3023.40 2902.10 2950.30 2951.40 2981.65 3118.10 3113.25 3095.35 3150.45 3111.65 3019.50 3102.90
2746.00 2840.65 2865.40 2794.85 2869.75 2938.40 3000.25 3006.80 2886.50 2929.05 2928.50 2967.40 3100.65 3097.65 3078.60 3138.65 3100.70 3006.50 3087.90
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11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
3116.15 3195.90 3169.30 3123.35 3007.55 2993.65 2932.75 3023.05 2945.00 2985.85 3040.50 3110.15 3156.15
3094.55 3180.80 3142.70 3091.40 2980.95 2973.10 2909.95 3018.75 2937.60 2987.40 3039.45 3111.40 3153.50
3071.70 3158.45 3121.95 3069.35 2955.70 2947.60 2886.10 2993.45 2908.05 2954.20 3011.65 3085.45 3124.45
3055.10 3139.05 3104.70 3056.25 2949.60 2935.35 2875.75 2974.70 2892.95 2936.65 2992.90 3066.40 3103.95
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3900.00
SPOT AND FORWARD NIFTY MOVEMENT
3700.00
3500.00
3300.00
Price
3100.00
2900.00
Nifty Spot 2 M th F t
2700.00
1 Month Future 3 M th F t
2500.00 1/16 1/30 2/13 2/27 3/13 3/27 4/10 4/24 5/22 6/19 Date 7/17 1/2 5/8 6/5 7/3
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Basis: Basis is defined as Spot price minus the Futures Price. In the normal market, the basis will be negative, since the futures price normally exceed the spot price. In the inverted market, the basis will be positive. The basis will approach zero as the delivery period nears. At the close of trading on the delivery date Basis must be zero else, there will be arbitrage opportunity. If the Basis is positive on the expiration date then one can take short position in the futures contract and take delivery and sell it in the spot market and earn risk less profits. The process of basis moving towards zero is called as Convergence. Basis= Spot Price-Future price of the contract used. St-F. Strengthening of Basis: when the spot price increases by more than the futures price. Weakening of Basis: when Futures price increases more than the pot price.
Basis risk: An Individual who is having an un hedged position will face the price risk (i.e.) if the current spot price is S1 and the price that will be in future is S2 the price risk faced by such an investor will be S1- S2. An hedger exchanges Price risk for Basis risk. Suppose someone has hedged his stock by buying Futures then the risk faced by such an investor will be (S1-S2) –(F1-F2) = (S1-F1) – (S2-F2) = Basis 1- Basis 2
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where Basis 1 is known but Basis 2 is unknown. Thus, an unhedged position will face Price risk but a Hedged position will face Basis risk. Table : 2. FUTURE& SPOT PRICES OF NIFTY
S&P CNX NIFTY CHANGES IN DATE SPOT SPOT RATE 1 MONTH 2 MONTH 3 MONTH BASIS
2-Jan-06 3-Jan-06 4-Jan-06 5-Jan-06 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 13-Jan-06 16-Jan-06 17-Jan-06 18-Jan-06 19-Jan-06 20-Jan-06
2835.95 2883.35 2904.40 2899.85 2914.00 2910.10 2870.80 2850.70 2850.55 2833.10 2829.10 2809.20 2870.85 2900.95 47.40 21.05 -4.55 14.15 -3.90 -39.30 -20.10 -0.15 -17.45 -4.00 -19.90 61.65 30.10
16.25 14.50 14.30 15.95 18.35 16.65 13.50 19.30 26.90 11.95 27.25 12.20 1.60 3.40
22.25 23.85 22.00 26.05 27.15 24.90 21.30 27.75 38.15 23.45 34.55 21.45 12.30 12.60
32.25 34.35 30.45 32.60 36.80 31.60 29.30 35.50 43.15 31.45 42.25 25.30 20.75 18.95
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23-Jan-06 24-Jan-06 25-Jan-06 27-Jan-06 30-Jan-06 31-Jan-06 1-Feb-06 2-Feb-06 3-Feb-06 6-Feb-06 7-Feb-06 8-Feb-06 10-Feb-06 13-Feb-06 14-Feb-06 15-Feb-06 16-Feb-06 17-Feb-06 20-Feb-06
2884.05 2908.00 2940.35 2982.75 2974.50 3001.10 2971.55 2967.45 2940.60 3000.45 3020.10 3008.95 3027.55 3041.15 3017.55 3022.20 3021.60 2981.50 3005.85
-16.90 23.95 32.35 42.40 -8.25 26.60 -29.55 -4.10 -26.85 59.85 19.65 -11.15 18.60 13.60 -23.60 4.65 -0.60 -40.10 24.35
2.40 1.75 -1.60 23.00 17.25 16.35 8.50 11.00 18.80 8.90 15.95 16.00 6.45 12.95 8.40 5.05 7.75 3.10 -4.25
17.70 9.10 18.10 4.20 2.15 -1.15 19.10 19.75 27.45 19.10 25.20 25.85 15.95 22.75 17.40 14.60 17.80 12.95 7.35
26.05 16.25 27.30 13.70 10.70 8.75 21.10 24.55 34.50 23.85 31.20 32.70 25.60 28.55 23.75 22.50 25.95 17.80 15.55
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21-Feb-06 22-Feb-06 23-Feb-06 24-Feb-06 27-Feb-06 28-Feb-06 1-Mar-06 2-Mar-06 3-Mar-06 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 13-Mar-06 14-Mar-06 16-Mar-06 17-Mar-06 20-Mar-06
3035.50 3050.80 3062.10 3050.05 3067.45 3074.70 3123.10 3150.70 3147.35 3190.40 3182.80 3116.70 3129.10 3183.90 3202.65 3195.35 3226.60 3234.05 3265.65
29.65 15.30 11.30 -12.05 17.40 7.25 48.40 27.60 -3.35 43.05 -7.60 -66.10 12.40 54.80 18.75 -7.30 31.25 7.45 31.60
-3.95 -6.05 -2.30 17.05 28.15 17.15 21.35 16.15 9.75 4.95 15.45 34.05 15.25 17.45 21.80 23.45 21.60 20.10 13.95
1.90 2.25 7.90 5.95 12.30 3.65 28.60 19.45 15.45 10.90 20.55 34.75 21.50 23.00 25.95 27.95 28.30 25.20 22.50
11.20 10.95 15.90 14.95 20.15 10.35 37.95 24.30 23.35 19.15 29.05 45.35 28.75 36.60 33.75 36.35 38.50 31.20 27.60
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21-Mar-06 22-Mar-06 23-Mar-06 24-Mar-06 27-Mar-06 28-Mar-06 29-Mar-06 30-Mar-06 31-Mar-06 3-Apr-06 4-Apr-06 5-Apr-06 7-Apr-06 10-Apr-06 12-Apr-06 13-Apr-06 17-Apr-06 18-Apr-06 19-Apr-06
3262.30 3240.15 3247.15 3279.80 3321.65 3325.00 3354.20 3418.95 3402.55 3473.30 3483.15 3510.90 3454.80 3478.45 3380.00 3345.50 3425.15 3518.10 3535.85
-3.35 -22.15 7.00 32.65 41.85 3.35 29.20 64.75 -16.40 70.75 9.85 27.75 -56.10 23.65 -98.45 -34.50 79.65 92.95 17.75
20.35 12.90 7.90 -0.10 -4.80 -7.40 -10.70 6.20 10.15 -0.70 -6.55 0.70 -3.35 -10.10 -7.00 -3.00 0.50 -5.95 -10.80
27.85 24.25 15.65 8.45 4.30 0.55 1.15 24.90 -1.05 10.15 0.80 7.00 -0.50 0.95 -4.35 2.20 11.65 -0.35 -4.95
30.25 27.30 17.25 17.30 11.00 15.30 9.90 32.30 5.70 15.70 8.10 15.05 2.00 6.10 -3.95 4.05 13.35 6.05 -0.95
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20-Apr-06 21-Apr-06 24-Apr-06 25-Apr-06 26-Apr-06 27-Apr-06 28-Apr-06 29-Apr-06 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06
3573.50 3573.05 3548.90 3462.65 3555.75 3508.10 3508.35 3557.60 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30
37.65 -0.45 -24.15 -86.25 93.10 -47.65 0.25 49.25 47.85 28.80 14.15 15.55 29.20 27.40 33.70 -53.20 -51.00 -147.10 20.35
-8.30 -10.85 -7.60 -2.85 -23.70 -0.70 15.75 33.90 10.45 21.85 21.00 19.85 7.30 7.60 8.85 8.15 17.05 40.90 3.00
-1.25 -3.75 -0.85 8.60 -6.75 6.05 10.75 12.20 19.65 29.15 28.05 30.05 16.35 17.75 24.75 19.25 29.15 54.05 14.15
5.40 1.30 1.45 11.40 -1.10 14.85 16.80 23.85 25.25 39.20 38.40 39.60 23.95 28.45 30.65 23.80 34.70 62.90 23.10
21
17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06
3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.60 3214.90 3185.30 3071.05 2962.25 3091.35 3016.65 2937.30 2860.45 2724.35 2866.30 2776.85
111.80 -246.20 -142.00 -165.55 118.00 -83.80 62.15 31.90 5.30 -29.60 -114.25 -108.80 129.10 -74.70 -79.35 -76.85 -136.10 141.95 -89.45
-6.15 25.05 22.55 60.45 8.85 28.30 -2.45 37.65 60.85 88.30 69.20 72.35 29.80 59.35 34.50 22.40 18.75 35.05 60.85
6.35 37.95 37.50 86.85 44.25 85.05 65.05 30.45 39.90 59.95 38.65 93.05 51.75 81.80 69.05 54.75 50.70 54.60 90.40
15.25 39.90 21.85 108.10 56.20 90.75 80.50 44.75 55.95 76.70 59.25 97.35 72.80 102.45 79.00 70.25 65.65 84.10 113.30
22
13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06
2663.30 2632.80 2798.80 2890.35 2916.90 2861.30 2923.45 2994.75 3042.70 3050.30 2943.20 2982.45 2981.10 2997.90 3128.20 3150.95 3138.65 3197.10 3156.40
-113.55 -30.50 166.00 91.55 26.55 -55.60 62.15 71.30 47.95 7.60 -107.10 39.25 -1.35 16.80 130.30 22.75 -12.30 58.45 -40.70
34.15 14.55 12.10 9.60 7.50 21.95 11.35 12.50 0.45 6.40 12.60 1.35 -2.40 -5.10 70.20 20.65 24.45 27.00 23.95
63.90 38.00 38.40 31.45 30.85 31.80 32.30 31.65 25.45 26.90 41.10 32.15 29.70 16.25 10.10 37.70 43.30 46.65 44.75
78.25 46.05 52.80 49.70 51.50 66.45 53.70 56.35 42.45 43.50 56.70 53.40 52.60 30.50 27.55 53.30 60.05 58.45 55.70
23
7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
3075.85 3142.00 3116.15 3195.90 3169.30 3123.35 3007.55 2993.65 2932.75 3023.05 2945.00 2985.85 3040.50 3110.15 3156.15
-80.55 66.15 -25.85 79.75 -26.60 -45.95 -115.80 -13.90 -60.90 90.30 -78.05 40.85 54.65 69.65 46.00
36.40 17.65 21.60 15.10 26.60 31.95 26.60 20.55 22.80 4.30 7.40 -1.55 1.05 -1.25 2.65
56.35 39.10 44.45 37.45 47.35 54.00 51.85 46.05 46.65 29.60 36.95 31.65 28.85 24.70 31.70
69.35 54.10 61.05 56.85 64.60 67.10 57.95 58.30 57.00 48.35 52.05 49.20 47.60 43.75 52.20
Graph 1: Convergence of Spot and Future Price
24
Convergence of Spot and Future Price 3900.00
3700.00
3500.00
3300.00
3100.00
2900.00
2700.00
2500.00
3/ 27 6/ 19 6/ 5 7/ 3 2/ 13 2/ 27 3/ 13 1/ 16 1/ 30
DATE
100.00
BASIS 1 MONTH
80.00
60.00
40.00
20.00
0.00
1/ 16 2/ 13 3/ 13 4/ 10 1/ 30 2/ 27 3/ 27 4/ 24 5/ 22 6/ 19 7/ 17 1/ 2 5/ 8 6/ 5 7/ 3
-20.00
-40.00
DATE
BASIS 1 MONTH
7/ 17
4/ 10
4/ 24
5/ 8
5/ 22
1/ 2
Spot
Future
25
BASIS 2 MONTH 100.00
80.00
60.00
40.00
20.00
0.00
1/ 16 1/ 30 2/ 13 2/ 27 3/ 27 3/ 13 4/ 10 4/ 24 5/ 22 6/ 19 7/ 17 5/ 8 1/ 2 6/ 5 7/ 3
-20.00 DATE BASIS 2 MONTH
BASIS 3 MONTH 120.00
100.00
80.00
60.00
40.00
20.00
0.00
1/2
5/8
6/5
1/16
1/30
2/13
2/27
3/13
3/27
4/10
4/24
5/22
6/19
7/3
-20.00
DATE
BASIS 3 MONTH
7/17
26
Chart Title 3900.00
3700.00
3500.00
3300.00 PRICE 3100.00 2900.00 2700.00 2500.00 1/16 1/30 2/13 2/27 3/13 3/27 4/10 4/24 5/22 6/19 DATE
NIFTY SPOT Log. (NIFTY SPOT)
PRICING OF FUTURES: Relationship between continuous compounding and compounding m times per year. Rc= m In(1+Rm/m) Rm=m( e Rc/m- 1) Rc= Rate of Interest for Continuous Compounding Rm= Rate of Interest for Compounding m times a year. FORWARD CONTRACTS ON A SECURITY THAT PROVIDES NO INCOME. F= S er (T-t) FORWARD CONTRACT ON A SECURITY THAT PROVIDES A KNOWN CASH INCOME: F= (S-I) er (T-t)
7/17
1/2
5/8
6/5
7/3
27
Where I is the present value of all cash incomes discounted at risk free rate of interest r. FORWARD CONTRACT ON A SECURITY THAT PROVIDES A KNOWN DIVIDEND YIELD: F= S e (r –q)(T-t)
FUTURES PRICE CALCULATOR INPUTS Current date Spot Price Risk free interest Annualised dividend yield Expiration date Days to expire Time in years Future Price Theototical Future Price INPUTS Current date 2-May-06 2-May-06 3605.45 4.00% 1.50% 31-May-06 29 days 0.079452055 F=S .e(r-q)t 3612.62
28
Spot Price Risk free interest Future Price Expiration date Days to expire Time in years
3605.45 4% 3612.62 31-May-06 29 0.079452055
Annualised Dividend Yield
Q=r-[In(F/S)]/t 1.50%
29
STRATEGY USING FUTURES: ARBITRAGE OPPORTUNITIES: When F>S Investor can borrow funds at risk free rate of interest to buy the asset and take short position in Futures market and then long the asset at time T . When F<S Investor can take Long position in the futures market , undertake the delivery of the asset at time T and short the asset in the spot market . Have funds- Lend them to the market: This works like repo transaction where the investors buys the security and simultaneously undertakes short position in the futures market. Here the investor can use the securities purchased in the spot market to dispose them at the expiration date of the futures contract. Thus the investor will gain the difference between the futures price and the cash price of the security. Have securities –Lend them to the market. Index futures market offers a risk less mechanism for loaning out shares and earning a positive return on them by selling shares at Nifty and invest the proceeds at risk free returns and buying the securities back at the future date by taking long position in the futures market.
30
HEDGING: SHORT HEDGE: A company knows that it is due to sell an asset at a particular time in future can hedge by taking Short Futures Position. If the price of the asset goes up then company gains from sale transaction and if the price of asset goes down the company gains from Futures Transaction. LONG HEDGE:
A company that knows that its due to buy an asset in the future can hedge by taking Long Futures Position. Similarly, in this case also if the price of asset goes up then the company gains in the Futures Transaction and if the price of asset goes down then the company can gain from Purchase transaction. Thus, we can see that in both the cases what Hedging as done is that it has made the result of the outcome more predictable. Hedging not necessarily brings greater returns but what it does is that it makes the result of the outcome more predictable and thus it minimizes the risks. Optimal hedge Ratio: H = ? ?s /?f Where ? is the co-efficient of correlation between ?s and ?F. ?s is the standard deviation of ?s ?f is the standard deviation of ?F.
31
HEDGING USING INDEX FUTURES: Stock index futures can be used to hedge the risk in well-diversified portfolio and removes the risk arising from the market moves and leaves the hedger exposed only to the performance of portfolio relative to the market. Optimal Number of contracts to short when Hedging : ?* ?/f Long security/Portfolio - short futures: Every buy position in the security is a simultaneous Long Position in the Index so if the index gains or loses the security also gains or loses simultaneously. In the sense, a Long Position on any security is also a Long position in the Index. So every time a security is bought a simultaneous short position in the index will hedge the security and offsets the index hidden exposure. The position Long Reliance + short Nifty will be pure play on the value of reliance stock without any extra risk from the fluctuations in the market. Short security –Long futures: A person may sell the stock thinking that its overvalued but if the index moves up he will lose because every sell position in the stock is simultaneous sell position in the index. Even thought the stock in this case may be overvalued the stock price will increase because index has increased and the person will regret his decision to sell the stock. In this case he can hedge by taking a long position in the futures contract so that it will offset the hidden exposure from the index.
HEDGING STATERGIES:
32
Long Portfolio - Short Futures If X has Portfolio worth Rs 10,00,000 of Index stocks as on 2nd May 2006 ,when index is at 3605.45 he will have No of shares : 277
In Order to hedge his portfolio against adverse movements in the stock market he can hedge by having Short Position in the Futures Number of Futures contract to short for perfect : hedge= No of Futures Contract Required : Beta* Portfolio/ Future
Index*lot size) 3 (2.7735789)
His position as on 25thMay when Spot is 3177.7 will be as below: Loss from Spot Transaction Gain from Futures Transaction Net gain/loss : : : -118486.8 125190 6703.25
Thus X has hedged his portfolio against fall in the index. Had he not hedged his portfolio he would have suffered loss of Rs118487 but due to hedging he has now made a profit of Rs 6703.25.
33
Short Portfolio- Long Futures On 2nd May if Mr X is having portfolio of NIFTY worth 277 Shares when they are traded at 3605.45 and Mr X feels that NIFTY is overpriced and he sells his portfolio. The Proceeds from the sale of his portfolio will be Cash proceeds from above : 998709.65
Suppose that he invests this money at risk free interest rate and takes long position in Futures market In order to hedge now he takes Long Position in Futures on the same date when the Futures for May Month are being traded at Rs 3595. On 25th May when the NIFTY has declined to Rs 3177.7 and he takes again Long position on 277 shares his total portfolio will be as follows Loss on Futures Gain on spot ransaction Risk free interest Net Position Value of Portfolio : : : : : -125190 118486.75 1887.971667 -4815.278333 1003524.928
Thus we can see that though in this particular case he has made loss on Spot transaction it has been compensated from profit in futures transaction. Thus the total Portfolio remains unchanged.
34
SPECULATION Bearish- Short Futures On 2nd May the Index is 3605.45 and Futures for month are at Rs 3595 and Mr X feels that the index will go down in the near Future( Bearish) then he can take short position in the futures . If he has Rs10,00,000 with him and he takes short position of 3 contracts which expire on 25th May, then his position as on 25th May will be Profit form futures Future price-Spot Price * Number of contracts 125190 If he has paid an initial margin of 20% (i.e.) Rs 215700 then will gain return of 58.03% on his initial investment. Bullish- Long Futures On 29th June when the index spot was at 2997.9 and July Futures were trading at 3130.3 and the investor who feels that the index will increase (bullish) then he can take a long position and if index moves in positive direction then he can make profits Suppose that Mr.X is bullish as on 29th June and he takes Long position in the futures for 3 contracts and squares off his position on 27th July, then his position as on 27th July will be as follows Futures price as on 29th April 3003.00 Sopt price on 26th may 3156.15 Profit from Futures 76575 Suppose the initial margin was 20% then his return on investment will be 42.50%.
35
OPTIONS Call Option : A Call Option gives the right (not obligation) to buyer of call option to buy an underlying asset. Put Option : A Put Option gives the right ( not obligation ) to holder of Put option to sell the underlying asset for exercise price. American Option : An American Option is one which can be exercised by the holder anytime prior to maturity date. European Option : European Option can be exercised by the holder only on the date of maturity.
Position in Option: Long Position in Call Option Short Position in Call Option Long Position in Put Option Short Position in Put Option Pay off from Option: Payoff from Long Position in Call Option : Max ( St – K , 0 ) Payoff from Long Position in Put Option : Max (K-St , 0) Adjusting Options to Share Split and Stock dividends: - Bullish. -Bearish. -Bearish. -Bullish.
36
Share Split: n for m shape split will cause the sock price to go down by m/n of its previous value and the number of share covered by one contract increases by n/m of its previous value. Stock dividends: The treatment is same as that for stock split.20% stock split means 6 for 5 stock split.
Terminology:
Premium : Premium is the amount paid by the holder of an Option for the right he gets to exercise the Option. Premium of an Option can be separated into two components –Intrinsic Value and Time Value. Intrinsic Value: Intrinsic Value of an Option is the amount which would be credited to holder of an Option if he were to exercise the Option and close out the position. A Call will have intrinsic value if exercise price is less than the current market price of the Underlying. Intrinsic value is equal to Current Market price – Exercise Price. A Put will have intrinsic value if the exercise price is more than the current market price of the underlying.(i.e.) Exercise Price – Current Market Price.
37
Time Value: Additional amount of premium over and above the Intrinsic value is the time value or extrinsic value of Option. At the Money and Out of Money Options will only have Time Value and no intrinsic value. In the money: An Option with intrinsic value is said to be in-the-money. In order to be in the money call should have exercise price less than the current market price and Put should have exercise price more than Current market price. At the money: An Option whose exercise price is equal to current market price is said to be at the money. Out of the money: A call option is said to be Out of money if the exercise price is more than the current market price of the Underlying. Put Option is said to be Out of money if exercise price is less than the current market price of underlying.
38
Factors affecting the Option Prices: Current Stock Price Strike Price Call option: Payoff from the Call Option will be the amount by which the spot price exceeds the strike price. Hence if the Stock price increase the payoff of call option will increase and hence the call will become more valuable. If the strike price increase the payoff from the call option will decrease and hence the call price will decrease. Put option: Payoff from put option is strike price – spot price. Hence if the spot price increases the put will become less valuable and if the strike price increases put will become more valuable. Time to expiration Time to expiration will affect only the American Options as European Options can be exercised only on the specific date. In case of American option , an owner of long life option has all the exercise opportunities that is available to the owner of short life option and more .So the value of long life American option will increase as the time to expiation increases. Volatility of the stock price Volatility refers to uncertainty about the movement of share prices both up and down. Owner of a call option benefits from price increase but has limited downside risk similarly put benefits from price decrease but has limited downside risk in case of price increase. Therefore the values of both call and put increase as the Volatility increases.
39
Risk free rate of interest In case of Call Option the owner has to pay for security if he decides to exercise the option at a later date so he will have to shell out money sometime in future. If in the mean time interest rate increase he will benefit from investing the money in the risk free returns. So the value of call option increases as the interest rate increase. In case of put the owner will receive the money if he exercises the put sometime in future , so if the interest rate increase in the meantime present value of the future cash flows that will be received by him will decline so the Put Option will decline in value if the interest rate increase. Dividends expected during the life of asset Dividends reduce the stock price on ex-divided date , so the value of call will decline if the dividends increase and the value of put will increase if the dividends increase.
40
European Variable Spot price Strike Price Time expiration Volatility Risk free rate Dividends + + to Call + ?
European Put
American Call
American Put
+ ?
+ +
+ +
+ +
+ + -
+ +
41
SCENARIO ANALYSIS We have done a scenario analysis to show how a change in the strike price on a given particular day will affect the Price of options along with change in the technical parameters (i.e.) how the option price and its technical indicators will respond to any change in spot price. We have taken 3000 series as on 1st June, 2006 when NIFTY was trading at 2962.25. Stock Price Exercise Price Current date Expiration date Risk free Interest rate Volatility Dividend yield Time 2962.25 3000.00 1-Jun-06 29-Jun-06 5.00% 14.68% 2.00% 0.076712329
Scenario Analysis of change in Call Price , Put Price and Other parameters of Option to change in Spot Price and effect of change in Volatility to change in Call Price and Put Price. Stock Price 2950 2960 2970 2980 2990 3000 3010 3020 29.63 33.47 37.63 42.11 46.91 52.05 57.51 63.29 0.3677 0.3994 0.4317 0.4644 0.4972 0.5298 0.5622 0.5941 0.003138 0.003205 0.003250 0.003274 0.003276 0.003255 0.003213 0.003151 -325.27 -336.34 -345.53 -352.72 -357.81 -360.77 -361.59 -360.32 307.49 316.20 322.89 327.45 329.80 329.93 327.85 323.63 -80.94 -88.13 -95.48 -102.93 -110.44 -117.94 -125.41 -132.77 Call Delta Gamma Theta Vega Rho
42
3030 3040 3050
69.39 75.79 82.49
0.6252 0.6554 0.6846
0.003070 0.002971 0.002857
-357.03 -351.84 -344.91
317.37 309.21 299.32
-139.99 -147.03 -153.84
stock price 2950 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050 Put 72.67 66.52 60.69 55.19 50.01 45.16 40.64 36.44 32.55 28.97 25.68 Delta -0.6308 -0.5990 -0.5667 -0.5341 -0.5013 -0.4686 -0.4363 -0.4044 -0.3733 -0.3431 -0.3139 Gamma 0.003138 0.003205 0.003250 0.003274 0.003276 0.003255 0.003213 0.003151 0.003070 0.002971 0.002857 Theta -234.76 -245.91 -255.19 -262.48 -267.69 -270.78 -271.75 -270.63 -267.51 -262.50 -255.76 Vega 307.49 316.20 322.89 327.45 329.80 329.93 327.85 323.63 317.37 309.21 299.32 Rho -148.32 -141.12 -133.78 -126.32 -118.82 -111.31 -103.85 -96.48 -89.26 -82.23 -75.41
43
Volatility 8.00% 9.00% 10.00% 11.00% 12.00% 13.00% 14.00% 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% 21.00% 22.00% 23.00% 24.00% 25.00% 26.00% 27.00% 28.00% 29.00% 30.00%
Call Price 13.70 16.68 19.72 22.80 25.92 29.06 32.22 35.39 38.58 41.79 45.00 48.21 51.44 54.67 57.90 61.14 64.38 67.63 70.87 74.12 77.38 80.63 83.89
Put Price 44.51 47.49 50.53 53.61 56.72 59.86 63.02 66.20 69.39 72.59 75.80 79.02 82.24 85.47 88.71 91.95 95.19 98.43 101.68 104.93 108.18 111.44 114.69
44
Scenario Analysis-Change in Call and Put to Change in Spot.
90.00 80.00 70.00 60.00 Option Price 50.00 40.00 30.00 20.00 10.00 0.00 2950 2960 2970 2980 2990 3000 Stock Price 3010 3020 3030 3040 3050
Call Price
Put Price
45
Scenario analysis-Change in Delta to Change in Stock Price
0.8000
0.6000
0.4000
Change in Delta
0.2000
0.0000 2950 -0.2000 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050
-0.4000
-0.6000
-0.8000 Stock Price Call Delta Put Delta
Scenario analysis: Change in Delta to Change in Stock Price Delta along with change in option price to Change in strike price also gives indication to probability that the Option will be in-the-money. In the given scenario as the Spot price is increasing, from 2950 onwards, the probability that the Option with exercise price of 3000 will be in-the-money increases as the buyer of call option will exercise the option at any level beyond 3000. As seen from the chart, Delta has increased from 0.3677 when spot price for 3000 exercise price was 2950 to 0.6846 when the NIFTY was changed to 3050. For Put option, any increase in Spot price will decrease the probability that the option will be in-themoney as the option will expire worthless on the expiry date. In the chart above, Delta of put
46
option is getting closer to 0 with increase in NIFTY spot price as their probability to be exercised decreases and they decline in value because their payoffs will decline with increase in spot price.
Scenario Analysis-Change in Gamma to Change in Spot
0.003400
0.003300
0.003200
0.003100 Gamma
0.003000
0.002900
0.002800
0.002700
0.002600 2950 2960 2970 2980 2990 3000 Stock Price Change in Gamma 3010 3020 3030 3040 3050
Scenario analysisChange in Gamma to Change in Stock Price
Gamma is the rate at which an Option’s Delta changes as the price of underlying changes. Gamma is greatest for an option that is at the money and becomes progressively small as the Option moves in the money or out of the money thus forming an inverted U shaped curve. In the above graph, Gamma is greatest when the Option is at the money (ie) when spot price is 2990 and 3000 for series which has exercise price of 3000. As the Call option gets in-themoney and out-of-the money with increase and decrease in spot price, the gamma of the Option progressively declines. 47
0.00
Scenario Analysis-Change in Rho to Change in Underlying Price
Stock Price
-20.00
-40.00
-60.00
-80.00 Rho -100.00 -120.00 -140.00 -160.00 -180.00 Stock Price Call Rho Put Rho
Scenario analysisChange in Rho to Change in Stock Price Rho of an option measures the sensitivity of the option price to changes in the interest rates. As Rho increases, Option price will be highly sensitive to changes in interest rates. In the above scenario analysis, as the Stock price increased from 2950 to 3050 call price has also increased. With increase in Call price, Call Options tend to get more sensitive to changes in interest rates, because higher the call price greater will be the affect of it in interest rates. This 48
can be verified from increase in Rho from absolute value of 80.94 to 153.84 as the Spot price has been increased from 2950 to 3050. Similarly when the spot price is increased , the Put Option get more dearer and the effect of interest rates on Put Option decline. This can be seen from decline in the absolute value of Rho from 148.32 to 75.41 when Spot price is increased.
Scenario Analysis-Change in Theta to Change in Underlying
-300.00 2950 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050
-310.00
-320.00
-330.00 Theta -340.00 -350.00 -360.00 -370.00 Stock Price Change in Theta to Change in Underlying
49
Change In Option price due to Volatility
140.00
120.00
100.00
Option Price
80.00
60.00
40.00
20.00
0.00
9. 00 % 10 .0 0% 11 .0 0% 18 .0 0% 19 .0 0% 20 .0 0% 21 .0 0% 22 .0 0% 23 .0 0% 24 .0 0% 25 .0 0% 8. 00 % 12 .0 0% 13 .0 0% 14 .0 0% 15 .0 0% 16 .0 0% 17 .0 0% 26 .0 0% 27 .0 0% 28 .0 0% 29 .0 0% 30 .0 0%
Volatility Price of Call Option Price of Put Option
Scenario analysisChange in Option price to Change in Volatility
In order to find the effect of Option price due to changes in Volatility, all the rest of parameters of the Option are kept constant and a scenario analysis was built to find out how the change in volatility impact the option price. As can be seen from the given graph as the underlying volatility increases, the price of both call and put options increase as the writer of Option will demand more premium when the market is volatile in order to cover his loss. The graph for both Call and Put option prices show similar patter for changes in volatility. The call price has increased from 13.70 when the volatility was 8% to 83.89 when the volatility was
50
increased to 30%. Similarly Put price has increased from 44.51 to 114.69 when volatility was changed from 8% to 30%. Thus other things kept constant, a mere change in underlying volatility of the stock price can cause significant changes to the price of option.
51
S&P CNX NIFTY
3900.00
3700.00
3500.00
3300.00
3100.00
2900.00
2700.00
2500.00
2M ay 9M ay ay ay ay 20 -J un 27 -J un 13 -J un 16 -M 23 -M 30 -M 11 -J ul 18 -J ul 25 -J ul 6Ju n 4Ju l
S&P CNX NIFTY
52
NIFTY Spot and Call
4000.00 800
700 3750.00 600 3500.00 500
3250.00
400
300 3000.00 200 2750.00 100
2500.00
-0 6 -0 6 -0 6 -0 6 -0 6 6Ju n06 13 -J un -0 6 20 -J un -0 6 l-0 6 27 -J un -0 6 11 -J ul -0 6 18 -J ul -0 6 9M ay 16 -M ay 2M ay 23 -M ay 30 -M ay 25 -J ul -0 6 4Ju
0
S&P CNX NIFTY
3000
3050
3100
3200
53
NIFTY Spot and Put
4000.00 800
700 3750.00 600 3500.00 500
3250.00
400
300 3000.00 200 2750.00 100
2500.00
-0 6 -0 6 -0 6 -0 6 -0 6 6Ju n06 13 -J un -0 6 20 -J un -0 6 l-0 6 27 -J un -0 6 11 -J ul -0 6 18 -J ul -0 6 9M ay 16 -M ay 2M ay 23 -M ay 30 -M ay 25 -J ul -0 6 4Ju
0
S&P CNX NIFTY
3000
3050
3100
3200
54
LIMITS ON UPPER AND LOWER BOUND FOR OPTIONS: Intrinsic Value of an Option: Call Option :Max ( S-X, 0) Put Option : Max (X-S,0) Upper Bounds and Lower Bounds for OPTION PRICES: Upper Bound: For Call Option: c ? S C ? S For Put Option: P ? X ? p ?X Lower Bounds: For European Call Option: c > S – D-X e – r (T-t) For European Put Option : p > D+ X e – r (T-t) –S Its never optimal to Exercise American Call Option on non – dividend paying stock early. Xe
-r ( T –t )
55
Put Call Parity: Put Call Parity says that one European Option plus an amount of cash equal to X e –r (T –t) and one share in underlying along with one Long Put must be equal in Value. Put-Call Parity holds only for European Options. C - P = S- X e – r (T-t) S- D-X < C –P < S – X e –r (T –t) Value of an European call with certain exercise price and exercise date can be deducted from value of an European Put with the same exercise price and date. Both the following portfolio should be equal: Portfolio A: One European Call Option plus an amount of Cash equal to X .e – r (T-t) . Portfolio B: One European Put Option plus one share. If Put – Call parity does not holds true then in would mean that there could be some arbitrage opportunities to exploit. If Portfolio A is greater than Portfolio B , then investor could take Long position in Call and take short position in both Put and the underlying stock. If Portfolio B is greater than Portfolio A, then investor could take Short Position in call and have Long Put and Long the Underlying. Both these cases will bring investor risk less profit.
PUT CALL PARITY Date SERIES 3000 3050 3100 3200
56
Strike Price
2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06
<S-X eC-P
598.5 613.3 627.15 648.8 681.6 713.35 741 693.9 632 469.6 517.35 632.75 379.4 219.45 24.35 186.15 82.85 176.4 175.75 173.85 125.8 29.8 -107.75 58.8 -44.45 -100.25 -159.3 -295.4 -171.8 -282.5 -361.1 -372.75
r (T-t)
<S-X C-P
549.85 571.75 572 576.2 576.2 599.7 675.1 675.1 609.4 609.2 611.6 540.8 533.3 508.1 -15.5 133.8 14.9 130.95 4.459886 -57.4127 -45.5535 42.90583 104.6152 39.1246 72.35318 123.3128 183.7225 292.2823 169.1421 233.8718 342.9319 371.6919
<S-X e-r C-P
-61.75 -71 -36.2 -17.7 -24.7 -93.1 -17.3 25.55 -13.95 -185.6 -148.85 6.7 -168.85 200.65 -57.4 126.65 -86.2 82 170.3401 227.5627 178.2535 59.89417 -40.2652 80.6754 4.646818 -66.6128 -144.523 -270.182 -137.192 -220.722 -331.682 -361.892
(T-t)
<S-X C-P
-193.228 -194.161 -196.095 -229.244 -192.228 -191.011 -106.894 -102.377 32.87478 -196.558 -299.591 107.0267 -10.6058 88.94683 -100.386 16.38222 -110.55 3 -47.7724 -56.0246 -60.7585 34.0076 116.6738 21.99001 71.13907 136.0555 201.3221 329.9386 195.7053 274.5055 386.7224 416.6393
e
-r (T-t)
e-r (T-t)
415.52 443.88 457.59 472.71 500.59 527.56 560.82 507.18 455.74 307.33 327.24 438.60 191.97 49.53 -117.34 0.23 -84.01 -22.30 24.47 28.46 -1.58 -116.26 -225.50 -96.84 -172.85 -252.63 -329.92 -466.46 -324.94 -415.71 -529.69 -560.63
3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70
3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8
614.89 643.28 657.02 672.16 700.13 727.12 760.41 706.80 655.39 507.06 527.00 638.39 391.78 249.36 82.58 200.17 115.96 177.70 223.54 227.61 197.60 82.94 -26.27 102.43 26.50 -53.26 -130.52 -267.03 -125.49 -216.17 -330.13 -361.04
565.04 593.43 607.16 622.29 650.24 677.23 710.51 656.89 605.48 457.13 477.06 588.44 341.82 199.41 32.60 150.19 65.97 127.70 173.77 177.82 147.81 33.14 -76.07 52.61 -23.34 -103.11 -180.37 -316.89 -175.36 -266.06 -380.02 -410.94
515.20 543.58 557.30 572.43 600.36 627.34 660.61 606.99 555.57 407.19 427.12 538.50 291.87 149.45 -17.38 100.20 15.97 77.70 124.00 128.04 98.01 -16.66 -125.88 2.79 -73.17 -152.95 -230.22 -366.75 -225.22 -315.94 -429.91 -460.84
57
15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
-216.65 -112.5 -89.3 -175.3 -92.05 -19.55 38.25 43.6 -69.1 -19.05 -17.1 1.8 51.1 61.8 50.9 95.15 65.85 -11.4 55.6 33.05 101 71.05 29.65 -55.05 -60.35 -106 -23.9 -78.85 -37 -7.75 27.4 52.65
-195.45 -104.31 -78.99 -135.00 -73.26 -2.37 45.16 51.94 -55.57 -16.73 -18.49 -2.10 139.28 160.80 148.09 206.13 165.02 84.06 148.98 122.72 202.06 175.05 128.69 11.66 -2.65 -63.96 25.93 -52.54 -12.92 41.32 110.56 156.15
216.2021 147.4623 123.9432 157.0536 94.81413 40.42467 8.38526 2.656615 69.41738 34.07819 26.93907 2.6 18.8246 -4.84682 -3.08718 -26.6275 -25.0177 8.142071 -11.7282 -2.81814 -29.2581 -38.5979 -30.4377 31.19322 38.00365 80.41413 12.52467 64.28526 28.66738 -12.6218 -43.8109 -53.1
-245.36 -154.22 -128.92 -184.94 -123.21 -52.33 -4.79 1.97 -105.55 -66.71 -68.48 -52.10 89.46 110.96 98.24 156.28 115.16 34.19 99.09 72.83 152.16 125.14 78.78 -38.27 -52.59 -113.91 -24.03 -102.49 -62.90 -8.66 60.57 106.15
-199.952 -116.712 -91.9932 -140.354 -79.9641 -16.8247 25.51474 29.99339 -61.1174 -25.1282 -23.6891 -2.4 108.6754 130.1968 119.3372 168.7275 144.8677 61.70793 119.0782 95.61814 161.8081 144.0479 103.4377 -3.24322 -15.8036 -70.1641 10.02533 -57.5353 -19.9174 23.97181 73.46093 105.8
-295.26 -204.13 -178.86 -234.88 -173.15 -102.28 -54.75 -48.00 -155.53 -116.70 -118.48 -102.10 39.64 61.13 48.40 106.43 65.30 -15.67 49.21 22.94 102.26 75.24 28.87 -88.21 -102.53 -163.85 -73.98 -152.45 -112.88 -58.65 10.57 56.15
253.9563 170.6733 143.9248 193.542 130.2094 62.42674 15.54418 10.82922 109.2468 69.2645 69.08222 52.35 -30.5254 -55.2968 -53.2872 -88.2775 -77.0677 -26.2579 -62.8282 -46.9681 -91.7581 -90.5479 -69.9377 14.44322 24.75365 75.06413 -4.77533 59.53526 22.81738 -22.2218 -71.2609 -105.7
-395.07 -303.96 -278.72 -334.76 -273.05 -202.18 -154.67 -147.95 -255.49 -216.67 -218.46 -202.10 -59.99 -38.55 -51.28 6.73 -34.41 -115.39 -50.56 -76.84 2.47 -24.57 -70.96 -188.07 -202.41 -263.75 -173.88 -252.37 -212.84 -158.62 -89.41 -43.85
Property distribution of a stock price: Probability distribution of the stock price St, for time T is given by : With mean and Standard deviation as follows: In St ~? { In St + (?-?2) * (T-t) , ? ? ( T-t) } 58
Where St is the Stock Price ? is the expected return per annum ? is the Volatility. T-t is the time period. Expected value of the Stock price at the end of t Time period is given by E(St) = S e ? (T-t). And the variance of the St is given by: Var(St )= S2 e2?( T-t) { e ?2 ( T-t) -1}. The Distribution of the Rate of Return: with Mean and Standard deviation of { ?- ?2/2, ?/ ?T-t}
59
PRICING OF OPTIONS BLACK SCHOLES MODEL:
Value of Call Option:
C= SN (d1)- X e –r(T-t) N (d2) Or C= e- r (T-t) { SN (d1) e r(T-t) - XN (d2)
Where D1 = In (S/X) +( r + ?2/2 )( T-t) / ? (?T-t) D2 = In (S/X) +( r -?2/2 )( T-t) / ? (?T-t) = Interpretation of the above model: N(d1) = Change in Option price due to change in the Stock Price.(Delta). Probability that the option will be in-the-money. N (d2) = Probability that the Option will be exercised. XN (d2) = Strike times the Probability. SN (d1) e r(T-t) = Expected Value of a Variable that equals St , if St > X and Zero otherwise in a Risk Neutral World. Since C= c , the Value of American Call Option will be Equal to that of European Call Optio D1- ?(?T-t).
60
Value of Put :
C= X e- r (T-t) N (-d2)- SN (-d1). By replacing S by S .e-q (T-t) we can find the price of an Option with known dividend yield q. If dividends are known then present value of dividends are subtracted from S. BLACK SCHOLES MODEL Input Variables: Stock Price Exercise Price Current date Expiration date Risk free Interest rate Volatility Dividend yield Time Price of Stock Option Theoretical Parameters of Option Delta Gamma Theta 3605.45 3000.00 2-May-06 25-May-06 5.00% 16.52% 2.00% 0.0630137 Call 610.3463 Call 0.9987371 1.071E-07 -77.52858 Put 0.0001 Put -3.41E-06 1.07E-07 -0.018618
61
Vega Rho
0.0144885 -188.4456
0.014488 -0.000781
62
THEORETICAL PRICE OF CALL ACTUAL PRICE OF CALL OPTION S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 3000 600 617 628.7 650.8 683.1 714.7 746 698.1 635.1 471.45 520 635 389.75 240 122.7 212.4 117.15 176.8 243.1 236.85 196.65 152.45 96.95 176.9 120.15 89.5 70.25 39.95 56.25 25.65 FOR NEAR MONTH EXERCISE PRICE 3050 555 576.9 576.9 580.2 580.2 603.2 680 680 615 615 615 544.5 544.5 544.5 99.55 173.35 63.65 131.5 228 170.2 152.05 125.85 78.35 141.55 98.85 70.05 53.2 25.25 43.65 17.7 3100 510 501 540 558.5 575 582 657.8 634.95 595.25 426 391.95 540 339.25 185.15 76.4 141.55 44.75 82 174.8 170.15 132.7 102.8 64.35 119.8 77 56.7 39.2 22.1 31.95 13.15 3200 400.2 413 426.2 421 485 519.5 550 503.1 490 280.5 288.85 448.85 188.8 121.55 49.8 82.35 17.15 3 126 121.8 87.05 67.15 40.6 74.6 47.8 32.95 20.95 13.05 20.35 8.45 223.35 226.63 198.77 103.67 40.25 116.80 62.78 25.70 7.67 0.32 7.22 0.61 179.31 181.77 155.59 71.94 23.60 82.23 38.64 13.32 3.21 0.09 2.89 0.16 139.02 140.51 116.80 47.03 12.82 54.46 21.91 6.26 1.21 0.02 1.02 0.03 73.92 73.60 56.80 16.53 2.99 19.48 5.41 1.02 0.12 0.00 0.09 0.00 3000 610.35 638.90 652.82 668.14 696.69 723.86 757.32 703.96 652.79 505.14 525.26 636.79 390.48 248.30 82.72 199.82 115.79 OPTION FOR NEAR MONTH EXERCISE PRICE 3050 560.50 589.05 602.97 618.28 646.81 673.97 707.43 654.06 602.88 455.21 475.32 586.85 340.52 198.37 38.66 149.84 65.86 3100 510.66 539.20 553.11 568.42 596.92 624.08 657.53 604.15 552.97 405.27 425.38 536.90 290.57 148.70 10.88 99.91 20.42 3200 411.05 439.53 453.41 468.70 497.16 524.30 557.73 504.34 453.14 305.42 325.51 437.01 190.80 58.04 0.09 15.54 0.01
63
13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
19.2 16 31.15 61.65 62.85 27.4 38.35 57.3 77.5 81.9 25.75 33.25 24.55 5.85 127.5 125.35 116.25 142.1 119.85 69.85 107.35 92.8 132.55 105.45 73 27.95 22.2 10.25 22.55 6.75 8.75 11.35 29.65 52.7
12.8 10.65 20.75 43.15 44.95 22.05 21.55 38.05 53.55 54.6 13.85 17.35 8.45 0.5 158.1 155.95 145 179.5 140 92.2 137.25 119.9 172.8 136.45 98.25 42.85 35.35 16.45 38.45 11.75 15.75 28.7 66.75 103.05
11.25 9.8 16.25 30.75 31.95 16.7 14.85 23.6 33.9 32.65 8.3 8.95 3.25 0.2 127.5 125.35 116.25 142.1 119.85 69.85 107.35 92.8 132.55 105.45 73 27.95 22.2 10.25 22.55 6.75 8.75 11.35 29.65 52.7
6.7 5.7 8.6 16.45 15 8.6 7 10.1 10.75 12.8 3.7 2.55 0.6 0.25 78.15 74.9 66.05 80.45 67.8 35.45 56.25 48.65 70.05 53.5 33.5 11.2 8.95 4.9 5.25 2 2.9 1.75 2.2 0.1
0.01 0.00 0.59 5.58 6.77 1.09 5.69 25.61 53.45 55.80 2.20 7.62 3.56 146.51 163.86 152.26 205.10 166.63 97.78 150.66 126.73 200.50 174.30 130.56 37.98 28.97 7.28 41.61 6.92 11.97 43.47 110.39
0.00 0.00 0.13 1.73 1.89 0.19 1.32 8.69 22.93 21.69 0.14 0.50 0.03 107.70 122.15 111.48 159.43 123.65 64.17 107.80 86.41 153.10 128.10 88.18 16.82 11.37 1.80 16.90 1.37 1.65 10.79 60.50
0.00 0.00 0.02 0.44 0.41 0.02 0.22 2.11 7.05 5.19 0.00 0.01 0.00 74.92 86.01 76.74 117.76 86.20 38.63 71.25 53.68 109.34 86.82 53.43 5.99 3.47 0.32 5.06 0.17 0.09 0.93 16.71
0.00 0.00 0.00 0.02 0.01 0.00 0.00 0.04 0.20 0.05 0.00 0.00 0.00 30.03 34.88 29.27 53.09 33.40 10.46 23.25 14.81 42.58 28.95 13.06 0.37 0.14 0.00 0.16 0.00 0.00 0.00 0.00
64
Technical Analysis of Option Parameters
Delta Delta is the rate of change of the option Price with respect to underlying asset. Delta hedging keeps the total wealth of an investor as close to unchanged as possible. Suppose the delta of a stock is .60. This means that when stock price changes by some amount the option price changes by 60% of that of underlying. If the call price is Rs 10 and the stock price is Rs 100 and investor has written 20 Call Option’s (Lot of 100 each) in order to hedge the investor can buy 1200 shares( 2000*.60).In this case gain(loss) in the option position will tend to setoff by loss(gain) in the stock position. The scheme generally involves selling the stock just after the price has gone down and buying the stock just after the price have gone up(delta will increase so to maintain the portfolio as delta neutral more of the underlying stock must be purchased). It might be termed as- Buy High- sell low scheme. Delta of the underlying stock is always 1.
Delta of European Call on Non-dividend paying stock: Delta of European Put on Non-Dividend paying stock Delta of European Call on stock paying a dividend yield q : Delta of European Put on stock paying a dividend yield q:
? = N. d 1. ?= N .d1 – 1 ?= e –q (T-t) . N. d 1 ?= e –q (T-t) . (N. d 1 -1).
Since the underlying stock always has delta of 1.00 ,each 100 deltas in an option represents a theoretical position in the underlying stock. (i.e.) if person is having options with delta of 500 this is equivalent to holding 5 underlying stocks.
65
If we ignore the sign of delta (for Put ) then Delta also shows the probability that the Option will be in-the-money. An Option with delta greater than 50 is in the money , equal to 50 is at the money and delta less than 50 is out of the money. Thus there are 4 important interpretation of Delta:
Hedge Ratio
Rate of change wrt to Underlying Probability of Option in the money Equivalent underlying position
66
Delta
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 0.92 0.93 0.91 0.72 0.42 0.77 0.58 0.33 0.13 0.01 0.13 0.02 0.00 0.00 0.02 0.13 0.86 0.88 0.84 0.59 0.29 0.64 0.42 0.20 0.06 0.00 0.06 0.01 0.00 0.00 0.00 0.05 0.78 0.80 0.74 0.45 0.18 0.50 0.28 0.11 0.03 0.00 0.02 0.00 0.00 0.00 0.00 0.01 0.55 0.57 0.49 0.21 0.05 0.24 0.09 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3000 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.76 1.00 0.99 EXERCISE PRICE 3050 3100 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.35 1.00 0.72 3200 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.76 0.01 0.50 0.00
67
19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
0.16 0.04 0.15 0.48 0.76 0.84 0.11 0.32 0.24 0.84 0.89 0.88 0.95 0.91 0.76 0.91 0.87 0.97 0.96 0.91 0.55 0.48 0.19 0.64 0.20 0.39 0.87 1.00
0.06 0.01 0.05 0.22 0.47 0.51 0.01 0.03 0.00 0.74 0.80 0.77 0.89 0.82 0.61 0.81 0.75 0.93 0.89 0.79 0.32 0.25 0.06 0.36 0.05 0.08 0.41 0.99
0.01 0.00 0.01 0.07 0.20 0.18 0.00 0.00 0.00 0.61 0.67 0.64 0.79 0.70 0.44 0.67 0.58 0.83 0.77 0.61 0.14 0.10 0.01 0.14 0.01 0.01 0.06 0.65
0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.33 0.38 0.34 0.52 0.39 0.17 0.32 0.24 0.51 0.40 0.23 0.01 0.01 0.00 0.01 0.00 0.00 0.00 0.00
68
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
3000 3050 3100 3200
0.10
0.00 2700.00
2900.00
3100.00
3300.00
3500.00
3700.00
69
0.0000
delta of put
-0.1000
-0.2000
-0.3000
-0.4000 delta
-0.5000
-0.6000
-0.7000
-0.8000
-0.9000
-1.0000 3000 3050 3100 3200
16 -M ay
23 -M ay
30 -M ay
2M ay
9M ay
un
n
27 -J un
20 -J u
11 -J ul
18 -J ul
6Ju n
4Ju l
13 -J
25 -J
ul
70
71
Delta of Call Option
1.00 0.90 0.80 0.70 0.60 Delta 0.50 0.40 0.30 0.20 0.10 0.00
ay ay ay -J un -J un -J un l 11 -J ul ay 16 -M 23 -M 30 -M 13 20 27 25 -J ul ay 18 -J ul 6Ju n 2M 9M 4Ju
3000
Date 3050
3100
3200
72
Delta Hedging strategies: Long Position in Call Option : Short position of N.d1 shares. Short position in Call Option : Long Position of N.d1 shares. Long position in Put Option : Long position in the underlying stock. Short position in Put Option : Short position in the underlying stock. DELTA HEDGING Portfolio= "-C1+N(d1)S"
In order to create delta neutral position a person should take Opposite position to that of Call Option so that the value of the Portfolio remains the same if there is any change in the value of Stock Price.
The amount of shares that have to be purchased in order to make the above portfolio delta neutral is given by N(d1). That is for every Option that is purchased Nd1 shares of the underlying must be bought so that the changes in the value of Stock will not affect the value of Portfolio.
Delta Hedging Strategies Long Position in Call Option : Short position of N.d1 shares Short position in Call Option : Long Position of N.d1 shares Long position in Put Option : Long position in the underlying stock Short position in Put Option : Short position in the underlying stock
73
If the call Price is Rs 7.97 and the Put Price is Rs 8.91 for a stock which has exercise price of 105 and strike price of 100.
The various parameters of the Option are Parameters of Option Delta Gamma Theta Vega Rho Call 0.52430 0.01889 -12.06104 27.95787 -27.92 Put -0.47570 0.01889 -3.98600 27.95787 -27.85
In the above case if the call price is 7.67 with the delta of .5243 then for every option that is purchased .5243 shares of the Underlying stock must be kept. If a person buys 100 calls for 79.70 then he should have short of roughly 53 shares so that he is delta neutral.
His portfolio will be Long 100 calls short 53 shares Portfolio -767 5243 4476
Now if the stock price changes to Rs 105 then the value of call option will be Rs 10.82 His portfolio now will be
74
Long 100 calls Short 53 calls Portfolio
-1082 5505.15 4423.15
Thus with help of delta hedging his portfolio has been hedged against the loss in value.
Gamma Gamma is the rate at which an Option’s Delta changes as the price of underlying changes. It is a measure that how fast an Option change sits directional characteristics. If the gamma is extremely large then Delta is highly sensitive to the price of underlying asset. Both the calls and puts have positive gammas. Gamma is greatest for an option that is at the money and becomes progressively small as the Option moves in the money or out of the money. Gamma of the underlying is always 0 because the delta is 1. Measurement of Gamma: N d1 / S ? ? (T-t). Making Portfolio Gamma neutral Since the underlying stock has zero gamma only way by which the portfolio can be made Gamma neutral is taking a position in the traded option. But by taking a position in the traded option will result in changing the delta so again a position must be taken in the underlying stock as a result of change in delta. The position that must be taken in the traded option to make it Gamma neutral : -?/ ?
75
GAMMA
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 0.00090 0.00082 0.00107 0.00236 0.00288 0.00218 0.00306 0.00296 0.00186 0.00022 0.00193 0.00043 0.00001 0.00000 0.00049 0.00230 0.00135 0.00130 0.00161 0.00272 0.00251 0.00268 0.00306 0.00230 0.00109 0.00008 0.00109 0.00015 0.00000 0.00000 0.00015 0.00109 0.00183 0.00182 0.00214 0.00276 0.00192 0.00287 0.00264 0.00153 0.00055 0.00002 0.00052 0.00004 0.00000 0.00000 0.00004 0.00040 0.00217 0.00226 0.00233 0.00171 0.00066 0.00193 0.00108 0.00036 0.00007 0.00000 0.00006 0.00000 0.00000 0.00000 0.00000 0.00002 EXERCISE PRICE 3000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00168 0.00000 0.00000 3050 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00007 0.00673 0.00000 0.00070 3100 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00049 0.00804 0.00035 0.01242 3200 0.00004 0.00002 0.00001 0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00000 0.00000 0.00019 0.00403 0.00033 0.00905 0.00011
76
19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
0.00308 0.00110 0.00332 0.00581 0.00484 0.00463 0.00413 0.00984 0.01196 0.00171 0.00141 0.00157 0.00081 0.00129 0.00261 0.00142 0.00190 0.00056 0.00084 0.00166 0.00480 0.00513 0.00375 0.00538 0.00449 0.00855 0.00575 0.00000
0.00142 0.00029 0.00133 0.00435 0.00617 0.00756 0.00056 0.00212 0.00049 0.00232 0.00210 0.00230 0.00145 0.00207 0.00322 0.00239 0.00294 0.00130 0.00181 0.00294 0.00434 0.00408 0.00164 0.00542 0.00172 0.00337 0.01043 0.00112
0.00046 0.00005 0.00035 0.00197 0.00432 0.00501 0.00002 0.00008 0.00000 0.00273 0.00269 0.00286 0.00219 0.00278 0.00332 0.00324 0.00362 0.00234 0.00297 0.00392 0.00275 0.00219 0.00046 0.00328 0.00037 0.00041 0.00315 0.01373
0.00002 0.00000 0.00001 0.00008 0.00033 0.00015 0.00000 0.00000 0.00000 0.00224 0.00250 0.00246 0.00272 0.00268 0.00180 0.00279 0.00248 0.00330 0.00331 0.00272 0.00034 0.00017 0.00001 0.00024 0.00000 0.00000 0.00000 0.00006
77
-0.00100 Gamma 0.00700 0.00900 0.01100 0.01300 0.00100 0.00300 0.00500
2-May 4-May 6-May 8-May 10-May 12-May 14-May 16-May 18-May 20-May 22-May 24-May 26-May 28-May 30-May 1-Jun 3-Jun 5-Jun 7-Jun
0.01500
3000
3050
9-Jun 11-Jun
Gamma of Put and Call
date
13-Jun 15-Jun 17-Jun 19-Jun 21-Jun 23-Jun 25-Jun 27-Jun 29-Jun 1-Jul 3-Jul 5-Jul 7-Jul 9-Jul 11-Jul 13-Jul 15-Jul 17-Jul 19-Jul 21-Jul 23-Jul 25-Jul
3100 3200
78
Analysis of Option parameters:
Methodology: The entire project deals with analysis of Option price and its technical parameters for three month period starting from 2nd May 2006 to 27th July 2006. Actual Nifty closing prices have been taken for the above period along with Call and Put prices for four series 3000, 3050, 3100 and 3200. These actual prices are then compared with theoretical Option price using black scholes model along with Option parameters Delta, Gamma, Vega, Theta and Rho.
NIFTY Movements for the three month period since May has been generally volatile as can be compared from the historical volatility .The historical volatility from 1st Jan to 30th april is 14.30% while historical volatility from 2nd may to 27th july was 43.45%. This volatility is attributable to general market perception regarding the future price movements as many investors were perceiving Indian market to be too highly priced compared with other markets with price multiple of 25.This along with high oil price, uncertainty regarding US interest rates and meltdown of metal prices lead to downfall of nifty from 3605.45 on 2nd may to 3156.15 on 27th july (High – 3754.25 / Low – 2632.80). Delta and Gamma: If we analyze the May series, NIFTY was trading at 3605.45 on 2nd may and all the given option series (i.e.) 3000, 3050, 3100 and 3200 were considerably deep in-the-money Call Options as they were expected to be exercised by the holder of call option on the day of expiry.
The Delta for 3200 series was 1.00 till 18th may along with other series of lower exercise price, but sudden collapse of NIFTY from 3635.10 on 17th may to 3081.35 on 22nd may, 79
changed the entire scenario. The options which were deep in the money till 18th may suddenly changed to out-of-the money, thereby declining the probability that they will yield positive returns as reflected by change in Delta from 0.99 to 0.33 and 0.79 to 0.00 for 3100 and 3200 series respectively as can been seen from the chart above in the month of may for the given series.
Also analyzing the above chart, it can be seen that Options with higher exercise price have lower delta when compared to Options with lower exercise price, as they are considered more volatile since they have higher probability that they will be exercised on the date of maturity. Since these options have higher delta, they are also expected to show significant fluctuations to change in strike price when compared to options of lower exercise price.
The reverse of the Call option is applicable in case of Put Options. All the series were out-of the money in the month of May with 0 Delta, as Put options were expected to go unexercised on the date of expiry but due to downward movement of NIFTY, these options turned out to be in in-the-money, 3200 series and 3100 series as NIFTY was in the range of 3100-3200 during the last trading days of may. The rest of the series with exercise price of 3000 and 3050 continued to be out-of money. The fall of delta on 22nd may can be explained by fall in NIFTY to 3081.35 from 3635.10 on 17th may.
Theta : Theta of a portfolio of derivatives, ? is the rate of change of the value of the portfolio with respect to time. Theta is negative for an Option because as the time to maturity decreases the Option becomes less valuable. Its expressed as points per day.
80
For European Call Option: ? = - SN (d1) ? – r X e-r (T-t) N (d 2) / 2 ? (T-t )
For European Put Option : ? = - SN (d1) ? + r X e-r (T-t) N (d 2) / 2 ? (T-t )
Vega (?) : Vega is the rate of change of the value of the Portfolio with respect to the volatility of the underlying asset. If Vega is high then the portfolio is highly sensitive to the small changes in the volatility. Since all the options gain value when the volatility increase , the Vegas for both Calls and Puts is positive. At the money option has always greater Vega than in the money or out of the money option .Vega of all the Options decline as the expiration approaches because less time to expiration means any change in volatility will only have minor effect on the options value. For Non-dividend paying stock: ? = S ?( T- t) N (d1) For stock that pays divided with annual yield of q ? = S ?( T- t) N (d1) e –q (T-t )
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 SPOT 3605.45 3634.25 3648.40 3663.95 EXERCISE PRICE 3000 0.01 0.00 0.00 0.00 3050 0.08 0.02 0.01 0.00 3100 0.37 0.13 0.06 0.02 3200 4.74 2.11 1.18 0.60
81
8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06
3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.14 21.64 142.29 118.59 147.93 291.84 320.04 254.76 302.13 266.27 151.16 15.74 143.24 25.73 0.72 0.13 24.39 112.95 118.65 36.53 102.80 165.22 121.65 78.07 48.58 79.20 48.13 204.87
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.91 86.78 214.79 188.01 222.28 336.32 278.57 312.52 302.52 206.13 88.51 5.37 81.10 8.68 0.13 0.02 7.35 53.50 54.54 9.57 41.12 123.64 155.06 127.27 6.63 17.05 1.97 276.93
0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.08 14.13 103.69 290.00 263.71 294.61 341.95 213.96 334.84 261.08 137.23 44.46 1.57 38.78 2.42 0.02 0.00 1.75 19.50 17.77 1.72 10.69 55.86 108.67 84.40 0.28 0.63 0.00 326.42
0.08 0.02 0.00 0.01 0.03 0.84 0.19 0.00 7.37 128.01 4.91 386.19 367.49 363.56 248.55 88.81 262.66 128.07 39.81 7.29 0.09 5.51 0.11 0.00 0.00 0.05 1.24 0.72 0.02 0.22 2.76 9.93 2.96 0.00 0.00 0.00 308.50
82
28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
151.68 160.93 82.32 121.94 223.35 108.02 133.66 39.15 53.64 95.44 196.63 187.26 116.71 155.81 105.82 103.46 48.15 0.01 0.00 0.00
226.85 235.63 147.44 195.96 275.83 181.75 206.94 90.39 115.01 168.95 177.80 148.99 50.97 156.93 40.53 40.78 87.31 4.91 0.04 3.06
290.52 293.62 222.44 263.71 284.05 245.87 254.57 162.35 188.82 225.23 112.73 80.06 14.45 94.96 8.70 4.97 26.37 60.13 3.22 54.57
307.97 289.67 312.41 289.81 180.71 243.53 201.73 258.17 240.00 180.28 16.71 7.67 0.34 8.30 0.08 0.00 0.02 0.30 94.45 0.57
83
Vega of Put
400.00
350.00
300.00
250.00 Vega
200.00
150.00
100.00
50.00
0.00
2M ay
9M ay
23 -M ay
16 -M ay
30 -M ay
27 -J un
4Ju l
un
un
13 -J
date 3000 3050 3100 3200
Analysis of Vega of Call and Put Options
A high vega implies that the Option price highly sensitive to the small changes in the volatility. In the above scenario for the may series, vega was quite low during the initial 18 days when the market was range bound, but as the may series reached close to expiry, Vega also fluctuated contrary to the general practice according to which Vega of an Option declines as expiration approaches , due to the fact that less time to expiration means any change in volatility will only have minor effect on the options value. But since the market was highly volatile during the ending period of may, Vega of may series increased to reflect those changes in volatility. As far as June and July series is concerned, we can see than Vega of all the four series have declined steadily towards the end of expiry.
20 -J
11 -J ul
18 -J ul
25 -J ul
6Ju n
84
Within the june and july series also towards the end of expiry, Vega was particulary lower for the series which had higher exercise price when compared to those series which had lower exercise price. RHO : Rho of a portfolio is the change in value of portfolio with respect to change in interest rate. It measures the sensitivity of the value of the portfolio with respect to interest rates. For Call Options: Rho = X (T-t) e- r (T-t) N (d 2) For Put Options: Rho = - X (T-t) e- r (T-t) N (-d 2) Elasticity: Elasticity is the percentage change in the Options value to the percentage change in the underlying. Elasticity of an Option is also referred as Leverage. Greater the Options Elasticity more leveraged the Option is. Elasticity = (Underlying Price * Delta )/ Theoretical Value.
85
Comparison of theoretical and actual price of Option: In the given model, we have assumed interest rate which is risk free interest rate of 5% and dividend yield of 2%. The Volatility used for the calculation purpose is 14.68% which is historical volatility for six month period beginning 1st January 2006.If we look at the above chart, it clearly shows that the Call Options of 3000 to 3200 were generally under priced in the month of may when the market was all the options were over priced in the month of June when the market was bearish. In the month of July when the market was volatile and range bound, all the series were under priced except 3000 which was overpriced.
Comparison of theoretical edge of Put option for the above series show that Put options were over priced for all the four series for entire three months since May 2006. In the month of May, where call were under priced, Put options were overpriced and in the month of June when Call option were also overpriced, Put options were too overpriced but they were comparatively higher priced than Call options. Similarly the above explanation also holds true for the month of July where Put options were comparatively overpriced than the Call Options. One reason for the above mismatch between Call and Put price can be attributed to the fact that writer of Put option in bearish market might expect more premium from the buyer in order to mitigate himself from further fall in the market.
86
THEORETICAL EDGE FOR CALL
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 -19.75 -10.22 2.12 -48.78 -56.70 -60.10 -57.37 -63.80 -62.58 -39.63 -49.03 -25.04 -19.19 -16.00 -30.56 -56.07 -48.69 11.57 3.54 -53.91 -54.75 -59.32 -60.21 -56.73 -49.99 -25.16 -40.76 -17.54 -12.80 -10.65 -20.62 -41.42 -35.78 -29.64 -15.90 -55.77 -51.53 -65.34 -55.09 -50.44 -37.99 -22.08 -30.93 -13.12 -11.25 -9.80 -16.23 -30.31 -52.08 -48.20 -30.25 -50.62 -37.61 -55.12 -42.39 -31.93 -20.83 -13.05 -20.26 -8.45 -6.70 -5.70 -8.60 -16.43 3000 10.35 21.90 24.12 17.34 13.59 9.16 11.32 5.86 17.69 33.69 5.26 1.79 0.73 8.30 -39.98 -12.58 -1.36 EXERCISE PRICE 3050 5.50 12.15 26.07 38.08 66.61 70.77 27.43 -25.94 -12.12 -159.79 -139.68 42.35 -203.98 -346.13 -60.89 -23.51 2.21 3100 0.66 38.20 13.11 9.92 21.92 42.08 -0.27 -30.80 -42.28 -20.73 33.43 -3.10 -48.68 -36.45 -65.52 -41.64 -24.33 3200 10.85 26.53 27.21 47.70 12.16 4.80 7.73 1.24 -36.86 24.92 36.66 -11.84 2.00 -63.51 -49.71 -66.81 -17.14
87
19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-July-06
2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
-56.08 -26.31 -32.66 -31.69 -24.05 -26.10 -23.55 -25.63 -20.99 -5.85 19.01 38.51 36.01 63.00 46.78 27.93 43.31 33.93 67.95 68.85 57.56 10.03 6.77 -2.97 19.06 0.17 3.22 32.12 80.74
-43.06 -21.86 -20.23 -29.36 -30.62 -32.91 -13.71 -16.85 -8.42 -0.50 -50.40 -33.80 -33.52 -20.07 -16.35 -28.03 -29.45 -33.49 -19.70 -8.35 -10.07 -26.03 -23.98 -14.65 -21.55 -10.38 -14.10 -17.91 -6.25
-31.54 -16.68 -14.63 -21.49 -26.85 -27.46 -8.30 -8.94 -3.25 -0.20 -52.58 -39.34 -39.51 -24.34 -33.65 -31.22 -36.10 -39.12 -23.21 -18.63 -19.57 -21.96 -18.73 -9.93 -17.49 -6.58 -8.66 -10.42 -12.94
-14.99 -8.60 -7.00 -10.06 -10.55 -12.75 -3.70 -2.55 -0.60 -0.25 -48.12 -40.02 -36.78 -27.36 -34.40 -24.99 -33.00 -33.84 -27.47 -24.55 -20.44 -10.83 -8.81 -4.90 -5.09 -2.00 -2.90 -1.75 -2.20
88
Comparison of Theoretical and Actual Price
100.00
50.00
Theoretical Edge
0.00
23 -M ay 16 -M ay 30 -M ay ay ay 13 -J un 20 -J un 27 -J un 6Ju n l l l 2M 9M 11 -J u 25 -J u 18 -J u 4Ju l
-50.00
-100.00
-150.00 3000 3050 3100 3200
THEORETICAL EDGE FOR CALL
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3000 -1.50 -3.70 -1.55 -2.00 -1.50 -1.35 -5.00 -4.20 -3.10 -1.85 -2.65 -2.25 -10.35 -20.55 -97.70 -26.25 3050 -5.15 -5.15 -4.90 -4.00 -4.00 -3.50 -4.90 -4.90 -5.60 -5.80 -3.40 -3.70 -11.20 -36.37 -108.48 -39.55 Exercise Price 3100 -3.40 -3.00 -5.00 -5.00 -3.00 -3.00 -4.90 -4.90 -4.50 -5.50 -4.15 -3.00 -17.25 -46.88 -106.39 -50.74 3200 -6.28 -5.02 -5.44 -4.89 -3.15 -4.65 -3.50 -3.10 -4.70 -6.04 -6.45 -4.35 -31.21 -74.47 -111.97 -74.48
89
24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06
3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3
-34.30 -61.57 -58.53 -64.45 -97.05 -133.65 -99.16 -124.35 -107.09 -87.92 -64.87 -92.20 -88.78 -47.83 -25.54 -49.61 -62.20 -64.79 -65.19 -50.16 -47.71 -29.97 -33.78 -36.59 -27.62 -19.44 -64.54 -56.34 -57.23 -44.13 -48.76 -64.16 -47.15 -53.01 -30.48 -32.72
-48.69 -70.49 -65.25 -73.44 -101.67 -130.44 -105.51 -119.85 -63.73 -58.57 -64.84 -36.62 50.80 30.06 80.10 -26.72 -61.99 -47.59 -24.46 -36.59 -52.83 -26.12 -38.36 -13.63 -17.51 -2.02 -71.94 -64.37 -67.11 -53.95 -58.83 -70.51 -54.67 -60.99 -36.38 -40.51
-55.78 -82.56 -79.62 -84.33 -104.33 -128.75 -103.57 -122.25 -92.50 -66.48 -55.55 -71.37 -73.44 -33.85 -24.30 -28.07 -42.87 -36.29 -28.69 -24.95 -42.66 -28.49 -32.39 -7.94 -12.71 7.04 -73.15 -68.17 -71.41 -58.27 -63.63 -70.98 -59.33 -64.43 -43.40 -49.14
-51.81 -94.58 -93.80 -97.59 -95.93 -122.92 -97.41 -109.93 -81.95 -51.71 -32.31 -56.33 -75.46 -33.47 -12.21 -27.63 -6.17 -10.67 -25.98 -17.47 -31.63 -11.57 -20.34 -8.23 -11.85 8.63 -63.66 -66.78 -67.70 -60.74 -62.72 -64.47 -56.07 -59.56 -48.86 -53.65
90
14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-July-06
3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
-39.25 -55.03 -49.46 -43.72 -29.61 -25.18 -20.37 -16.62 -2.25
-48.23 -56.56 -45.56 -37.36 -25.96 -17.82 -15.02 -18.02 -4.94
-54.07 -50.11 -41.18 -31.59 -23.30 -14.05 -7.44 -13.63 -12.45
-54.26 -39.71 -31.58 -23.92 -13.15 -8.31 -0.42 -2.29 -4.16
91
Theoretical edge 100.00 -150.00 50.00 -50.00 0.00 -100.00
2M ay
9M ay
16 -M
ay 23 -M
ay 30 -M
ay
6Ju n
Theoritical Egde Put
3000 3050 3100 3200
13 -J un 20 -J un 27 -J un
4Ju l 11 -J ul 18 -J ul 25 -J ul
92
Relative Strength Index (RSI)
Date Close 47.4 21.1 -4.6 14.2 -3.9 -39.3 -20.1 -0.1 -17.5 -4.0 -19.9 61.7 30.1 -16.9 23.9 32.3 42.4 -8.3 26.6 -29.5 -4.1 -26.8 59.8 19.7 -11.2 18.6 13.6 -23.6 4.6 -0.6 -40.1 24.3 29.7 24.3 29.7 4.6 0.6 40.1 18.6 13.6 23.6 59.8 19.7 11.2 26.6 29.5 4.1 26.8 23.9 32.3 42.4 8.3 61.7 30.1 16.9 12.45 13.27 14.64 16.62 15.43 16.23 15.07 13.99 13.00 16.34 16.58 15.39 15.62 15.48 14.37 13.68 12.70 11.79 12.69 13.90 9.02 1.38 58.00 8.37 1.59 61.32 7.78 1.88 65.31 7.22 2.30 69.71 7.29 2.12 67.91 6.77 2.40 70.56 8.40 1.79 64.21 8.09 1.73 63.36 9.43 1.38 57.94 8.76 1.87 65.11 8.13 2.04 67.09 8.35 1.84 64.84 7.75 2.02 66.84 7.20 2.15 68.26 8.37 1.72 63.20 7.77 1.76 63.77 7.26 1.75 63.63 9.61 1.23 55.11 8.92 1.42 58.73 8.28 1.68 62.67 14.2 3.9 39.3 20.1 0.1 17.5 4.0 19.9 Up 47.4 21.1 4.6 Down AvgGain AvgLoss RS RSI
2-Jan-06 2835.95 3-Jan-06 2883.35 4-Jan-06 2904.4
5-Jan-06 2899.85 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 2914 2910.1 2870.8 2850.7
13-Jan-06 2850.55 16-Jan-06 17-Jan-06 18-Jan-06 2833.1 2829.1 2809.2
19-Jan-06 2870.85 20-Jan-06 2900.95 23-Jan-06 2884.05 24-Jan-06 2908
25-Jan-06 2940.35 27-Jan-06 2982.75 30-Jan-06 31-Jan-06 2974.5 3001.1
1-Feb-06 2971.55 2-Feb-06 2967.45 3-Feb-06 2940.6
6-Feb-06 3000.45 7-Feb-06 3020.1
8-Feb-06 3008.95 10-Feb-06 3027.55 13-Feb-06 3041.15 14-Feb-06 3017.55 15-Feb-06 16-Feb-06 17-Feb-06 3022.2 3021.6 2981.5
20-Feb-06 3005.85 21-Feb-06 3035.5
93
22-Feb-06 23-Feb-06
3050.8 3062.1
15.3 11.3 -12.0 17.4 7.3 48.4 27.6 -3.3 43.1 -7.6 -66.1 12.4 54.8 18.8 -7.3 31.3 7.5 31.6 -3.3 -22.2 7.0 32.7 41.8 3.3 29.2 64.8 -16.4 70.8 9.8 27.8 -56.1 23.6 -98.4 -34.5 79.7 92.9 17.8
15.3 11.3 12.0 17.4 7.3 48.4 27.6 3.3 43.1 7.6 66.1 12.4 54.8 18.8 7.3 31.3 7.5 31.6 3.3 22.2 7.0 32.7 41.8 3.3 29.2 64.8 16.4 70.8 9.8 27.8 56.1 23.6 98.4 34.5 79.7 92.9 17.8
14.00 13.81 12.82 13.15 12.73 15.28 16.16 15.00 17.01 15.79 14.66 14.50 17.38 17.48 16.23 17.30 16.60 17.67 16.41 15.24 14.65 15.93 17.78 16.75 17.64 21.01 19.51 23.17 22.22 22.61 21.00 21.19 19.67 18.27 22.65 27.67 26.96
7.69 1.82 64.55 7.14 1.93 65.91 7.49 1.71 63.12 6.96 1.89 65.40 6.46 1.97 66.33 6.00 2.55 71.80 5.57 2.90 74.36 5.41 2.77 73.49 5.02 3.38 77.19 5.21 3.03 75.20 9.56 1.53 60.54 8.88 1.63 62.03 8.24 2.11 67.83 7.65 2.28 69.55 7.63 2.13 68.03 7.08 2.44 70.95 6.58 2.52 71.62 6.11 2.89 74.32 5.91 2.78 73.52 7.07 2.15 68.30 6.57 2.23 69.05 6.10 2.61 72.33 5.66 3.14 75.86 5.26 3.19 76.12 4.88 3.61 78.33 4.53 4.64 82.25 5.38 3.63 78.38 5.00 4.64 82.26 4.64 4.79 82.73 4.31 5.25 84.00 8.01 2.62 72.39 7.44 2.85 74.02 13.94 1.41 58.53 15.40 1.19 54.25 14.30 1.58 61.29 13.28 2.08 67.57 12.33 2.19 68.61
24-Feb-06 3050.05 27-Feb-06 3067.45 28-Feb-06 1-Mar-06 2-Mar-06 3074.7 3123.1 3150.7
3-Mar-06 3147.35 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 3190.4 3182.8 3116.7 3129.1 3183.9
13-Mar-06 3202.65 14-Mar-06 3195.35 16-Mar-06 3226.6
17-Mar-06 3234.05 20-Mar-06 3265.65 21-Mar-06 3262.3
22-Mar-06 3240.15 23-Mar-06 3247.15 24-Mar-06 3279.8
27-Mar-06 3321.65 28-Mar-06 29-Mar-06 3325 3354.2
30-Mar-06 3418.95 31-Mar-06 3402.55 3-Apr-06 3473.3
4-Apr-06 3483.15 5-Apr-06 7-Apr-06 3510.9 3454.8
10-Apr-06 3478.45 12-Apr-06 13-Apr-06 3380 3345.5
17-Apr-06 3425.15 18-Apr-06 3518.1
19-Apr-06 3535.85
94
20-Apr-06
3573.5
37.7 -0.4 -24.2 -86.3 93.1 -47.7 0.3 49.3 47.8 28.8 14.2 15.5 29.2 27.4 33.7 -53.2 -51.0
37.7 0.4 24.2 86.3 93.1 47.7 0.3 49.3 47.8 28.8 14.2 15.5 29.2 27.4 33.7 53.2 51.0 147.1 20.4
27.73 25.75 23.91 22.20 27.26 25.32 23.53 25.36 26.97 27.10 26.18 25.42 25.69 25.81 26.37 24.49 22.74 21.12 21.06 27.54 246.2 142.0 165.6 25.58 23.75 22.05 28.91 83.8 26.84 29.36 29.54 27.81 29.6 114.3 108.8 25.83 23.98 22.27 29.90 74.7 79.3 76.9 136.1 27.76 25.78 23.94 22.23 30.78
11.45 2.42 70.77 10.67 2.41 70.71 11.63 2.06 67.27 16.96 1.31 56.69 15.75 1.73 63.39 18.03 1.40 58.41 16.74 1.41 58.43 15.54 1.63 62.00 14.43 1.87 65.14 13.40 2.02 66.91 12.45 2.10 67.78 11.56 2.20 68.74 10.73 2.39 70.53 9.96 2.59 72.15 9.25 2.85 74.03 12.39 1.98 66.40 15.15 1.50 60.02 24.57 0.86 46.21 22.82 0.92 48.00 21.19 1.30 56.52 37.26 0.69 40.70 44.74 0.53 34.67 53.37 0.41 29.24 49.56 0.58 36.84 52.01 0.52 34.04 48.29 0.61 37.81 44.84 0.66 39.72 41.64 0.67 40.05 40.78 0.63 38.77 46.03 0.52 34.25 50.51 0.44 30.60 46.90 0.64 38.93 48.89 0.57 36.22 51.06 0.50 33.55 52.91 0.45 31.15 58.85 0.38 27.42 54.64 0.56 36.03
21-Apr-06 3573.05 24-Apr-06 3548.9
25-Apr-06 3462.65 26-Apr-06 3555.75 27-Apr-06 3508.1
28-Apr-06 3508.35 29-Apr-06 3557.6
2-May-06 3605.45 3-May-06 3634.25 4-May-06 3648.4
5-May-06 3663.95 8-May-06 3693.15 9-May-06 3720.55 10-May-06 3754.25 11-May-06 3701.05 12-May-06 3650.05
15-May-06 3502.95 -147.1 16-May-06 17-May-06 18-May-06 19-May-06 3523.3 20.4
3635.1 111.8 111.8 3388.9 -246.2 3246.9 -142.0
22-May-06 3081.35 -165.6 23-May-06 3199.35 118.0 118.0 24-May-06 3115.55 25-May-06 26-May-06 29-May-06 30-May-06 3177.7 3209.6 3214.9 3185.3 -83.8 62.1 31.9 5.3 -29.6 62.1 31.9 5.3
31-May-06 3071.05 -114.3 1-Jun-06 2962.25 -108.8 2-Jun-06 3091.35 129.1 129.1 5-Jun-06 3016.65 6-Jun-06 2937.3 -74.7 -79.3 -76.9
7-Jun-06 2860.45
8-Jun-06 2724.35 -136.1 9-Jun-06 2866.3 142.0 142.0
95
12-Jun-06 2776.85 13-Jun-06 14-Jun-06 15-Jun-06
-89.5
89.5 113.6 30.5
28.58 26.54 24.64 34.74 38.80 37.92
57.13 0.50 33.35 61.16 0.43 30.26 58.97 0.42 29.47 54.76 0.63 38.82 50.85 0.76 43.28 47.22 0.80 44.54 47.81 0.74 42.41 44.40 0.84 45.55 41.23 0.96 48.98 38.28 1.05 51.21 35.55 1.06 51.57 40.66 0.86 46.36 37.75 0.94 48.42 35.15 0.94 48.35 32.64 0.97 49.31 30.31 1.28 56.14 28.15 1.34 57.22 27.01 1.29 56.41 25.09 1.46 59.36 26.20 1.30 56.49 30.08 1.05 51.22 27.93 1.22 54.94 27.78 1.14 53.23 25.80 1.36 57.61 25.86 1.26 55.74 27.29 1.11 52.56 33.61 0.84 45.51 32.21 0.81 44.73 34.26 0.71 41.41 31.81 0.91 47.63 35.11 0.77 43.34 32.60 0.85 46.08 30.28 0.98 49.58 28.11 1.16 53.71 26.10 1.29 56.26 26.05 1.20 54.48 24.19 1.23 55.23
2663.3 -113.6 2632.8 -30.5
2798.8 166.0 166.0 91.5 26.6 -55.6 62.1 71.3 47.9 7.6 62.1 71.3 47.9 7.6 107.1 39.3 1.3 16.8 91.5 26.6 55.6
16-Jun-06 2890.35 19-Jun-06 20-Jun-06 2916.9 2861.3
35.22 37.14 39.58 40.18 37.85 35.15 35.44 32.91 31.76 38.80 37.65
21-Jun-06 2923.45 22-Jun-06 2994.75 23-Jun-06 25-Jun-06 26-Jun-06 3042.7 3050.3
2943.2 -107.1 39.3 -1.3 16.8
27-Jun-06 2982.45 28-Jun-06 29-Jun-06 30-Jun-06 2981.1 2997.9
3128.2 130.3 130.3 22.8 -12.3 58.4 -40.7 -80.6 66.2 -25.8 79.8 -26.6 -46.0 79.8 26.6 46.0 115.8 13.9 60.9 90.3 78.1 40.8 54.7 69.7 46.0 25.3 12.4 66.2 25.8 58.4 40.7 80.6 22.8 12.3
3-Jul-06 3150.95 4-Jul-06 3138.65 5-Jul-06 6-Jul-06 3197.1 3156.4
34.96 36.64 34.02 31.59 34.06 31.63 35.06 32.56 30.23 28.07 26.07 24.21 28.93 26.86 27.86 29.77 32.62 33.58 31.18 29.84
7-Jul-06 3075.85 10-Jul-06 3142
11-Jul-06 3116.15 12-Jul-06 13-Jul-06 3195.9 3169.3
14-Jul-06 3123.35
17-Jul-06 3007.55 -115.8 18-Jul-06 2993.65 19-Jul-06 2932.75 20-Jul-06 3023.05 21-Jul-06 2945 -13.9 -60.9 90.3 -78.1 40.8 54.7 69.7 46.0 -25.3 12.4
24-Jul-06 2985.85 25-Jul-06 3040.5
26-Jul-06 3110.15 27-Jul-06 3156.15 28-Jul-06 31-Jul-06 3130.8 3143.2
96
1-Aug-06 2-Aug-06 3-Aug-06
3147.8 3182.1 3190
4.6 34.3 7.9 -13.3 -25.7 61.3 42.2 5.5 14.3 38.8 43.0 -2.2 2.8 9.3 -1.4
4.6 34.3 7.9 13.3 25.7 61.3 42.2 5.5 14.3 38.8 43.0 2.2 2.8 9.3 1.4
28.04 28.48 27.01 25.08 23.29 26.01 27.16 25.62 24.80 25.80 27.03 25.09 23.51 22.49 20.88 19.39
22.46 1.25 55.52 20.86 1.37 57.73 19.37 1.39 58.24 18.93 1.33 56.99 19.41 1.20 54.54 18.02 1.44 59.06 16.74 1.62 61.88 15.54 1.65 62.24 14.43 1.72 63.22 13.40 1.93 65.82 12.44 2.17 68.47 11.71 2.14 68.19 10.87 2.16 68.38 10.10 2.23 69.02 9.47 2.20 68.79 8.80 2.20 68.79
4-Aug-06 3176.75 7-Aug-06 8-Aug-06 9-Aug-06 10-Aug-06 3151.1 3212.4 3254.6 3260.1
11-Aug-06 3274.35 14-Aug-06 3313.1
16-Aug-06 3356.05 17-Aug-06 3353.9
18-Aug-06 3356.75 21-Aug-06 22-Aug-06 3366 3364.6
97
100.00
SNP Nifty
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 0.00 23-Jan 30-Jan 6-Feb 13-Feb 20-Feb 27-Feb 6-Mar 13-Mar 20-Mar 27-Mar 3-Apr 10-Apr 17-Apr 24-Apr
2500
1-May 8-May 15-May 22-May 29-May 5-Jun 12-Jun 19-Jun 26-Jun 3-Jul 10-Jul 17-Jul 24-Jul 31-Jul 7-Aug 14-Aug 21-Aug RSI
2700
2900
3100
3300
3500
3700
3900
RSI
NIFTY
Date
Close
23 -J 30 an -J a 6- n F 13 eb -F 20 eb -F 27 eb -F e 6- b M 13 ar -M 20 ar -M 27 ar -M a 3- r Ap 10 r -A 17 pr -A 24 pr -A 1- pr M a 8- y M 15 ay -M 22 ay -M 29 ay -M a 5- y Ju 12 n -J 19 un -J 26 un -J un 3Ju 10 l -J 17 ul -J 24 ul -J 31 ul -J 7- ul A 14 ug -A 21 ug -A ug
98
RSI RSI = 100 - [100/(1 + RS)] where: RS = (Avg. of n-day up closes)/(Avg. of n-day down closes) n= days (9 - 15 day RSI)
The RSI ranges from 0 to 100. At around the 70 level, a stock is considered overbought and one should expect fall in the price of stock. Levels below 30 refer to oversold position and one can expect upward movement in the price of stock from the current level. I
Methodology for RSI calculation For the calculation of RSI, 14 day moving average period is used.
In the above chart, three month NIFTY data is used starting since 2
nd
January till 22nd August.
Interpretation In the above RSI chart, RSI was hovering around the level of 60-70 in the month of JanuaryFebruary, suggesting the early indications that the market may heat up in the days to come. In the month of March and April and 1st 15 days of May ,when NIFTY was at its peak, RSI levels went further to 80 , thus giving a clear indication that market has heaten up and the bull phase is about to get over and one should expect the prices to cool down from the current levels of 3500-3600. In the end of may , after the bull phase as indicated by RSI, market went crashing down and the bear phase continued till mid June , where again RSI level turned to 30 , thus suggesting that market may gain in the near period. The end of bear phase after mid june paved the way for anpther bull phase which continued till end of august. Implications for Option traders
99
In January and February, since RSI was at 60 levels and increasing towards 70-80, once could have expected NIFTY to go up and thus a Long Call/ Short put would have been appropriate strategy.
In April and May RSI was at 80 levels, indicating at bearish market, one should have taken short call/ long put.
In mid June as the RSI was at 30 levels, indicating another bull phase, Long Call and Short put should have been appropriate strategy to take.
100
Trading Strategy using Options:
Using Single Option and the stock: Long Position in the stock + Short Position in the Call Option. Short Position in the stock + Long Position in the call Option. Long Position in the stock +Long Position in the Put option Short Position in the stock + Short Position in the Put option Bull Spread: Buying the call option with a strike price and selling the call option on the same stock with a higher strike price. In the Bull Spread if the Stock price does well then the payoff for the investor will be the difference between 2 exercise price. If on the expiration date the stock price lies in between the two exercise price then the payoff will be Strike Price less the Lower exercise price( Long Call). If the stock price is less than both the exercise price then both the calls remain unexercised and investor will lose the initial cost of the spread. In Bull spread the loss as well as the maximum payoff is limited. In return for giving upside potential investor reduces the Spread cost by initial outlay from writing the call option. 3 types of Bull spreads can be distinguished: Both the calls initially out of the money – Most Aggressive One call in the money and other call out of money- Less aggressive Both the calls in the money- Conservative
101
Bull Spread with Calls:
Long Call -Lower Strike Price Short Call -Higher Strike Price
Bull spreads with Puts:
In Bull spread with Put one put is written with higher strike price and investor buys one put with lower exercise price. Because Put that is written with higher strike price in involves an initial cash inflows. If on the expiration date , the strike price is higher than both the Exercise price , then both the Put will exercise worthless and investor will gain an amount equal to initial cash inflow. If on the expiation date , the strike price is lower than both the exercise price then both the Put will be exercised and there will be loss equal to difference between both the exercise price. If on the expiration date, the strike price is between two exercise price ,then the Put that is written (i.e.) with higher strike price will be exercised and the Put that is bought will expire worthless. The resulting loss in this case will be Higher exercise price less the strike price.
Bull spread with put
Long Put - Lower Strike Price. Short Put – Higher Strike Price
BULL SPREAD WITH PUT
102
On 2nd may when the index was at 1916.75 and if investor is bullish about the market but at the same time he wants to reduce his risk he can use Bull Spread. Suppose an investor buys 2050 Put and at the same time sells 2100 Put then initial inflow will be:
Proceeds from writing a Put Initial outlay from Long Put Initial Inflow 195.00 147.65 47.35
His position as on 26th may when the index was at 2074.70 will be Put that is written for 2100 will be exercised resulting in loss of Rs 25.30 and Put that is bought will expire worthless Thus investor has earned Rs 22.05(47.35-25.30).
Payoff Structure from Bull Spread with Puts: Short Put with exercise Spot Price 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 price of 2100 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 Long Put with exercise price of 2050 10 5 0 0 0 0 0 0 0 0 0 0 Payoff -50 -50 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 Initial Inflow 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 Total Payoff -2.65 -2.65 -2.65 2.35 7.35 12.35 17.35 22.35 27.35 32.35 37.35 42.35
103
2100 2105 2110 2115
0 0 0 0
0 0 0 0
0 0 0 0
47.35 47.35 47.35 47.35
47.35 47.35 47.35 47.35
Pay off Bull -Put
50.00
40.00
30.00
Payoff
20.00
Pay off Bull -Put
10.00
0.00 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 2100 2105 2110 2115
-10.00 Spot Pricd
BULL SPREAD WITH CALL
On 2nd may when the index was at 1916.75 and if investor is bullish about the market but at the same time he wants to reduce his risk he can buy Spread.Suppose an investor buys 2050 call and at the same time sells 2100 call then the total investment will be: Proceeds from writing a call Initial outlay from Long Call Initial Cost of Spread 1.90 3.80 1.90
His position as on 26th may when the index was at 2074.70 will be 104
Short Call of 2100 will be unexercised Long Call of 2050 will be exercised resulting in pay off of 24.70 Thus investor has earned Rs24.70 against initail investment of just Rs 1.90
Payoff Structure from Bull Spread with Calls: Long call with Short Call with exercise Spot Price 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 2100 2105 2110 2115 price of 2100 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 -10 -15 exercise price of 2050 0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Payoff 0 0 0 5 10 15 20 25 30 35 40 45 50 50 50 50 Cost 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 Total Payoff -1.90 -1.90 -1.90 3.10 8.10 13.10 18.10 23.10 28.10 33.10 38.10 43.10 48.10 48.10 48.10 48.10
105
60.00
50.00
40.00
30.00 Payoff 20.00 10.00 0.00 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 2100 2105 2110 2115 -10.00 Spot price Bull -Put
Bear spread :
Bear spread with Call :
Buying a call Option with one strike price and selling a call with another strike price with lower strike price. Long Call -Higher Strike Price. Short Call -Lower Strike Price.
Bear Spread with Put :
Long Put - Higher Strike Price. Short Put Volatility Spread: Backspread Ratio Vertical Spread Straddle - Lower Strike Price
106
Strangle Butterfly
Back spread:
Back spread is a delta neutral position which consists of more long Options than short Options where all the Options expire at the same time. In order to achieve this Options with smaller deltas must be purchased and Option with larger deltas must be sold. The primary consideration of a Backspread is that some movement will occur. A trader will go for Call Backspread if he expects market to go up and will take Put Backspread if he expects market to go down. Call Back Spread : Long Calls - Higher exercise price Short Calls - Lower exercise price. Put Back spread : Long Puts - Lower exercise price Short Puts - Higher exercise price.
(Long calls should be more than short calls to make it delta neutral).
Ratio Vertical Spread:
In this trader takes opposite position of backspread , and is short more contracts than long with all the options expiring on the same date. Ratio vertical spread realizes its maximum value when stock price finishes right at the exercise price. Its taken by someone who expects the market to be quite stable.
107
Call ratio vertical Spread : Long calls - Lower exercise price Short calls - Higher exercise price. Put ratio vertical spread : Long put - Higher exercise price Short put - Lower exercise price. ( short calls will be more to make it delta neutral). Backspread will gain if the market moves outside the limits and will lose if the stock price remains with the range of Higher and lower strike price.
Ratio Vertical Spread will gain if the market is within the range of lower and higher exercise price and will lose if the stock price is outside this range.
108
Butterfly spread:
Long Butterfly :
Buying a call Option with higher and lower strike price and selling two call options with strike price average of the above two strike price. This strategy is suited for an investor who feels that the large price changes are unlikely. Long Butterfly acts like a ratio vertical spread. If the strike price is less than Lowest strike price all the calls will not be exercised and will result in loss to the amount of initial investment. If Strike price is higher than H then all the calls will be exercised and it will result in the loss because gains from buying call will be equalized by loss from writing call option. If on the expiration date if the spot price is between H and L then the strategy will result in a profit with maximum profit when the strike price is in the mid way between the H and L.
Short Butterfly:
Write 2 calls with higher and lower strike price and buy 2 calls with the exercise price in between H and L. This strategy works like backspread and is undertaken by the trader when he expects the market to move sharply in either direction. If the market remains within H and L range then Short butterfly results in loss to the trader. Straddle : Investors buys(sells) Call and Put with same expiration date with same strike price. If both Call and Put Option are purchased then it is Long Straddle ( Bottom Straddle)and if both Call and Put Option are sold then it is Short Straddle. Trader’s buy Straddles and Strangles when they believe that the underlying asset will be volatile but do not have any belief about the direction of the underlying. They will benefit from Put option when the market turns bearish and they will benefit from Call Option when the market turns Bullish..
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With a Long straddle , the trader’s potential profit is unlimited if market moves in either direction. A loss will be incurred if the market does not move away from the exercise price since in that case both Call and Put will not be exercised. Buying a straddle is an appropriate strategy when large price changes are expected in the stock. A short Straddle( Top Straddle) will realize maximum profit if the market stays close to the call and put exercise price. The writer of straddle benefits from the price stability. They buy a straddle when they believe that the market will remain stable. Strangle: Buying a call and Put with same strike price and maturity date but with different strike price. In case of Long Strangle again the investor is not sure about the direction of the stock price but is expecting volatility. In case of Strangle the stock price has to move further away than the Straddle for an investor to make profit but at the same time downward risk in Strangle is less when compared to straddle when the stock ends up at the Central value. Thus the volatility spreads can be distinguished into 2 categories. Helped by the fluctuations in the Underlying Asset and those that are hurt by changes in the underlying asset. Strategies which are helped by changes in the underlying asset ( market is volatile) will have Positive Gamma and Positive Vega. So if the volatility increases then these strategies will bring positive payoff. The strategies which are helped by changes in the underlying price( direction immaterial ) movements are : Backspread Long straddle Long Strangle 110
Short Butterfly. Strategies which bring positive payoffs when the market is quite stable , have negative Gamma and Negative Vega. If the volatility decreases then the payoff from these strategies will increase. The strategies which come under this type are: Ratio vertical spread Short straddle Short Strangle Long Butterfly If an option is under priced (low implied volatility) then one should look for spreads with positive Vega (i.e.) Backspreads/Long Straddle /Long Strangle/ Short Butterfly. If an option is overpriced (high implied volatility) then one should look for spreads with negative Vega (i.e.) Ratio vertical Spread / Short Straddle / Short Strangle / Long Butterfly.
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Calendar spread: Selling a call option and buying a longer maturity call option with the same strike price. Diagonal Spread : Where both the expiration date and strike price differ. Strap : Long Position in two calls and one put all with same strike price and expiration date. In this case investor is expecting sharp movement in the price of stock but is expecting strong intuition for upward movement so he buys 2 calls . Strips: Long Position in one call and two puts all with same strike price and expiration date. In the case of strips investor is expecting sharp movement in the stock price with greater expectation for downward movement in the stock price hence he buys 2 puts . Long Strangle If the Index on 1st April is at 2067.65 and investor is expecting Volatility and at the same time he wants to minimize the downward risk that occurs from straddle he can buy a strangle.If he buys a 2100 call and 1900 put for april then the total cost for him will be Long Call Long Put 2100 2050 3.00 37.95
Total Cost
40.95
Position at expiration (28th April) 1941.3
112
Call Option Put Option
2100 2050
0 108.7
Net returns
67.75
Individual Pay off Call Spot Price 1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 Put Call 2100 Put 2050 Payoff Cost of Straddle 175 150 125 100 75 50 25 0 0 0 25 50 75 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 Total Payoff 134.05 109.05 84.05 59.05 34.05 9.05 -15.95 -40.95 -40.95 -40.95 -15.95 9.05 34.05 Strategy Pay off
2100 2050 0 0 0 0 0 0 0 0 0 0 25 50 75 175 150 125 100 75 50 25 0 0 0 0 0 0
-3.00 137.05 -3.00 112.05 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 22.00 47.00 72.00 87.05 62.05 37.05 12.05 -12.95 -37.95 -37.95 -37.95 -37.95 -37.95 -37.95
113
2200 2225 2250 2275
100 125 150 175
0
97.00
-37.95 -37.95 -37.95 -37.95
100 125 150 175
40.95 40.95 40.95 40.95
59.05 84.05 109.05 134.05
0 122.00 0 147.00 0 172.00
200
Long Strangle
Long Strangle 150 Call 2100 Put 2050
100
Payoff
50
0 1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225 2250 2275
-50
-100 Spot
114
Short Strangle On 6th May when index was at 1977.50, if an investor shorts 100 2050 Calls and 100 2100 puts for May month with exercise price 2050 having an expiration date on 26th may, then the total credit to the investor will be: Short Call Short Put Initail Inflow Position on expiration date (may 26th) 2050 2100 8.30 139.75 148.05 2074.7
Call
Put
Short Call
Short Put Initial Total Payoff -79.20 -54.20 -29.20 -4.20 20.80 45.80 70.80 95.80 95.80
Spot Price 1875 1900 1925 1950 1975 2000 2025 2050 2075
2050 0 0 0 0 0 0 0 0 -25
2100 -225 -200 -175 -150 -125 -100 -75 -50 -25
2050 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 -16.70
2100 Payoff -85.25 -60.25 -35.25 -10.25 14.75 39.75 64.75 89.75 114.75 -225 -200 -175 -150 -125 -100 -75 -50 -50
Credit 145.80 145.80 145.80 145.80 145.80 145.80 145.80 145.80 145.80
115
2100 2125 2150 2175 2200 2225 2250 2275
-50 -75 -100 -125 -150 -175 -200 -225
0 0 0 0 0 0 0 0
-41.70 -66.70 -91.70 -116.70 -141.70 -166.70 -191.70 -216.70
139.75 139.75 139.75 139.75 139.75 139.75 139.75 139.75
-50 -75 -100 -125 -150 -175 -200 -225
145.80 145.80 145.80 145.80 145.80 145.80 145.80 145.80
95.80 70.80 45.80 20.80 -4.20 -29.20 -54.20 -79.20
200.00
Pay off from Short Strangle
150.00
100.00
50.00
Pay off
0.00 1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225 2250 2275
-50.00
-100.00
-150.00
Pay off from Short Straddle
Short Call 2050
Short Put 2100
Spot Price on expiry -200.00
-250.00
Long Strangle On 9th march when index was at 2160.80 ,if an investor buys 100 calls and 100 puts
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for January month with exercise price 2100 having an expiration date on 31st march, then the total cost to the investor will be:
Long Call Long Put Total cost
2100 2100
400.20 17.80 418
Index on expiration date Call Option Put Option Net payoff 2100 2100 2030.65 0 69.35 -348.65
Payoff from Long Spot Price Call 2100 1925 1950 1975 2000 2025 2050 2075 2100 0 0 0 0 0 0 0 0 Put 2100 175 150 125 100 75 50 25 0 Individual Payoff Long Call 2100 -400.20 -400.20 -400.20 -400.20 -400.20 -400.20 -400.20 -400.20 Long Put 2100 157.20 132.20 107.20 82.20 57.20 32.20 7.20 -17.80 175 150 125 100 75 50 25 0 418 418 418 418 418 418 418 418 -243 -268 -293 -318 -343 -368 -393 -418 Total Payoff Cost of Straddle Net Pay off
117
2125 2150 2175 2200 2225 2250 2275
25 50 75 100 125 150 175
0 0 0 0 0 0 0
-375.20 -350.20 -325.20 -300.20 -275.20 -250.20 -225.20
-17.80 -17.80 -17.80 -17.80 -17.80 -17.80 -17.80
25 50 75 100 125 150 175
418 418 418 418 418 418 418
-393 -368 -343 -318 -293 -268 -243
200
Long Straddle
100
Long Straddle Long Call 2100 Long Put 2100
0 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225 2250 2275
-100 Payoff -200 -300 -400
-500
Spot
Short Straddle On 6th May when index was at 1977.50, if an investor shorts 100 calls and 100 puts for May month with exercise price 2050 having an expiration date on 26th may, then the total
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credit to the investor will be:
Short Call Short Put Initial Credit
2050 2050
8.30 80.65 88.95 2074.70 -24.70 0.00 64.25
Position At expiration date. Short Call Short Put Net Position 2050 2050
Example: Short Stradle
On 6th May when index was at 1977.50, if an investor shorts 100 calls and 100 puts for May month with exercise price 2050 having an expiration date on 26th may, then the total credit to the investor will be:
Short Call Short Put Initial Credit
2050 2050
8.30 80.65 88.95 2074.70 -24.70 0.00 64.25
Position At expiration date. Short Call Short Put Net Position 2050 2050
119
loss from short
Individual Strategies
Total
Income from Net Pay
Spot Price
Call 2050
Put 2050 -175 -150 -125 -100 -75 -50 -25 0 0 0 0 0 0 0 0
Call 2050 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 -16.70 -41.70 -66.70 -91.70 -116.70 -141.70 -166.70
Put 2050 -94.35 -69.35 -44.35 -19.35 5.65 30.65 55.65 80.65 80.65 80.65 80.65 80.65 80.65 80.65 80.65
loss
straddle off
1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225
0 0 0 0 0 0 0 0 -25 -50 -75 -100 -125 -150 -175
-175 -150 -125 -100 -75 -50 -25 0 -25 -50 -75 -100 -125 -150 -175
88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95
-86.05 -61.05 -36.05 -11.05 13.95 38.95 63.95 88.95 63.95 38.95 13.95 -11.05 -36.05 -61.05 -86.05
120
150.00
Short Straddle
100.00
50.00
0.00 Pay off 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 -16.70 -41.70 -66.70 -91.70 -116.70 -141.70 -166.70
-50.00
-100.00
-150.00
Pay off from Short Straddle Call 2050 Put 2050
Spot Price on expiration -200.00
Volatility Spot Date Nifty Daily returns Date Spot Nifty Daily returns
2-Jan-06 2835.95 3-Jan-06 2883.35 4-Jan-06 2904.4 0.0166 0.0073 -0.0016 0.0049 -0.0013 -0.0136 -0.0070 -0.0001
21-Apr-06 24-Apr-06 25-Apr-06 26-Apr-06 27-Apr-06 28-Apr-06 29-Apr-06 2-May-06 3-May-06
3573.05 3548.9 3462.65 3555.75 3508.1 3508.35 3557.6 3605.45 3634.25
-0.0001 -0.0068 -0.0246 0.0265 -0.0135 0.0001 0.0139 0.0134 0.0080
5-Jan-06 2899.85 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 2914 2910.1 2870.8 2850.7
13-Jan-06 2850.55
121
16-Jan-06 17-Jan-06 18-Jan-06
2833.1 2829.1 2809.2
-0.0061 -0.0014 -0.0071 0.0217 0.0104 -0.0058 0.0083 0.0111 0.0143 -0.0028 0.0089 -0.0099 -0.0014 -0.0091 0.0201 0.0065 -0.0037 0.0062 0.0045 -0.0078 0.0015 -0.0002 -0.0134 0.0081
4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06
3648.4 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.3 3635.1 3388.9 3246.9 3081.35 3199.35 3115.55 3177.7 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3
0.0039 0.0043 0.0079 0.0074 0.0090 -0.0143 -0.0139 -0.0411 0.0058 0.0312 -0.0701 -0.0428 -0.0523 0.0376 -0.0265 0.0198 0.0100 0.0016 -0.0092 -0.0365 -0.0361 0.0427 -0.0245 -0.0267
19-Jan-06 2870.85 20-Jan-06 2900.95 23-Jan-06 2884.05 24-Jan-06 2908
25-Jan-06 2940.35 27-Jan-06 2982.75 30-Jan-06 31-Jan-06 2974.5 3001.1
1-Feb-06 2971.55 2-Feb-06 2967.45 3-Feb-06 2940.6
6-Feb-06 3000.45 7-Feb-06 3020.1
8-Feb-06 3008.95 10-Feb-06 3027.55 13-Feb-06 3041.15 14-Feb-06 3017.55 15-Feb-06 16-Feb-06 17-Feb-06 3022.2 3021.6 2981.5
20-Feb-06 3005.85
122
21-Feb-06 22-Feb-06 23-Feb-06
3035.5 3050.8 3062.1
0.0098 0.0050 0.0037 -0.0039 0.0057 0.0024 0.0156 0.0088 -0.0011 0.0136 -0.0024 -0.0210 0.0040 0.0174 0.0059 -0.0023 0.0097 0.0023 0.0097 -0.0010 -0.0068 0.0022 0.0100 0.0127
7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06
2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85
-0.0265 -0.0487 0.0508 -0.0317 -0.0418 -0.0115 0.0611 0.0322 0.0091 -0.0192 0.0215 0.0241 0.0159 0.0025 -0.0357 0.0132 -0.0005 0.0056 0.0425 0.0072 -0.0039 0.0185 -0.0128 -0.0259
24-Feb-06 3050.05 27-Feb-06 3067.45 28-Feb-06 1-Mar-06 2-Mar-06 3074.7 3123.1 3150.7
3-Mar-06 3147.35 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 3190.4 3182.8 3116.7 3129.1 3183.9
13-Mar-06 3202.65 14-Mar-06 3195.35 16-Mar-06 3226.6
17-Mar-06 3234.05 20-Mar-06 3265.65 21-Mar-06 3262.3
22-Mar-06 3240.15 23-Mar-06 3247.15 24-Mar-06 3279.8
27-Mar-06 3321.65
123
28-Mar-06 29-Mar-06
3325 3354.2
0.0010 0.0087 0.0191 -0.0048 0.0206 0.0028 0.0079 -0.0161 0.0068 -0.0287 -0.0103 0.0235 0.0268 0.0050 0.0106
10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
0.0213 -0.0083 0.0253 -0.0084 -0.0146 -0.0378 -0.0046 -0.0206 0.0303 -0.0262 0.0138 0.0181 0.0226 0.0147
30-Mar-06 3418.95 31-Mar-06 3402.55 3-Apr-06 3473.3
4-Apr-06 3483.15 5-Apr-06 7-Apr-06 3510.9 3454.8
10-Apr-06 3478.45 12-Apr-06 13-Apr-06 3380 3345.5
17-Apr-06 3425.15 18-Apr-06 3518.1
19-Apr-06 3535.85 20-Apr-06 3573.5
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CALCULATION OF HISTORICAL VOLATILITY: Standard deveation of daily Historical Volatility = No of Days return * ? No of days 252 Trading days
Average NIFTY
3119.44
STANDARD DEVEATION
210.85
Average daily returns
0.003256
Annual Returns
82.05%
Standard deveation of daily return
0.010450
Historical Volatility
16.52%
Calculation of Implied Volatility
Input Variables: Stock Price Exercise Price 2724.35 3000.00
125
Current date Expiration date Risk free Interest rate Dividend yield
8-Jun-06 29-Jun-06 5.00% 2.00%
Time
0.057534247 years Call 39.95 Put 335.35
Theorotical Price of Stock Option
Parameters of Option Delta Gamma Theta Vega Rho
Call 0.2276 0.00094 -856.45 197.10 -33.37
Put -0.7713 0.00094 -761.30 197.10 -138.74
Actual Option Price
39.95
335.35
Implied Volatility of Call Implied Volatility of Put
49.03% 61.04%
126
In order to Calculate Implied Volatility of Call and Put Option when all other inputs of the Black scholes model are given, we can do it by solving using Corrado Miller Approach or Newton Raphson Technique. The Implied Volatility for Call and Put Option obtained is 47.03% and 53.07% when strike price is 20 for Stock selling at 17.5 having Call Price in Market at 3.5 and Put price as 0.85.
127
OBJECTIVE BEHIND THE RESEARCH:
Investment Decision Making Factors in STOCK & DERIVATIVE form of Investment:
1) To determine the important macro-economic factors that determines the investment decision. 2) To find out which of the important factors influence investor to choose a particular company and particular sector while making investment decisions. 3) Cluster the respondents according to their according to the factors that determine their investment decisions. 4) To construct a perceptual map to find out the perception of each sector according to various factors. 5) To find out the investment behavior of respondents (speculative, long term, hedger or arbitrager) using discriminant analysis. 6) To determine the most ideal strategy considered by investors and brokers • • When market is bullish When market is bearish
7) To find out which option strategy can command the maximum premium.
SAMPLE SIZE: 30 respondents.
128
EXECUTIVE SUMMARY: The objective of this research is to determine the factors that determine the investing decision for an investor for a particular Company as well as particular firm. It also determines the perception of some of the industrial sectors based on the attributes give by the respondents. In addition to that the investors have been segregated based on the cluster analysis into groups so that investors can be segregated into groups for better understanding the motives for investment. Through Discriminate analysis, the behavior of investors is predicted so that investors could be classified into various groups based on their investing activity by getting score on the factors that they consider while investing in a stock. The research also determines the most optimal strategy while investing in Options through use of Conjoint analysis for both the market conditions (Bullish and Bearish.)
ADVANCE STATISTICAL METHODS:
129
Research Area Research Problem:
: Stocks and Derivatives.
Forecasting the future stock trends based on past movements.
Parameters reflecting on Index or Stock Movement
1. Financial performance of Company. 2. Daily volumes (Transactions of particular stock). 3. Exchange rate movement. 4. GDP growth rate. 5. Interest rate movements. 6. FII inflows and outflows. 7. Volatility. 8. Inflation. 9. Dividends, Bonus shares, right issue, and IPO’s. Analyzing the impact of the above macro-economic variables on sector performance. Clustering of Shares based on their annualized returns and determination of cause of inter-relationship between shares within each groups and explanation of inter and intra group effects.
Analyzing the impact of spot price on Future’s and Option price. Determination of inter-relationship between theoretical Call and Put price (using Black-Scholes pricing model) with actual market price of Call and Put.
130
Call Option and Put Option are influenced by the following 5 factors (Black- Schloes pricing model). Analyzing how much each of the factor is actually reflected in the Option Price. 1. Spot price. 2. Exercise price. 3. Volatility. 4. Time to expiry. 5. Interest rate.
131
EXHIBIT 1: Age profile of respondents
50
40
30
20
10
Percent
0 <24 24-35 36-45 >45
Age
Age Cumulative Percent 23.3 66.7 83.3 100.0
Valid
<24 24-35 36-45 >45 Total
Frequency 7 13 5 5 30
Percent 23.3 43.3 16.7 16.7 100.0
Valid Percent 23.3 43.3 16.7 16.7 100.0
132
Income Profile:
50
40
30
20
10
Percent
0 <3,00,000 6,00,000-10,00,000 3,00,000-6,00,000 >10,00,000
Income
Income Cumulative Percent 26.7 70.0 90.0 100.0
Valid
<3,00,000 3,00,000-6,00,000 6,00,000-10,00,000 >10,00,000 Total
Frequency 8 13 6 3 30
Percent 26.7 43.3 20.0 10.0 100.0
Valid Percent 26.7 43.3 20.0 10.0 100.0
133
40
30
20
10
Percent
0 50,000 1,50,000-3,00,000 50,000-1,50,000 3,00,000-7,00,000
Yearly volume
Yearly volume Cumulative Percent 26.7 63.3 90.0 100.0
Valid
50,000 50,000-1,50,000 1,50,000-3,00,000 3,00,000-7,00,000 Total
Frequency 8 11 8 3 30
Percent 26.7 36.7 26.7 10.0 100.0
Valid Percent 26.7 36.7 26.7 10.0 100.0
40
30
20
10
Percent
0 < 50,000 1,50,000-3,00,000 7,00,000=10,00,000 >10,00,000 50,000-1,50,000 3,00,000-7,00,000
Portfolio
134
Portfolio Cumulative Percent 3.3 16.7 46.7 73.3 90.0 100.0
Valid
< 50,000 50,000-1,50,000 1,50,000-3,00,000 3,00,000-7,00,000 7,00,000=10,00,000 >10,00,000 Total
Frequency 1 4 9 8 5 3 30
Percent 3.3 13.3 30.0 26.7 16.7 10.0 100.0
Valid Percent 3.3 13.3 30.0 26.7 16.7 10.0 100.0
Option
Spot
Futures
135
Arbitrage
Speculation
Hedging Long term investment
Motive for investment Cumulative Percent 20.0 46.7 80.0 100.0
Valid
Speculation Hedging Long term investment Arbitrage Total
Frequency 6 8 10 6 30
Percent 20.0 26.7 33.3 20.0 100.0
Valid Percent 20.0 26.7 33.3 20.0 100.0
136
Cluster Membership Case Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Cluster 3 2 3 2 3 3 3 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 Distance 5.316 3.929 4.481 4.054 2.314 2.795 6.134 4.823 3.502 3.410 5.734 3.942 2.968 5.334 4.207 4.484 3.401 3.656 2.763 3.826 4.021 3.711 5.601 5.413 7.557 4.806 3.221 3.373 6.616 4.677
137
STATISTICS FOR RESTONDENTS: For the purpose of research , a sample of 30 respondents were selected. Age Profile of respondents: Out of 30 respondents, 66.67% of them were under the age group of 35 and (20) and 10 respondents were above of the age 36 and above.
Income
profile of respondents: Of the 30,respondents were under the upper income
category 30% were with income category of Rs6,00,00 and above family income and 26.65 of them were under the income category of Rs3,00,00 and below. For the purpose of income, annual family income of the respondent was used to segregate them into the groups.
Investment Profile of Respondents: Most of the sample population studied for the purpose were actively trading in the stock market with 36.7% of sample size were having annual volume of transactions worth more than Rs1,50,000 an year and 36.65 of them had annual volume of transactions worth Rs50,00 to Rs 1,50,000. Only 26.75 of them traded thinly in the stock markets who had annual volume of transactions worth less than Rs50,000 an year.
83.4% of respondents had overall portfolio worth more than Rs3,00,00 invested in shares and futures over a period of time. Thus most of the respondents had invested huge amount of money in the shares market. Nature of respondents :33.335 of the sample size were long term investors ,20% speculators and arbitragers and 26.75 of them were hedgers. Thus the sample size was evenly distributed according to the nature of activity performed.
138
Trading instruments used: 46.75 of the sample size were active traders in the cash segment and 30% were actively involved in Options market.23.3% of them were primarily operating in the Futures segment.
Market awareness: Out of 30 respondents, 16 of them followed market on daily basis and only 4 of them followed on weekly basis. 10 respondents followed market on hourly basis. All the respondents who followed market on weekly basis were Long term investors and 83.35 of the arbitragers followed market on hourly basis.
Row and Column Points Symmetrical Normalization
1.0 .5 Speculation 0.0 Hourly Long term investment Motive for investmen weekly t How often makt follo -1.5 -1.5 -1.0 -.5 0.0 .5 1.0 1.5 2.0 wed -.5 Hedging Daily
Dimension 2
Arbitrage
-1.0
Dimension 1
The correspondence analysis conducted to get insight about the nature of investing activities and its relationship with following the market , concludes that Arbitragers follow market on Hourly basis, and long term investors follow market on less continuous basis. Most of the Hedgers and Speculators follow market on daily basis.
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Market and Motive for investment :
Row and Column Points Symmetrical Normalization
1.0 Option .5 Long term investment Spot 0.0 Speculation -.5
Dimension 2
Hedging Futures Motive for investmen t
-1.0
-1.5 -1.5 -1.0 -.5 0.0 .5 1.0 1.5
Actively traded
Dimension 1
As seen by the above results of the correspondence analysis between nature of investing activity and Market actively traded, we can conclude that Long term investors invest in Spot market ,Hedgers in Futures market and Arbitragers in Option market. Speculators are in someway mid between Spot , Future and Options market concludes the fact that they tend to take a favorable position in any of the market according to the situation. These results can further be validate by the empirical studies and nature of these investors as Futures are the primary tool for taking hedged positions in order to minimize their overall risk of the portfolio. Also Long term investors operate in spot market as in India in Futures and Options market an investor can take a position only for maximum of 90 days which makes them short term investors.
140
Actively traded * Motive for investment Crosstabulation Count Motive for investment Long term Hedging investment 1 10 4 3 8 10
Actively traded Total
Spot Futures Option
Speculation 3 2 1 6
Arbitrage 1 5 6
Total 14 7 9 30
How often makt followed Count
How often makt followed Total
Hourly Daily weekly
Speculation 3 3
6
7
6
5
4
3
Motive for investmen
Speculation Hedging
2
1
C ount
Long term investment Arbitrage Hourly Daily w eekly
0
How often makt followed
Important Factors Determination While Choosing a Stock
FACTOR ANALYSIS In order to determine the important factors that investors consider while choosing a particular company over other provided three most important factors that together explained 77.935 of the total variance. 141
Total Variance Explained Initial Eigenvalues xtraction Sums of Squared Loading Rotation Sums of Squared Loadings Componen Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative % 1 5.387 53.866 53.866 5.387 53.866 53.866 3.213 32.133 32.133 2 1.388 13.883 67.749 1.388 13.883 67.749 2.526 25.263 57.395 3 1.018 10.181 77.930 1.018 10.181 77.930 2.053 20.534 77.930 4 .688 6.875 84.805 5 .510 5.098 89.903 6 .405 4.046 93.949 7 .220 2.204 96.154 8 .206 2.064 98.217 9 .131 1.312 99.530 10 704E-02 .470 100.000 Extraction Method: Principal Component Analysis.
Scree Plot
6
5
4
3
2
Eigenvalue
1
0 1 2 3 4 5 6 7 8 9 10
Component Number
142
Component Score Coefficient Matrix Component 2 -.121 -.088 .269 .360 .014 .217 .572 .240 .066 .201
1 Company Brand Name Sector of company Profits Dividends Mkt scenario Mkt share Promoters Management News Future price .068 .085 .103 .058 .303 .351 .203 .069 .361 .368
3 .496 .496 .150 -.008 .112 -.046 -.214 .159 .182 -.016
Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. Component Scores.
Three factors are identified based on Eigen Values one, are as follows:
Factor One:
Market Scenario, Market Share, News about the company and the price of
Company’s share in the Futures Market.
Factor two: Profits, Dividends, Promoters goodwill, Management.
Factor three: Company Brand name, Sector of the company,.
Factor 1 is termed as Current Market scenario that explains 32.13% of the variance, Factor 2 as Company’s profitability and goodwill that explains 25.62% of the variance and Factor 3 is named as Company’s reputation and sector which explains 20.53% of the variance. Thus the important factors that determine an investors decision to invest in a particular stock are :
143
Current Market Scenario. Company’s Profitability. Company’s reputation and sector.
Factors Determining Investors Investment Decision (Macro economic factors that are taken into account before investing)
FACTOR ANALYSIS TO DETERMINE THE MOST IMPORTANT FACTORS THAT DETERMINE THE INVESTMENT DECISION: ( Macro level decisions)
KMO and Bartlett's Test Kaiser-Meyer-Olkin Measure of Sampling Adequacy. Bartlett's Test of Sphericity Approx. Chi-Square df Sig. .439 172.576 105 .000
Validity of test: Bartlett’s test of Sphericity indicates whether correlation matrix is an identity matrix, which would indicate that our variables are unrelated. Since the sig level is less than .05, it indicates that there are probably significant relationships among variables. Thus, Bartlett’s Test of Significance shows that our data is suitable for Factor analysis.
144
Total Variance Explained Initial Eigenvalues % of Variance Cumulative % 22.449 22.449 15.339 37.788 13.286 51.074 9.358 60.432 8.610 69.042 6.887 75.929 5.931 81.860 4.500 86.360 3.945 90.305 3.311 93.617 2.303 95.920 1.715 97.635 1.213 98.848 .711 99.560 .440 100.000 Extraction Sums of Squared Loadings Total % of Variance Cumulative % 3.367 22.449 22.449 2.301 15.339 37.788 1.993 13.286 51.074 1.404 9.358 60.432 Rotation Sums of Squared Loadings Total % of Variance Cumulative % 3.268 21.784 21.784 2.200 14.664 36.449 2.013 13.420 49.869 1.585 10.563 60.432
Component Total 1 3.367 2 2.301 3 1.993 4 1.404 5 1.291 6 1.033 7 .890 8 .675 9 .592 10 .497 11 .346 12 .257 13 .182 14 .107 15 6.604E-02
Extraction Method: Principal Component Analysis.
Scree Plot
4
3
2
Eigenvalue
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Component Number
145
Rotated Component Matrix
a
Component Bullish teand Bearish treand sensex movements Political factors- Internal Poliical factors -External Monsoon Sports Festival Govy policy statments RBI statments Interest rates FII movments Exchange rate Inflation rate Bank rate 1 -1.73E-02 -.156 -8.67E-02 .838 .815 -4.58E-02 .103 -.100 .891 .739 -1.19E-03 .219 .329 -.211 .553 2 -3.73E-02 .632 .637 -5.19E-02 -5.55E-02 .299 .157 -.172 -2.47E-02 -2.97E-02 .652 .763 -.215 .311 .306 3 .770 -8.53E-02 .307 -.208 .166 -1.63E-02 .667 -3.96E-02 -6.09E-02 .177 -7.48E-02 -9.07E-03 -.596 -.565 -.293 4 -9.30E-02 .209 -.210 1.214E-02 4.991E-02 .587 .559 .777 -.165 -.190 .207 -.141 -.170 .206 .170
Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 6 iterations.
The above analysis tells that there are four factors that have been identified to be significant while deciding the investment decision:
Factor one: Political Factors: (Political (Internal), Political (External), Government policy, RBI Statements, Bank rate.) which explains 21,74% of the variance, Factor two: Market Indicators (Bearish trend, Sensex movements, FII Movements. Interest rates) which explains 15.34% of the variance. Factor three: Economic Indicators: Bullish, Exchange rate, Inflation rate, which explains 13,26% of the variance. Factor four: External and Uncontrollable Factors: Monsoon, Sports, festival, which explains 9.36% of the total variance.
Overall these four factors explain 60.43% of the total variance.
146
Thus based on the above two tests we can conclude following factors explain the overall investing decision while investing in general and investing in a particular company.
147
CLUSTER ANALYSIS: CLUSTER ANALYSIS OF RESPONDENTS BASED ON THE FACTORS THAT THEY CONSIDER IMPORTANT WHILE INVESTING IN SHARE OF A PARTICULAR COMPANY.
Agglomeration Schedule Stage Cluster First Appears Cluster 1 Cluster 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 6 0 4 0 7 1 0 0 3 0 8 0 9 11 10 5 0 0 0 14 0 0 12 0 0 13 17 0 15 0 18 0 21 19 22 16 20 23 25 24 27 0 26 28
Stage 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Cluster Combined Cluster 1 Cluster 2 17 18 5 13 20 27 16 21 3 9 5 6 2 15 5 10 16 19 2 17 22 26 20 28 5 12 16 22 2 3 23 25 4 16 7 8 20 30 1 5 4 29 2 24 7 14 4 20 2 23 1 7 2 4 2 11 1 2
Coefficients 3.000 6.000 10.000 11.000 12.000 13.000 14.000 16.667 17.500 17.500 18.000 20.000 23.000 24.333 27.750 28.000 29.400 30.000 38.000 38.000 39.167 41.833 47.000 50.786 52.143 53.333 71.768 103.550 124.947
Next Stage 10 6 12 9 15 8 10 13 14 15 14 19 20 17 22 25 21 23 24 26 24 25 26 27 27 29 28 29 0
Since there is sudden jump in the co-efficient , from 71.78 to 103.55, there are three cluster solution.
148
The three cluster analysis by using K-means Cluster show the following results.
The cluster analysis using K-means cluster for three clusters show that there are significant difference between the distances between the three clusters and number of cases in each cluster is 30.
Final Cluster Centers Cluster 2 6.80 5.60 3.40 2.20 8.80 7.70 3.80 3.00 8.50 8.40
1 Company Brand Name Sector of company Profits Dividends Mkt scenario Mkt share Promoters Management News Future price 8.30 6.60 7.50 8.00 5.10 5.70 6.90 8.20 5.20 4.90
3 6.60 6.70 5.80 5.70 7.30 6.40 4.80 4.90 7.30 7.40
Distances between Final Cluster Centers Cluster 1 2 3 1 11.453 6.509 2 11.453 5.500 3 6.509 5.500
149
Number of Cases in each Cluster Cluster 1 2 3 4.000 15.000 11.000 30.000 .000
Valid Missing
Cluster Membership for each case The cluster analysis using K-means cluster for three clusters show that there are significant difference between the distances between the three clusters and number of cases in each cluster is 30.
THE RESPONDENT’S CHARACTERISTICS FOR THE CLUSTERS: Cluster one: The means for cluster one is maximum for these variables which show that for them Brand name, profits, Dividends, Promoters, and Management matter most while investing in shares. Respondent’s in cluster one tend to invest in mostly known companies who have reputable image in the public domain. Cluster two: The mean for cluster three is maximum for the variables Market scenario, Market share of the company, News and Price of stocks’ share in Futures market. This means that these investors take into account the current market situations as the most important variable while investing in shares of a particular company. Cluster three:
150
Respondents in cluster three-show average mean of 5-6 in all the variables, these investors are mostly cautious investors who take into account all the relevant factors while investing in shares.
151
PERCEPUAL MAPPING: BASED ON FACTOR SCORES: In order to get the perceptual map of different sectors based on the attributes, the mean score for each sector on different attributes was identified and factor analysis for these attributes was generated which resulted in two significant factors. Factor 1: Consistency, Profitability, Volume, and Growth - Returns Factor 2: Volatility and risk - Risk
Sector Auto Bank Cement Communication Construction Electronic FMCG Hotel Oil Pharma Power Technology
Consistency 5.77 7.27 4.33 4.97 3.97 6.07 6.13 4.67 7.7 6.23 4.87 5.3
Profitability 5.3 7.43 5.33 6.13 3.6 7.37 5.9 2.8 7.43 7.2 5.53 6.13
Volume 4.1 7.57 5.03 5.8 3.37 5.27 6.2 2.7 7.77 6.03 4.97 4.73
Growth 5.9 7.7 3.73 7.3 3.9 6.57 5.1 4.67 7.23 7.53 5.87 7.43
Volatility 3.87 5.83 4.43 6.17 5.6 6.07 4.3 6.3 4.17 6.63 5.73 5.9
Risk 4.6 4.03 4.1 5.7 4.8 5.2 4.57 6.3 5.67 6.93 4.7 6.9
fac1_1 -0.23938 1.409 -0.79594 0.15501 -1.56996 0.45415 0.21144 -1.59812 1.54364 0.72216 -0.34993 0.05794
fac2_1 -1.07003 -0.40675 -1.38829 0.79603 -0.26009 0.34647 -1.19855 0.96915 -0.5913 1.56529 -0.0877 1.32577
152
Rotated Component Matrix Component 1 Consistency Profitability Volume Growth Volatility Risk .920 .945 .933 .822 -8.74E-02 3.902E-02
a
2 -9.08E-02 3.453E-02 -.181 .486 .868 .873
Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 3 iterations.
These factors were plotted in the two dimensional scale to get the perceptual map on the above two dimensions.
2.0 Oil 1.5 Bank
1.0 .5 FMCG 0.0 Auto Electronic
Pharma
Communication Technology Power
-.5 Cement -1.0 Construction Hotel
Return
-1.5 -2.0 -1.5 -1.0
-.5
0.0
.5
1.0
1.5
2.0
Risk
153
INTERPRETATION OF THE PERCEPTUAL MAP: Dimensions for the perceptual map are Risk and Return. Following sectors are associated with high risk and high returns- Electronic, Communication, Technology, and Pharma. Hotel industry is the only sector that has highest risk and lowest returns. Cement, Automobile, Power, and Construction are the sectors that are perceived to have low risk and low returns and are more suitable for investors who have less risk appetite. Oil and Banking sector are the industries that are the least risky and provide the highest returns.
MULTI-DIMENSIONAL SCALING: Multi-dimensional scaling for each of the sectors, based on the Euclidean Distance Method provide similar results as obtained using the factor scores.
154
Derived Stimulus Configuration Euclidean distance model
1.5 cement 1.0 oil banking .5 fmcg automobile construction power 0.0 electronic communication pharma -1.0 -1.5 -2 -1 0 1 2 3 hotel technology
Dimension 2
-.5
Dimension 1
155
Derived Stimulus Configuration Euclidean distance model
1.5 cement volume fmcg consistency oil .5 banking automobile profitability construction 0.0 power electronic volatility communication growth pharma -1.0 -3 -2 -1 0 1 2 technology hotel 3 risk
1.0
Dimension 2
-.5
Dimension 1
Multidimensional scaling for different industrial sectors based on the six attributes is presented in the above two charts. These show the relative position of various industrial sector based on different attributes. The results of Multi-Dimensional scaling is summarized as follows:
Pharma, technology, Electronic and Communication industries stocks are perceived similar. Oil and Banking companies stock are perceived as similar in attributes. Automobile, Power, Construction and Cement are perceived similarly.
156
Oil and Banking sector are considered to be the most Profitable sector. Pharma, technology, Electronic and Communication industries are considered to be the most growth oriented sector . FMCG stocks are considered to be most consistent in returns and have highest volumes in turnover in the market thereby providing most liquidity. Hotel industries stock are considered to be the least profitable and most dissimilar among the above mentioned sectors and are least favorable for investing.
CONJOINT ANALYSIS: For determining the most Optimal Strategy while choosing Option when the market is Bullish, In order to determine the most Optimum Strategy while choosing Options, respondents were given 9 combinations of strategy to choose from.
These combination were developed after conducting fractional factorial Orthogonal design.
The strategies were combination of four factors as follows: Strategy : Long Call or Short Put ( 2 levels) (Since under Bullish trend, a rational investor will only opt for Long call or short put and under Bearish scenario , he will opt for Short Call or Long Put) Premium( 3 levels) : In the money Option (In the money Options have Highest Premium), At the Money Option and Out of money Option (These kinds of Options have lowest premium). Time( 3 levels): Near month option, Next month Option and Far month Option.(Currently in India an Investor has only three dated options to choose from- one which expires on current
157
month, those which expire next month and those which expire tow months later called as Far month) Symbol (2 levels) : Index Option( European Option) and Stock Option.( American Option).
158
Conjoint Result
Summary Utilities
.1
0.0
Utility
-.1 Call put
STRATEGY
Summary Utilities
3
2
1
0
-1
-2
Utility
-3 in the money at the money out of the money
PREMIUM
159
Summary Utilities
1.5
1.0
.5
0.0
-.5
-1.0
Utility
-1.5 near month next month far month
TIME
Summary Utilities
.4
.2
0.0
-.2
Utility
-.4 stock index
SYMBOL
160
Importance summary
70 60
50
40
30
20
Importance
10 0 STRATEGY PREMIUM TIME SYMBOL
Factor
Based on the Utilities score for each variable we can conclude that , under Bullish Trend investors favor the following :
Put option over Call Option. In the money option , At the money Option and Out of the money option.( In the money options are the least risky )
Near month option over next month and far month. (Due to uncerainity in the future trend investors prefer option that expires in the immediate month as their expectations of market may not hold true for long period of time.)
Index Option as compared to Stock Option. (Index option are better representative of overall market scenario.) Thus the most optimal strategy based on the utility scores is :
161
In the money – Index Put Option that expires on near month.
Most important criteria while determining an Option is the Premium which is to be paid for the option. Next most important factor is the time and symbol and the least important variable is the kind of Option that will be purchased (Long call or short put) as both of them provide returns if the market actually turns bullish.
CONJOINT ANALYSIS: When Market is Bearish In order to determine the most optimal strategy while selecting a Option , respondents were given 9 combinations of strategies that were developed after Orthogonal Design of four factors. Symbol ( 2 levels): Index Option and Stock Option Strategy (2 levels): Long Put and Short Call Premium (3 levels) : In the money Option, At the money option and Out of money Option Time (3 levels) : Near month, next month and Far month.
162
Summary Utilities
.3
.2
.1
-.0
-.1
-.2
Utility
-.3 Short Calll Long Put
STRATEGY
Summary Utilities
1.0
.5
0.0
-.5
-1.0
Utility
-1.5 In the Money At the Money Out of the Money
PREMIUM
163
Summary Utilities
.6
.4
.2
0.0
-.2
Utility
-.4 Near Month Next Month Far Month
TIME
Importance summary
60
50
40
30
20
Importance
10
0 STRATEGY SYMBOL PREMIUM TIME
Factor
164
Interpretation of the results : Based on the utility score for each of the above factors the following results emerge out.
Long Put has higher utility when compared to Short Put. In the money option has more utility when compared to out of money and at the money option. Index option is preferred over Stock Option and while deciding the time period of Option, Next month option is more preferred when compared to near month and far month. Thus on the basis of the above analysis, the most optimal strategy while choosing an Option is Index In the money Put Option which expires on next month.
The most important factor that is used while deciding a particular option strategy is Premium followed by time and symbol and the least most factor is the kind of Option and Long Put ). ………………………………………………………………………………………….. ( Short Call
165
Annexure The annexure which has been prepared for this particular report required high involvement of excel sheets, where in I had to use huge data, then I had to apply complex formulas, where in if I would have given these annexure in my report, the formulas would not have made any sense.
So all the annexure, I am putting it separately on a C.D., if you wish you can have a look at it.
The primary research which was done for this particular report, I am enclosing the questionnaire prepared.
166
Questionnaire.
1) How often do you follow market?
o o o o o o o o o
Hour by hour basis Daily basis Weekly basis
4) In which of the following are do you actively traded in? Spot market Futures Option
6) What is your primary motive behind investment? Speculation Hedging Long term investment
7) Please rate the following factors on a scale of one to seven, which you consider important while investing in a stock for a particular company?
1) Company brand name 2) Industrial Sector of the company 3) Profitability of Company 4) Dividends paid by the company 5) Current market scenario 6) Market share of company 7) Promoter’s goodwill
1
2
3
4
5
6
7 8 9 10
167
8) Management strength 9) News about the company 10) Price in futures market for company 8) Please rate each of the following factors on a scale of one to ten, which decide/influence your investment decision?
1) Bullish trend 2) Bearish tread 3) BSE /NSE Sensex 4) Political factors Indian External
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
10 10 10
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
5) Non-Political factors Monsoon Sports news Festivals 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10
6) Govt Policy 7) RBI statements 8) Interest rate scenario 9) FII Movements 10) Exchange rate Movements 11) Inflation
1
2
3
4
5
6
7
8
9
10
168
12) Bank rate
1
2
3
4
5
6
7
8
9
10
9) Please, rate each of the following sectors on a scale of one to ten in order of attractiveness for the following factors.
Sector/Attractiveness Consistency
Profit ability
Volumes
Growth
Volatility
risk
Auto Banking Cement Communication Construction Electronic FMCG Hotel Oil Pharmaceuticals Power Technology
10) Please rank the following sectors of stock that you consider as the most promising for the “next six months”?
o Auto
169
o Banking o Cements o Communication o Construction o Electronic o FMCG o Hotel o Oil o Pharmaceuticals o Power o Technology/Software
11) While selecting a particular Option strategy please rank the particular strategy from one to nine? When outlook is -Bullish
Long call , index option,
in the money call,
next month
170
Long call , stock option, Short put, stock option, Short put , index option, Long call , stock option, Long call , stock option, Long call , stock option, Short put , index option, Long call , index option ,
in the money call , in the money put, at the money put , at the money call , at the money call, out of the money call , out of the money put , out of the money call ,
near month far month near month next month far month near month next month far month
When outlook is –Bearish Short call , index option, Short call , stock option, Long Put, stock option, in the money call, in the money call , in the money put, at the money put , at the money call , at the money call, out of the money call , out of the money put , out of the money call , next month near month far month near month next month far month near month next month far month 2 3 8 1 5 6 7 4 9
Long Put , index option, Short call , stock option, Short call , stock option, Short call , stock option, Long Put , index option, Short call , index option ,
12) What is your annual family income?
o o o
<3,00,000 3,00,000-6,00,000 6,00,000-10,00,000 171
o o o o o o o o o
>10,00,000
13) Age less than 24 24-35 36-45 >45
2) What is your yearly volume of transactions? <1,50,000 Rs 1,50,000 – Rs 5,00,000 Rs 5,00,000 – Rs 10,00,000 >Rs 10,00,000
3) What is your overall portfolio of investments in trading at a particular point of time?
o o o o
<1,50,000 Rs 1,50,000 – Rs 5,00,000 Rs 5,00,000 – Rs 10,00,000 >Rs 10,00,000
172
Bibliography
John.C.Hull Shelden Nattenberg NSE Website
173
doc_485158224.pdf
IIPM
“A Report On Pricing and Technical Analysis of Derivatives”
THE INDIAN INSTITUTE OF PLANNING AND MANAGEMENT
EXECUTIVE SUMMARY
The emergence of Derivatives market especially Futures and Options can be traced back to the willingness of the risk adverse economic agents to guard against themselves against the fluctuations in the price of Underlying asset. Derivatives, whose price is determined by the price of underlying asset, generally do not cause any fluctuations in the price of underlying asset. But impact of any change in the price of underlying asset may cause swift change in the price of Derivatives instrument. This project concerns one of the core issues in DerivativesPricing of Derivatives and impact of change in price of underlying to the price of Futures and Option through scenario analysis , valuation of Option and Futures through appropriate mathematical models and comparison of actual market price with theoretical price and exploiting arbitrage opportunities when even there are any deviations in the pricing , past trend of Options and Futures market and daily movements in Nifty Spot , Nifty Futures and Options for the past three months.
Another important issue in Derivatives is the appropriate position to choose from plethora of series of Call options and Put Options on a single day and permutations and combinations of strategies along with various option positions can be daunting task. This project seeks to answer some of the questions regarding appropriate strategy to choose in order to maximize total payoff through technical analysis of the parameters of Option.
1
TABLE OF CONTENTS DERIVATIVES:....................................................................................................................... 6 FORWARD CONTRACT:...................................................................................................... 6 FUTURES CONTRACT: ........................................................................................................ 6
PAYOFFS FROM THE FORWARD CONTRACT: ........................................................................................................6
BASIS: ..................................................................................................................................... 16 BASIS RISK: .......................................................................................................................... 16 PRICING OF FUTURES: ..................................................................................................... 27
FUTURES PRICE CALCULATOR ................................................................................................................. 28
STRATEGY USING FUTURES: ......................................................................................... 30
ARBITRAGE OPPORTUNITIES:...................................................................................................................30 HAVE FUNDS- LEND THEM TO THE MARKET: .....................................................................................................30 HAVE SECURITIES –LEND THEM TO THE MARKET. .............................................................................................30
HEDGING: ............................................................................................................................. 31
SHORT HEDGE...............................................................................................................................................31 LONG HEDGE:................................................................................................................................................31 OPTIMAL HEDGE RATIO:....................................................................................................................................31
HEDGING USING INDEX FUTURES: .............................................................................. 32
LONG SECURITY/PORTFOLIO - SHORT FUTURES: ................................................................................................32 SHORT SECURITY –LONG FUTURES: ...................................................................................................................32
HEDGING STATERGIES:................................................................................................... 32
LONG PORTFOLIO - SHORT FUTURES ................................................................................................................33 SHORT PORTFOLIO- LONG FUTURES ..................................................................................................................34
LOSS ON FUTURES ............................................................................................................. 34 GAIN ON SPOT RANSACTION ......................................................................................... 34 RISK FREE INTEREST ....................................................................................................... 34 NET POSITION ..................................................................................................................... 34 VALUE OF PORTFOLIO .................................................................................................... 34 SPECULATION ..................................................................................................................... 35
BEARISH- SHORT FUTURES ................................................................................................................................35
PROFIT FORM FUTURES .................................................................................................. 35 FUTURE PRICE-SPOT PRICE * NUMBER OF CONTRACTS..................................... 35
BULLISH- LONG FUTURES .................................................................................................................................35
OPTIONS................................................................................................................................ 36
CALL OPTION : ..................................................................................................................................................36 PUT OPTION : ....................................................................................................................................................36 AMERICAN OPTION :..........................................................................................................................................36 EUROPEAN OPTION :..........................................................................................................................................36 POSITION IN OPTION: .........................................................................................................................................36 PAY OFF FROM OPTION:.....................................................................................................................................36
2
ADJUSTING OPTIONS TO SHARE SPLIT AND STOCK DIVIDENDS:..................... 36
SHARE SPLIT:.....................................................................................................................................................37 STOCK DIVIDENDS: ............................................................................................................................................37
TERMINOLOGY: ................................................................................................................. 37
PREMIUM : .........................................................................................................................................................37 INTRINSIC VALUE: .............................................................................................................................................37 TIME VALUE:.....................................................................................................................................................38 IN THE MONEY: ..................................................................................................................................................38 AT THE MONEY:.................................................................................................................................................38 OUT OF THE MONEY:..........................................................................................................................................38
FACTORS AFFECTING THE OPTION PRICES: ........................................................... 39
CALL OPTION:....................................................................................................................................................39 PUT OPTION: ......................................................................................................................................................39 TIME TO EXPIRATION .........................................................................................................................................39 VOLATILITY OF THE STOCK PRICE ......................................................................................................................39 RISK FREE RATE OF INTEREST ............................................................................................................................40 DIVIDENDS EXPECTED DURING THE LIFE OF ASSET ............................................................................................40
SCENARIO ANALYSIS........................................................................................................ 42
CHANGE IN DELTA TO CHANGE IN STOCK PRICE ...............................................................................................46 CHANGE IN GAMMA TO CHANGE IN STOCK PRICE .............................................................................................47 CHANGE IN RHO TO CHANGE IN STOCK PRICE ...................................................................................................48 CHANGE IN OPTION PRICE TO CHANGE IN VOLATILITY .....................................................................................50
LIMITS ON UPPER AND LOWER BOUND FOR OPTIONS: ....................................... 55
INTRINSIC VALUE OF AN OPTION:......................................................................................................................55
PUT CALL PARITY: ............................................................................................................ 56 PROPERTY DISTRIBUTION OF A STOCK PRICE: ..................................................... 58 PRICING OF OPTIONS ....................................................................................................... 60
BLACK SCHOLES MODEL:......................................................................................................................... 60 Value of Call Option: ...................................................................................................................................60 Value of Put : ...............................................................................................................................................61 BLACK SCHOLES MODEL ...........................................................................................................................61
TECHNICAL ANALYSIS OF OPTION PARAMETERS ................................................ 65
DELTA ...............................................................................................................................................................65 Hedge Ratio .................................................................................................................................................66 DELTA HEDGING STRATEGIES: ..........................................................................................................................73
GAMMA ................................................................................................................................. 75
MAKING PORTFOLIO GAMMA NEUTRAL ............................................................................................................75
ANALYSIS OF OPTION PARAMETERS: ........................................................................ 79
METHODOLOGY:................................................................................................................................................79 DELTA AND GAMMA:.........................................................................................................................................79
THETA :.................................................................................................................................. 80
VEGA (?) : .........................................................................................................................................................81 ANALYSIS OF VEGA OF CALL AND PUT OPTIONS ...............................................................................................84
RHO : ...................................................................................................................................... 85 ELASTICITY:........................................................................................................................ 85
3
COMPARISON OF THEORETICAL AND ACTUAL PRICE OF OPTION:................ 86
THEORETICAL EDGE FOR CALL................................................................................................................ 87
RELATIVE STRENGTH INDEX (RSI).............................................................................. 93
METHODOLOGY FOR RSI CALCULATION ...........................................................................................................99 INTERPRETATION ...............................................................................................................................................99
IMPLICATIONS FOR OPTION TRADERS...................................................................... 99 TRADING STRATEGY USING OPTIONS: .................................................................... 101
USING SINGLE OPTION AND THE STOCK: ......................................................................................................... 101 BULL SPREAD:................................................................................................................................................. 101 Bull Spread with Calls: .............................................................................................................................. 102 Bull spreads with Puts: .............................................................................................................................. 102 Bull spread with put ................................................................................................................................... 102 BULL SPREAD WITH CALL ..................................................................................................................... 104 BEAR SPREAD : ................................................................................................................................................ 106 Bear spread with Call : .............................................................................................................................. 106 Bear Spread with Put :............................................................................................................................... 106 VOLATILITY SPREAD: ...................................................................................................................................... 106 Back spread: .............................................................................................................................................. 107 Ratio Vertical Spread: ............................................................................................................................... 107 BUTTERFLY SPREAD: ....................................................................................................................................... 109 Long Butterfly : .......................................................................................................................................... 109 Short Butterfly:........................................................................................................................................... 109 STRADDLE : ..................................................................................................................................................... 109 STRANGLE: ...................................................................................................................................................... 110 CALENDAR SPREAD: ........................................................................................................................................ 112 DIAGONAL SPREAD :........................................................................................................................................ 112 STRAP : ............................................................................................................................................................ 112 STRIPS: ............................................................................................................................................................ 112 LONG STRANGLE ............................................................................................................................................. 112 SHORT STRANGLE............................................................................................................................................ 115 LONG STRANGLE ............................................................................................................................................. 116 SHORT STRADDLE............................................................................................................................................ 118
VOLATILITY ...................................................................................................................... 121 CALCULATION OF HISTORICAL VOLATILITY: ..................................................... 125 OBJECTIVE BEHIND THE RESEARCH: ...................................................................... 128 INVESTMENT DECISION MAKING FACTORS IN STOCK & DERIVATIVE FORM OF INVESTMENT:.................................................................................................................... 128
EXECUTIVE SUMMARY:............................................................................................................................ 129
ADVANCE STATISTICAL METHODS: ......................................................................... 129
PARAMETERS REFLECTING ON INDEX OR STOCK MOVEMENT.......................................................................... 130
MARKET AND MOTIVE FOR INVESTMENT : ........................................................... 140 IMPORTANT FACTORS DETERMINATION WHILE CHOOSING A STOCK ..... 141
FACTOR ANALYSIS .................................................................................................................................... 141
FACTORS DETERMINING INVESTORS INVESTMENT DECISION...................... 144 CLUSTER ANALYSIS:....................................................................................................... 148
THE RESPONDENT’S CHARACTERISTICS FOR THE CLUSTERS:....................................................... 150
4
PERCEPUAL MAPPING: .................................................................................................. 152 CONJOINT ANALYSIS: .................................................................................................... 157 CONJOINT RESULT.......................................................................................................... 159
CONJOINT ANALYSIS: WHEN MARKET IS BEARISH ................................................................................... 162 INTERPRETATION OF THE RESULTS :................................................................................................................. 165
ANNEXURE ......................................................................................................................... 166 BIBLIOGRAPHY ................................................................................................................ 173
5
Derivatives: Derivative is a financial instrument whose value depends upon the underlying instrument. Forward Contract: A Forward contract is an agreement between two parties to buy or sell an asset at a certain future time for certain price. In this, one of the parties assumes a Long Position and agrees to buy the underlying asset at certain specified future date and the other party assumes Short Position and agrees to see the asset on the same date for the same price. A forward contract is settled at Maturity and the holder of short position delivers the asset to the holder of the long position in return for a cash amount equal to the Delivery Price. Futures contract: Like a Forward Contract, a Futures Contract is an agreement between two parties to buy or sell an asset at certain future date price but Futures Contract unlike forward contract are traded on the exchange and are standardized. Contango: Where the price of a more distant delivery is greater than the price of the near month. Backwardation: Markets where near by delivery is trading at the premium to the more distinct months are said to be in Backwardation. Payoffs from the Forward Contract: Payoff from a Long Position in the Forward Contract: St-k Payoff from a Short Position in the Forward Contract: K- St K: Delivery Price. St : Spot Price.
6
Table: 1. FUTURE AND SPOT PRICES OF NIFTY S&P CNX NIFTY FUTURE DATE 2-Jan-06 3-Jan-06 4-Jan-06 5-Jan-06 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 13-Jan-06 16-Jan-06 17-Jan-06 18-Jan-06 19-Jan-06 20-Jan-06 23-Jan-06 24-Jan-06 SPOT 2835.95 2883.35 2904.40 2899.85 2914.00 2910.10 2870.80 2850.70 2850.55 2833.10 2829.10 2809.20 2870.85 2900.95 2884.05 2908.00 1 MONTH 2819.70 2868.85 2890.10 2883.90 2895.65 2893.45 2857.30 2831.40 2823.65 2821.15 2801.85 2797.00 2869.25 2897.55 2881.65 2906.25 2 MONTH 2813.70 2859.50 2882.40 2873.80 2886.85 2885.20 2849.50 2822.95 2812.40 2809.65 2794.55 2787.75 2858.55 2888.35 2866.35 2898.90 3 MONTH 2803.70 2849.00 2873.95 2867.25 2877.20 2878.50 2841.50 2815.20 2807.40 2801.65 2786.85 2783.90 2850.10 2882.00 2858.00 2891.75
7
25-Jan-06 27-Jan-06 30-Jan-06 31-Jan-06 1-Feb-06 2-Feb-06 3-Feb-06 6-Feb-06 7-Feb-06 8-Feb-06 10-Feb-06 13-Feb-06 14-Feb-06 15-Feb-06 16-Feb-06 17-Feb-06 20-Feb-06 21-Feb-06 22-Feb-06
2940.35 2982.75 2974.50 3001.10 2971.55 2967.45 2940.60 3000.45 3020.10 3008.95 3027.55 3041.15 3017.55 3022.20 3021.60 2981.50 3005.85 3035.50 3050.80
2941.95 2959.75 2957.25 2984.75 2963.05 2956.45 2921.80 2991.55 3004.15 2992.95 3021.10 3028.20 3009.15 3017.15 3013.85 2978.40 3010.10 3039.45 3056.85
2922.25 2978.55 2972.35 3002.25 2952.45 2947.70 2913.15 2981.35 2994.90 2983.10 3011.60 3018.40 3000.15 3007.60 3003.80 2968.55 2998.50 3033.60 3048.55
2913.05 2969.05 2963.80 2992.35 2950.45 2942.90 2906.10 2976.60 2988.90 2976.25 3001.95 3012.60 2993.80 2999.70 2995.65 2963.70 2990.30 3024.30 3039.85
8
23-Feb-06 24-Feb-06 27-Feb-06 28-Feb-06 1-Mar-06 2-Mar-06 3-Mar-06 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 13-Mar-06 14-Mar-06 16-Mar-06 17-Mar-06 20-Mar-06 21-Mar-06 22-Mar-06
3062.10 3050.05 3067.45 3074.70 3123.10 3150.70 3147.35 3190.40 3182.80 3116.70 3129.10 3183.90 3202.65 3195.35 3226.60 3234.05 3265.65 3262.30 3240.15
3064.40 3033.00 3039.30 3057.55 3101.75 3134.55 3137.60 3185.45 3167.35 3082.65 3113.85 3166.45 3180.85 3171.90 3205.00 3213.95 3251.70 3241.95 3227.25
3054.20 3044.10 3055.15 3071.05 3094.50 3131.25 3131.90 3179.50 3162.25 3081.95 3107.60 3160.90 3176.70 3167.40 3198.30 3208.85 3243.15 3234.45 3215.90
3046.20 3035.10 3047.30 3064.35 3085.15 3126.40 3124.00 3171.25 3153.75 3071.35 3100.35 3147.30 3168.90 3159.00 3188.10 3202.85 3238.05 3232.05 3212.85
9
23-Mar-06 24-Mar-06 27-Mar-06 28-Mar-06 29-Mar-06 30-Mar-06 31-Mar-06 3-Apr-06 4-Apr-06 5-Apr-06 7-Apr-06 10-Apr-06 12-Apr-06 13-Apr-06 17-Apr-06 18-Apr-06 19-Apr-06 20-Apr-06 21-Apr-06
3247.15 3279.80 3321.65 3325.00 3354.20 3418.95 3402.55 3473.30 3483.15 3510.90 3454.80 3478.45 3380.00 3345.50 3425.15 3518.10 3535.85 3573.50 3573.05
3239.25 3279.90 3326.45 3332.40 3364.90 3412.75 3392.40 3474.00 3489.70 3510.20 3458.15 3488.55 3387.00 3348.50 3424.65 3524.05 3546.65 3581.80 3583.90
3231.50 3271.35 3317.35 3324.45 3353.05 3394.05 3403.60 3463.15 3482.35 3503.90 3455.30 3477.50 3384.35 3343.30 3413.50 3518.45 3540.80 3574.75 3576.80
3229.90 3262.50 3310.65 3309.70 3344.30 3386.65 3396.85 3457.60 3475.05 3495.85 3452.80 3472.35 3383.95 3341.45 3411.80 3512.05 3536.80 3568.10 3571.75
10
24-Apr-06 25-Apr-06 26-Apr-06 27-Apr-06 28-Apr-06 29-Apr-06 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06
3548.90 3462.65 3555.75 3508.10 3508.35 3557.60 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90
3556.50 3465.50 3579.45 3508.80 3492.60 3523.70 3595.00 3612.40 3627.40 3644.10 3685.85 3712.95 3745.40 3692.90 3633.00 3462.05 3520.30 3641.25 3363.85
3549.75 3454.05 3562.50 3502.05 3497.60 3545.40 3585.80 3605.10 3620.35 3633.90 3676.80 3702.80 3729.50 3681.80 3620.90 3448.90 3509.15 3628.75 3350.95
3547.45 3451.25 3556.85 3493.25 3491.55 3533.75 3580.20 3595.05 3610.00 3624.35 3669.20 3692.10 3723.60 3677.25 3615.35 3440.05 3500.20 3619.85 3349.00
11
19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06
3246.90 3081.35 3199.35 3115.55 3177.70 3209.60 3214.90 3185.30 3071.05 2962.25 3091.35 3016.65 2937.30 2860.45 2724.35 2866.30 2776.85 2663.30 2632.80
3224.35 3020.90 3190.50 3087.25 3180.15 3171.95 3154.05 3097.00 3001.85 2889.90 3061.55 2957.30 2902.80 2838.05 2705.60 2831.25 2716.00 2629.15 2618.25
3209.40 2994.50 3155.10 3030.50 3112.65 3179.15 3175.00 3125.35 3032.40 2869.20 3039.60 2934.85 2868.25 2805.70 2673.65 2811.70 2686.45 2599.40 2594.80
3225.05 2973.25 3143.15 3024.80 3097.20 3164.85 3158.95 3108.60 3011.80 2864.90 3018.55 2914.20 2858.30 2790.20 2658.70 2782.20 2663.55 2585.05 2586.75
12
15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06
2798.80 2890.35 2916.90 2861.30 2923.45 2994.75 3042.70 3050.30 2943.20 2982.45 2981.10 2997.90 3128.20 3150.95 3138.65 3197.10 3156.40 3075.85 3142.00
2786.70 2880.75 2909.40 2839.35 2912.10 2982.25 3042.25 3043.90 2930.60 2981.10 2983.50 3003.00 3058.00 3130.30 3114.20 3170.10 3132.45 3039.45 3124.35
2760.40 2858.90 2886.05 2829.50 2891.15 2963.10 3017.25 3023.40 2902.10 2950.30 2951.40 2981.65 3118.10 3113.25 3095.35 3150.45 3111.65 3019.50 3102.90
2746.00 2840.65 2865.40 2794.85 2869.75 2938.40 3000.25 3006.80 2886.50 2929.05 2928.50 2967.40 3100.65 3097.65 3078.60 3138.65 3100.70 3006.50 3087.90
13
11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
3116.15 3195.90 3169.30 3123.35 3007.55 2993.65 2932.75 3023.05 2945.00 2985.85 3040.50 3110.15 3156.15
3094.55 3180.80 3142.70 3091.40 2980.95 2973.10 2909.95 3018.75 2937.60 2987.40 3039.45 3111.40 3153.50
3071.70 3158.45 3121.95 3069.35 2955.70 2947.60 2886.10 2993.45 2908.05 2954.20 3011.65 3085.45 3124.45
3055.10 3139.05 3104.70 3056.25 2949.60 2935.35 2875.75 2974.70 2892.95 2936.65 2992.90 3066.40 3103.95
14
3900.00
SPOT AND FORWARD NIFTY MOVEMENT
3700.00
3500.00
3300.00
Price
3100.00
2900.00
Nifty Spot 2 M th F t
2700.00
1 Month Future 3 M th F t
2500.00 1/16 1/30 2/13 2/27 3/13 3/27 4/10 4/24 5/22 6/19 Date 7/17 1/2 5/8 6/5 7/3
15
Basis: Basis is defined as Spot price minus the Futures Price. In the normal market, the basis will be negative, since the futures price normally exceed the spot price. In the inverted market, the basis will be positive. The basis will approach zero as the delivery period nears. At the close of trading on the delivery date Basis must be zero else, there will be arbitrage opportunity. If the Basis is positive on the expiration date then one can take short position in the futures contract and take delivery and sell it in the spot market and earn risk less profits. The process of basis moving towards zero is called as Convergence. Basis= Spot Price-Future price of the contract used. St-F. Strengthening of Basis: when the spot price increases by more than the futures price. Weakening of Basis: when Futures price increases more than the pot price.
Basis risk: An Individual who is having an un hedged position will face the price risk (i.e.) if the current spot price is S1 and the price that will be in future is S2 the price risk faced by such an investor will be S1- S2. An hedger exchanges Price risk for Basis risk. Suppose someone has hedged his stock by buying Futures then the risk faced by such an investor will be (S1-S2) –(F1-F2) = (S1-F1) – (S2-F2) = Basis 1- Basis 2
16
where Basis 1 is known but Basis 2 is unknown. Thus, an unhedged position will face Price risk but a Hedged position will face Basis risk. Table : 2. FUTURE& SPOT PRICES OF NIFTY
S&P CNX NIFTY CHANGES IN DATE SPOT SPOT RATE 1 MONTH 2 MONTH 3 MONTH BASIS
2-Jan-06 3-Jan-06 4-Jan-06 5-Jan-06 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 13-Jan-06 16-Jan-06 17-Jan-06 18-Jan-06 19-Jan-06 20-Jan-06
2835.95 2883.35 2904.40 2899.85 2914.00 2910.10 2870.80 2850.70 2850.55 2833.10 2829.10 2809.20 2870.85 2900.95 47.40 21.05 -4.55 14.15 -3.90 -39.30 -20.10 -0.15 -17.45 -4.00 -19.90 61.65 30.10
16.25 14.50 14.30 15.95 18.35 16.65 13.50 19.30 26.90 11.95 27.25 12.20 1.60 3.40
22.25 23.85 22.00 26.05 27.15 24.90 21.30 27.75 38.15 23.45 34.55 21.45 12.30 12.60
32.25 34.35 30.45 32.60 36.80 31.60 29.30 35.50 43.15 31.45 42.25 25.30 20.75 18.95
17
23-Jan-06 24-Jan-06 25-Jan-06 27-Jan-06 30-Jan-06 31-Jan-06 1-Feb-06 2-Feb-06 3-Feb-06 6-Feb-06 7-Feb-06 8-Feb-06 10-Feb-06 13-Feb-06 14-Feb-06 15-Feb-06 16-Feb-06 17-Feb-06 20-Feb-06
2884.05 2908.00 2940.35 2982.75 2974.50 3001.10 2971.55 2967.45 2940.60 3000.45 3020.10 3008.95 3027.55 3041.15 3017.55 3022.20 3021.60 2981.50 3005.85
-16.90 23.95 32.35 42.40 -8.25 26.60 -29.55 -4.10 -26.85 59.85 19.65 -11.15 18.60 13.60 -23.60 4.65 -0.60 -40.10 24.35
2.40 1.75 -1.60 23.00 17.25 16.35 8.50 11.00 18.80 8.90 15.95 16.00 6.45 12.95 8.40 5.05 7.75 3.10 -4.25
17.70 9.10 18.10 4.20 2.15 -1.15 19.10 19.75 27.45 19.10 25.20 25.85 15.95 22.75 17.40 14.60 17.80 12.95 7.35
26.05 16.25 27.30 13.70 10.70 8.75 21.10 24.55 34.50 23.85 31.20 32.70 25.60 28.55 23.75 22.50 25.95 17.80 15.55
18
21-Feb-06 22-Feb-06 23-Feb-06 24-Feb-06 27-Feb-06 28-Feb-06 1-Mar-06 2-Mar-06 3-Mar-06 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 13-Mar-06 14-Mar-06 16-Mar-06 17-Mar-06 20-Mar-06
3035.50 3050.80 3062.10 3050.05 3067.45 3074.70 3123.10 3150.70 3147.35 3190.40 3182.80 3116.70 3129.10 3183.90 3202.65 3195.35 3226.60 3234.05 3265.65
29.65 15.30 11.30 -12.05 17.40 7.25 48.40 27.60 -3.35 43.05 -7.60 -66.10 12.40 54.80 18.75 -7.30 31.25 7.45 31.60
-3.95 -6.05 -2.30 17.05 28.15 17.15 21.35 16.15 9.75 4.95 15.45 34.05 15.25 17.45 21.80 23.45 21.60 20.10 13.95
1.90 2.25 7.90 5.95 12.30 3.65 28.60 19.45 15.45 10.90 20.55 34.75 21.50 23.00 25.95 27.95 28.30 25.20 22.50
11.20 10.95 15.90 14.95 20.15 10.35 37.95 24.30 23.35 19.15 29.05 45.35 28.75 36.60 33.75 36.35 38.50 31.20 27.60
19
21-Mar-06 22-Mar-06 23-Mar-06 24-Mar-06 27-Mar-06 28-Mar-06 29-Mar-06 30-Mar-06 31-Mar-06 3-Apr-06 4-Apr-06 5-Apr-06 7-Apr-06 10-Apr-06 12-Apr-06 13-Apr-06 17-Apr-06 18-Apr-06 19-Apr-06
3262.30 3240.15 3247.15 3279.80 3321.65 3325.00 3354.20 3418.95 3402.55 3473.30 3483.15 3510.90 3454.80 3478.45 3380.00 3345.50 3425.15 3518.10 3535.85
-3.35 -22.15 7.00 32.65 41.85 3.35 29.20 64.75 -16.40 70.75 9.85 27.75 -56.10 23.65 -98.45 -34.50 79.65 92.95 17.75
20.35 12.90 7.90 -0.10 -4.80 -7.40 -10.70 6.20 10.15 -0.70 -6.55 0.70 -3.35 -10.10 -7.00 -3.00 0.50 -5.95 -10.80
27.85 24.25 15.65 8.45 4.30 0.55 1.15 24.90 -1.05 10.15 0.80 7.00 -0.50 0.95 -4.35 2.20 11.65 -0.35 -4.95
30.25 27.30 17.25 17.30 11.00 15.30 9.90 32.30 5.70 15.70 8.10 15.05 2.00 6.10 -3.95 4.05 13.35 6.05 -0.95
20
20-Apr-06 21-Apr-06 24-Apr-06 25-Apr-06 26-Apr-06 27-Apr-06 28-Apr-06 29-Apr-06 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06
3573.50 3573.05 3548.90 3462.65 3555.75 3508.10 3508.35 3557.60 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30
37.65 -0.45 -24.15 -86.25 93.10 -47.65 0.25 49.25 47.85 28.80 14.15 15.55 29.20 27.40 33.70 -53.20 -51.00 -147.10 20.35
-8.30 -10.85 -7.60 -2.85 -23.70 -0.70 15.75 33.90 10.45 21.85 21.00 19.85 7.30 7.60 8.85 8.15 17.05 40.90 3.00
-1.25 -3.75 -0.85 8.60 -6.75 6.05 10.75 12.20 19.65 29.15 28.05 30.05 16.35 17.75 24.75 19.25 29.15 54.05 14.15
5.40 1.30 1.45 11.40 -1.10 14.85 16.80 23.85 25.25 39.20 38.40 39.60 23.95 28.45 30.65 23.80 34.70 62.90 23.10
21
17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06
3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.60 3214.90 3185.30 3071.05 2962.25 3091.35 3016.65 2937.30 2860.45 2724.35 2866.30 2776.85
111.80 -246.20 -142.00 -165.55 118.00 -83.80 62.15 31.90 5.30 -29.60 -114.25 -108.80 129.10 -74.70 -79.35 -76.85 -136.10 141.95 -89.45
-6.15 25.05 22.55 60.45 8.85 28.30 -2.45 37.65 60.85 88.30 69.20 72.35 29.80 59.35 34.50 22.40 18.75 35.05 60.85
6.35 37.95 37.50 86.85 44.25 85.05 65.05 30.45 39.90 59.95 38.65 93.05 51.75 81.80 69.05 54.75 50.70 54.60 90.40
15.25 39.90 21.85 108.10 56.20 90.75 80.50 44.75 55.95 76.70 59.25 97.35 72.80 102.45 79.00 70.25 65.65 84.10 113.30
22
13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06
2663.30 2632.80 2798.80 2890.35 2916.90 2861.30 2923.45 2994.75 3042.70 3050.30 2943.20 2982.45 2981.10 2997.90 3128.20 3150.95 3138.65 3197.10 3156.40
-113.55 -30.50 166.00 91.55 26.55 -55.60 62.15 71.30 47.95 7.60 -107.10 39.25 -1.35 16.80 130.30 22.75 -12.30 58.45 -40.70
34.15 14.55 12.10 9.60 7.50 21.95 11.35 12.50 0.45 6.40 12.60 1.35 -2.40 -5.10 70.20 20.65 24.45 27.00 23.95
63.90 38.00 38.40 31.45 30.85 31.80 32.30 31.65 25.45 26.90 41.10 32.15 29.70 16.25 10.10 37.70 43.30 46.65 44.75
78.25 46.05 52.80 49.70 51.50 66.45 53.70 56.35 42.45 43.50 56.70 53.40 52.60 30.50 27.55 53.30 60.05 58.45 55.70
23
7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
3075.85 3142.00 3116.15 3195.90 3169.30 3123.35 3007.55 2993.65 2932.75 3023.05 2945.00 2985.85 3040.50 3110.15 3156.15
-80.55 66.15 -25.85 79.75 -26.60 -45.95 -115.80 -13.90 -60.90 90.30 -78.05 40.85 54.65 69.65 46.00
36.40 17.65 21.60 15.10 26.60 31.95 26.60 20.55 22.80 4.30 7.40 -1.55 1.05 -1.25 2.65
56.35 39.10 44.45 37.45 47.35 54.00 51.85 46.05 46.65 29.60 36.95 31.65 28.85 24.70 31.70
69.35 54.10 61.05 56.85 64.60 67.10 57.95 58.30 57.00 48.35 52.05 49.20 47.60 43.75 52.20
Graph 1: Convergence of Spot and Future Price
24
Convergence of Spot and Future Price 3900.00
3700.00
3500.00
3300.00
3100.00
2900.00
2700.00
2500.00
3/ 27 6/ 19 6/ 5 7/ 3 2/ 13 2/ 27 3/ 13 1/ 16 1/ 30
DATE
100.00
BASIS 1 MONTH
80.00
60.00
40.00
20.00
0.00
1/ 16 2/ 13 3/ 13 4/ 10 1/ 30 2/ 27 3/ 27 4/ 24 5/ 22 6/ 19 7/ 17 1/ 2 5/ 8 6/ 5 7/ 3
-20.00
-40.00
DATE
BASIS 1 MONTH
7/ 17
4/ 10
4/ 24
5/ 8
5/ 22
1/ 2
Spot
Future
25
BASIS 2 MONTH 100.00
80.00
60.00
40.00
20.00
0.00
1/ 16 1/ 30 2/ 13 2/ 27 3/ 27 3/ 13 4/ 10 4/ 24 5/ 22 6/ 19 7/ 17 5/ 8 1/ 2 6/ 5 7/ 3
-20.00 DATE BASIS 2 MONTH
BASIS 3 MONTH 120.00
100.00
80.00
60.00
40.00
20.00
0.00
1/2
5/8
6/5
1/16
1/30
2/13
2/27
3/13
3/27
4/10
4/24
5/22
6/19
7/3
-20.00
DATE
BASIS 3 MONTH
7/17
26
Chart Title 3900.00
3700.00
3500.00
3300.00 PRICE 3100.00 2900.00 2700.00 2500.00 1/16 1/30 2/13 2/27 3/13 3/27 4/10 4/24 5/22 6/19 DATE
NIFTY SPOT Log. (NIFTY SPOT)
PRICING OF FUTURES: Relationship between continuous compounding and compounding m times per year. Rc= m In(1+Rm/m) Rm=m( e Rc/m- 1) Rc= Rate of Interest for Continuous Compounding Rm= Rate of Interest for Compounding m times a year. FORWARD CONTRACTS ON A SECURITY THAT PROVIDES NO INCOME. F= S er (T-t) FORWARD CONTRACT ON A SECURITY THAT PROVIDES A KNOWN CASH INCOME: F= (S-I) er (T-t)
7/17
1/2
5/8
6/5
7/3
27
Where I is the present value of all cash incomes discounted at risk free rate of interest r. FORWARD CONTRACT ON A SECURITY THAT PROVIDES A KNOWN DIVIDEND YIELD: F= S e (r –q)(T-t)
FUTURES PRICE CALCULATOR INPUTS Current date Spot Price Risk free interest Annualised dividend yield Expiration date Days to expire Time in years Future Price Theototical Future Price INPUTS Current date 2-May-06 2-May-06 3605.45 4.00% 1.50% 31-May-06 29 days 0.079452055 F=S .e(r-q)t 3612.62
28
Spot Price Risk free interest Future Price Expiration date Days to expire Time in years
3605.45 4% 3612.62 31-May-06 29 0.079452055
Annualised Dividend Yield
Q=r-[In(F/S)]/t 1.50%
29
STRATEGY USING FUTURES: ARBITRAGE OPPORTUNITIES: When F>S Investor can borrow funds at risk free rate of interest to buy the asset and take short position in Futures market and then long the asset at time T . When F<S Investor can take Long position in the futures market , undertake the delivery of the asset at time T and short the asset in the spot market . Have funds- Lend them to the market: This works like repo transaction where the investors buys the security and simultaneously undertakes short position in the futures market. Here the investor can use the securities purchased in the spot market to dispose them at the expiration date of the futures contract. Thus the investor will gain the difference between the futures price and the cash price of the security. Have securities –Lend them to the market. Index futures market offers a risk less mechanism for loaning out shares and earning a positive return on them by selling shares at Nifty and invest the proceeds at risk free returns and buying the securities back at the future date by taking long position in the futures market.
30
HEDGING: SHORT HEDGE: A company knows that it is due to sell an asset at a particular time in future can hedge by taking Short Futures Position. If the price of the asset goes up then company gains from sale transaction and if the price of asset goes down the company gains from Futures Transaction. LONG HEDGE:
A company that knows that its due to buy an asset in the future can hedge by taking Long Futures Position. Similarly, in this case also if the price of asset goes up then the company gains in the Futures Transaction and if the price of asset goes down then the company can gain from Purchase transaction. Thus, we can see that in both the cases what Hedging as done is that it has made the result of the outcome more predictable. Hedging not necessarily brings greater returns but what it does is that it makes the result of the outcome more predictable and thus it minimizes the risks. Optimal hedge Ratio: H = ? ?s /?f Where ? is the co-efficient of correlation between ?s and ?F. ?s is the standard deviation of ?s ?f is the standard deviation of ?F.
31
HEDGING USING INDEX FUTURES: Stock index futures can be used to hedge the risk in well-diversified portfolio and removes the risk arising from the market moves and leaves the hedger exposed only to the performance of portfolio relative to the market. Optimal Number of contracts to short when Hedging : ?* ?/f Long security/Portfolio - short futures: Every buy position in the security is a simultaneous Long Position in the Index so if the index gains or loses the security also gains or loses simultaneously. In the sense, a Long Position on any security is also a Long position in the Index. So every time a security is bought a simultaneous short position in the index will hedge the security and offsets the index hidden exposure. The position Long Reliance + short Nifty will be pure play on the value of reliance stock without any extra risk from the fluctuations in the market. Short security –Long futures: A person may sell the stock thinking that its overvalued but if the index moves up he will lose because every sell position in the stock is simultaneous sell position in the index. Even thought the stock in this case may be overvalued the stock price will increase because index has increased and the person will regret his decision to sell the stock. In this case he can hedge by taking a long position in the futures contract so that it will offset the hidden exposure from the index.
HEDGING STATERGIES:
32
Long Portfolio - Short Futures If X has Portfolio worth Rs 10,00,000 of Index stocks as on 2nd May 2006 ,when index is at 3605.45 he will have No of shares : 277
In Order to hedge his portfolio against adverse movements in the stock market he can hedge by having Short Position in the Futures Number of Futures contract to short for perfect : hedge= No of Futures Contract Required : Beta* Portfolio/ Future
Index*lot size) 3 (2.7735789)
His position as on 25thMay when Spot is 3177.7 will be as below: Loss from Spot Transaction Gain from Futures Transaction Net gain/loss : : : -118486.8 125190 6703.25
Thus X has hedged his portfolio against fall in the index. Had he not hedged his portfolio he would have suffered loss of Rs118487 but due to hedging he has now made a profit of Rs 6703.25.
33
Short Portfolio- Long Futures On 2nd May if Mr X is having portfolio of NIFTY worth 277 Shares when they are traded at 3605.45 and Mr X feels that NIFTY is overpriced and he sells his portfolio. The Proceeds from the sale of his portfolio will be Cash proceeds from above : 998709.65
Suppose that he invests this money at risk free interest rate and takes long position in Futures market In order to hedge now he takes Long Position in Futures on the same date when the Futures for May Month are being traded at Rs 3595. On 25th May when the NIFTY has declined to Rs 3177.7 and he takes again Long position on 277 shares his total portfolio will be as follows Loss on Futures Gain on spot ransaction Risk free interest Net Position Value of Portfolio : : : : : -125190 118486.75 1887.971667 -4815.278333 1003524.928
Thus we can see that though in this particular case he has made loss on Spot transaction it has been compensated from profit in futures transaction. Thus the total Portfolio remains unchanged.
34
SPECULATION Bearish- Short Futures On 2nd May the Index is 3605.45 and Futures for month are at Rs 3595 and Mr X feels that the index will go down in the near Future( Bearish) then he can take short position in the futures . If he has Rs10,00,000 with him and he takes short position of 3 contracts which expire on 25th May, then his position as on 25th May will be Profit form futures Future price-Spot Price * Number of contracts 125190 If he has paid an initial margin of 20% (i.e.) Rs 215700 then will gain return of 58.03% on his initial investment. Bullish- Long Futures On 29th June when the index spot was at 2997.9 and July Futures were trading at 3130.3 and the investor who feels that the index will increase (bullish) then he can take a long position and if index moves in positive direction then he can make profits Suppose that Mr.X is bullish as on 29th June and he takes Long position in the futures for 3 contracts and squares off his position on 27th July, then his position as on 27th July will be as follows Futures price as on 29th April 3003.00 Sopt price on 26th may 3156.15 Profit from Futures 76575 Suppose the initial margin was 20% then his return on investment will be 42.50%.
35
OPTIONS Call Option : A Call Option gives the right (not obligation) to buyer of call option to buy an underlying asset. Put Option : A Put Option gives the right ( not obligation ) to holder of Put option to sell the underlying asset for exercise price. American Option : An American Option is one which can be exercised by the holder anytime prior to maturity date. European Option : European Option can be exercised by the holder only on the date of maturity.
Position in Option: Long Position in Call Option Short Position in Call Option Long Position in Put Option Short Position in Put Option Pay off from Option: Payoff from Long Position in Call Option : Max ( St – K , 0 ) Payoff from Long Position in Put Option : Max (K-St , 0) Adjusting Options to Share Split and Stock dividends: - Bullish. -Bearish. -Bearish. -Bullish.
36
Share Split: n for m shape split will cause the sock price to go down by m/n of its previous value and the number of share covered by one contract increases by n/m of its previous value. Stock dividends: The treatment is same as that for stock split.20% stock split means 6 for 5 stock split.
Terminology:
Premium : Premium is the amount paid by the holder of an Option for the right he gets to exercise the Option. Premium of an Option can be separated into two components –Intrinsic Value and Time Value. Intrinsic Value: Intrinsic Value of an Option is the amount which would be credited to holder of an Option if he were to exercise the Option and close out the position. A Call will have intrinsic value if exercise price is less than the current market price of the Underlying. Intrinsic value is equal to Current Market price – Exercise Price. A Put will have intrinsic value if the exercise price is more than the current market price of the underlying.(i.e.) Exercise Price – Current Market Price.
37
Time Value: Additional amount of premium over and above the Intrinsic value is the time value or extrinsic value of Option. At the Money and Out of Money Options will only have Time Value and no intrinsic value. In the money: An Option with intrinsic value is said to be in-the-money. In order to be in the money call should have exercise price less than the current market price and Put should have exercise price more than Current market price. At the money: An Option whose exercise price is equal to current market price is said to be at the money. Out of the money: A call option is said to be Out of money if the exercise price is more than the current market price of the Underlying. Put Option is said to be Out of money if exercise price is less than the current market price of underlying.
38
Factors affecting the Option Prices: Current Stock Price Strike Price Call option: Payoff from the Call Option will be the amount by which the spot price exceeds the strike price. Hence if the Stock price increase the payoff of call option will increase and hence the call will become more valuable. If the strike price increase the payoff from the call option will decrease and hence the call price will decrease. Put option: Payoff from put option is strike price – spot price. Hence if the spot price increases the put will become less valuable and if the strike price increases put will become more valuable. Time to expiration Time to expiration will affect only the American Options as European Options can be exercised only on the specific date. In case of American option , an owner of long life option has all the exercise opportunities that is available to the owner of short life option and more .So the value of long life American option will increase as the time to expiation increases. Volatility of the stock price Volatility refers to uncertainty about the movement of share prices both up and down. Owner of a call option benefits from price increase but has limited downside risk similarly put benefits from price decrease but has limited downside risk in case of price increase. Therefore the values of both call and put increase as the Volatility increases.
39
Risk free rate of interest In case of Call Option the owner has to pay for security if he decides to exercise the option at a later date so he will have to shell out money sometime in future. If in the mean time interest rate increase he will benefit from investing the money in the risk free returns. So the value of call option increases as the interest rate increase. In case of put the owner will receive the money if he exercises the put sometime in future , so if the interest rate increase in the meantime present value of the future cash flows that will be received by him will decline so the Put Option will decline in value if the interest rate increase. Dividends expected during the life of asset Dividends reduce the stock price on ex-divided date , so the value of call will decline if the dividends increase and the value of put will increase if the dividends increase.
40
European Variable Spot price Strike Price Time expiration Volatility Risk free rate Dividends + + to Call + ?
European Put
American Call
American Put
+ ?
+ +
+ +
+ +
+ + -
+ +
41
SCENARIO ANALYSIS We have done a scenario analysis to show how a change in the strike price on a given particular day will affect the Price of options along with change in the technical parameters (i.e.) how the option price and its technical indicators will respond to any change in spot price. We have taken 3000 series as on 1st June, 2006 when NIFTY was trading at 2962.25. Stock Price Exercise Price Current date Expiration date Risk free Interest rate Volatility Dividend yield Time 2962.25 3000.00 1-Jun-06 29-Jun-06 5.00% 14.68% 2.00% 0.076712329
Scenario Analysis of change in Call Price , Put Price and Other parameters of Option to change in Spot Price and effect of change in Volatility to change in Call Price and Put Price. Stock Price 2950 2960 2970 2980 2990 3000 3010 3020 29.63 33.47 37.63 42.11 46.91 52.05 57.51 63.29 0.3677 0.3994 0.4317 0.4644 0.4972 0.5298 0.5622 0.5941 0.003138 0.003205 0.003250 0.003274 0.003276 0.003255 0.003213 0.003151 -325.27 -336.34 -345.53 -352.72 -357.81 -360.77 -361.59 -360.32 307.49 316.20 322.89 327.45 329.80 329.93 327.85 323.63 -80.94 -88.13 -95.48 -102.93 -110.44 -117.94 -125.41 -132.77 Call Delta Gamma Theta Vega Rho
42
3030 3040 3050
69.39 75.79 82.49
0.6252 0.6554 0.6846
0.003070 0.002971 0.002857
-357.03 -351.84 -344.91
317.37 309.21 299.32
-139.99 -147.03 -153.84
stock price 2950 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050 Put 72.67 66.52 60.69 55.19 50.01 45.16 40.64 36.44 32.55 28.97 25.68 Delta -0.6308 -0.5990 -0.5667 -0.5341 -0.5013 -0.4686 -0.4363 -0.4044 -0.3733 -0.3431 -0.3139 Gamma 0.003138 0.003205 0.003250 0.003274 0.003276 0.003255 0.003213 0.003151 0.003070 0.002971 0.002857 Theta -234.76 -245.91 -255.19 -262.48 -267.69 -270.78 -271.75 -270.63 -267.51 -262.50 -255.76 Vega 307.49 316.20 322.89 327.45 329.80 329.93 327.85 323.63 317.37 309.21 299.32 Rho -148.32 -141.12 -133.78 -126.32 -118.82 -111.31 -103.85 -96.48 -89.26 -82.23 -75.41
43
Volatility 8.00% 9.00% 10.00% 11.00% 12.00% 13.00% 14.00% 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% 21.00% 22.00% 23.00% 24.00% 25.00% 26.00% 27.00% 28.00% 29.00% 30.00%
Call Price 13.70 16.68 19.72 22.80 25.92 29.06 32.22 35.39 38.58 41.79 45.00 48.21 51.44 54.67 57.90 61.14 64.38 67.63 70.87 74.12 77.38 80.63 83.89
Put Price 44.51 47.49 50.53 53.61 56.72 59.86 63.02 66.20 69.39 72.59 75.80 79.02 82.24 85.47 88.71 91.95 95.19 98.43 101.68 104.93 108.18 111.44 114.69
44
Scenario Analysis-Change in Call and Put to Change in Spot.
90.00 80.00 70.00 60.00 Option Price 50.00 40.00 30.00 20.00 10.00 0.00 2950 2960 2970 2980 2990 3000 Stock Price 3010 3020 3030 3040 3050
Call Price
Put Price
45
Scenario analysis-Change in Delta to Change in Stock Price
0.8000
0.6000
0.4000
Change in Delta
0.2000
0.0000 2950 -0.2000 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050
-0.4000
-0.6000
-0.8000 Stock Price Call Delta Put Delta
Scenario analysis: Change in Delta to Change in Stock Price Delta along with change in option price to Change in strike price also gives indication to probability that the Option will be in-the-money. In the given scenario as the Spot price is increasing, from 2950 onwards, the probability that the Option with exercise price of 3000 will be in-the-money increases as the buyer of call option will exercise the option at any level beyond 3000. As seen from the chart, Delta has increased from 0.3677 when spot price for 3000 exercise price was 2950 to 0.6846 when the NIFTY was changed to 3050. For Put option, any increase in Spot price will decrease the probability that the option will be in-themoney as the option will expire worthless on the expiry date. In the chart above, Delta of put
46
option is getting closer to 0 with increase in NIFTY spot price as their probability to be exercised decreases and they decline in value because their payoffs will decline with increase in spot price.
Scenario Analysis-Change in Gamma to Change in Spot
0.003400
0.003300
0.003200
0.003100 Gamma
0.003000
0.002900
0.002800
0.002700
0.002600 2950 2960 2970 2980 2990 3000 Stock Price Change in Gamma 3010 3020 3030 3040 3050
Scenario analysisChange in Gamma to Change in Stock Price
Gamma is the rate at which an Option’s Delta changes as the price of underlying changes. Gamma is greatest for an option that is at the money and becomes progressively small as the Option moves in the money or out of the money thus forming an inverted U shaped curve. In the above graph, Gamma is greatest when the Option is at the money (ie) when spot price is 2990 and 3000 for series which has exercise price of 3000. As the Call option gets in-themoney and out-of-the money with increase and decrease in spot price, the gamma of the Option progressively declines. 47
0.00
Scenario Analysis-Change in Rho to Change in Underlying Price
Stock Price
-20.00
-40.00
-60.00
-80.00 Rho -100.00 -120.00 -140.00 -160.00 -180.00 Stock Price Call Rho Put Rho
Scenario analysisChange in Rho to Change in Stock Price Rho of an option measures the sensitivity of the option price to changes in the interest rates. As Rho increases, Option price will be highly sensitive to changes in interest rates. In the above scenario analysis, as the Stock price increased from 2950 to 3050 call price has also increased. With increase in Call price, Call Options tend to get more sensitive to changes in interest rates, because higher the call price greater will be the affect of it in interest rates. This 48
can be verified from increase in Rho from absolute value of 80.94 to 153.84 as the Spot price has been increased from 2950 to 3050. Similarly when the spot price is increased , the Put Option get more dearer and the effect of interest rates on Put Option decline. This can be seen from decline in the absolute value of Rho from 148.32 to 75.41 when Spot price is increased.
Scenario Analysis-Change in Theta to Change in Underlying
-300.00 2950 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050
-310.00
-320.00
-330.00 Theta -340.00 -350.00 -360.00 -370.00 Stock Price Change in Theta to Change in Underlying
49
Change In Option price due to Volatility
140.00
120.00
100.00
Option Price
80.00
60.00
40.00
20.00
0.00
9. 00 % 10 .0 0% 11 .0 0% 18 .0 0% 19 .0 0% 20 .0 0% 21 .0 0% 22 .0 0% 23 .0 0% 24 .0 0% 25 .0 0% 8. 00 % 12 .0 0% 13 .0 0% 14 .0 0% 15 .0 0% 16 .0 0% 17 .0 0% 26 .0 0% 27 .0 0% 28 .0 0% 29 .0 0% 30 .0 0%
Volatility Price of Call Option Price of Put Option
Scenario analysisChange in Option price to Change in Volatility
In order to find the effect of Option price due to changes in Volatility, all the rest of parameters of the Option are kept constant and a scenario analysis was built to find out how the change in volatility impact the option price. As can be seen from the given graph as the underlying volatility increases, the price of both call and put options increase as the writer of Option will demand more premium when the market is volatile in order to cover his loss. The graph for both Call and Put option prices show similar patter for changes in volatility. The call price has increased from 13.70 when the volatility was 8% to 83.89 when the volatility was
50
increased to 30%. Similarly Put price has increased from 44.51 to 114.69 when volatility was changed from 8% to 30%. Thus other things kept constant, a mere change in underlying volatility of the stock price can cause significant changes to the price of option.
51
S&P CNX NIFTY
3900.00
3700.00
3500.00
3300.00
3100.00
2900.00
2700.00
2500.00
2M ay 9M ay ay ay ay 20 -J un 27 -J un 13 -J un 16 -M 23 -M 30 -M 11 -J ul 18 -J ul 25 -J ul 6Ju n 4Ju l
S&P CNX NIFTY
52
NIFTY Spot and Call
4000.00 800
700 3750.00 600 3500.00 500
3250.00
400
300 3000.00 200 2750.00 100
2500.00
-0 6 -0 6 -0 6 -0 6 -0 6 6Ju n06 13 -J un -0 6 20 -J un -0 6 l-0 6 27 -J un -0 6 11 -J ul -0 6 18 -J ul -0 6 9M ay 16 -M ay 2M ay 23 -M ay 30 -M ay 25 -J ul -0 6 4Ju
0
S&P CNX NIFTY
3000
3050
3100
3200
53
NIFTY Spot and Put
4000.00 800
700 3750.00 600 3500.00 500
3250.00
400
300 3000.00 200 2750.00 100
2500.00
-0 6 -0 6 -0 6 -0 6 -0 6 6Ju n06 13 -J un -0 6 20 -J un -0 6 l-0 6 27 -J un -0 6 11 -J ul -0 6 18 -J ul -0 6 9M ay 16 -M ay 2M ay 23 -M ay 30 -M ay 25 -J ul -0 6 4Ju
0
S&P CNX NIFTY
3000
3050
3100
3200
54
LIMITS ON UPPER AND LOWER BOUND FOR OPTIONS: Intrinsic Value of an Option: Call Option :Max ( S-X, 0) Put Option : Max (X-S,0) Upper Bounds and Lower Bounds for OPTION PRICES: Upper Bound: For Call Option: c ? S C ? S For Put Option: P ? X ? p ?X Lower Bounds: For European Call Option: c > S – D-X e – r (T-t) For European Put Option : p > D+ X e – r (T-t) –S Its never optimal to Exercise American Call Option on non – dividend paying stock early. Xe
-r ( T –t )
55
Put Call Parity: Put Call Parity says that one European Option plus an amount of cash equal to X e –r (T –t) and one share in underlying along with one Long Put must be equal in Value. Put-Call Parity holds only for European Options. C - P = S- X e – r (T-t) S- D-X < C –P < S – X e –r (T –t) Value of an European call with certain exercise price and exercise date can be deducted from value of an European Put with the same exercise price and date. Both the following portfolio should be equal: Portfolio A: One European Call Option plus an amount of Cash equal to X .e – r (T-t) . Portfolio B: One European Put Option plus one share. If Put – Call parity does not holds true then in would mean that there could be some arbitrage opportunities to exploit. If Portfolio A is greater than Portfolio B , then investor could take Long position in Call and take short position in both Put and the underlying stock. If Portfolio B is greater than Portfolio A, then investor could take Short Position in call and have Long Put and Long the Underlying. Both these cases will bring investor risk less profit.
PUT CALL PARITY Date SERIES 3000 3050 3100 3200
56
Strike Price
2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06
<S-X eC-P
598.5 613.3 627.15 648.8 681.6 713.35 741 693.9 632 469.6 517.35 632.75 379.4 219.45 24.35 186.15 82.85 176.4 175.75 173.85 125.8 29.8 -107.75 58.8 -44.45 -100.25 -159.3 -295.4 -171.8 -282.5 -361.1 -372.75
r (T-t)
<S-X C-P
549.85 571.75 572 576.2 576.2 599.7 675.1 675.1 609.4 609.2 611.6 540.8 533.3 508.1 -15.5 133.8 14.9 130.95 4.459886 -57.4127 -45.5535 42.90583 104.6152 39.1246 72.35318 123.3128 183.7225 292.2823 169.1421 233.8718 342.9319 371.6919
<S-X e-r C-P
-61.75 -71 -36.2 -17.7 -24.7 -93.1 -17.3 25.55 -13.95 -185.6 -148.85 6.7 -168.85 200.65 -57.4 126.65 -86.2 82 170.3401 227.5627 178.2535 59.89417 -40.2652 80.6754 4.646818 -66.6128 -144.523 -270.182 -137.192 -220.722 -331.682 -361.892
(T-t)
<S-X C-P
-193.228 -194.161 -196.095 -229.244 -192.228 -191.011 -106.894 -102.377 32.87478 -196.558 -299.591 107.0267 -10.6058 88.94683 -100.386 16.38222 -110.55 3 -47.7724 -56.0246 -60.7585 34.0076 116.6738 21.99001 71.13907 136.0555 201.3221 329.9386 195.7053 274.5055 386.7224 416.6393
e
-r (T-t)
e-r (T-t)
415.52 443.88 457.59 472.71 500.59 527.56 560.82 507.18 455.74 307.33 327.24 438.60 191.97 49.53 -117.34 0.23 -84.01 -22.30 24.47 28.46 -1.58 -116.26 -225.50 -96.84 -172.85 -252.63 -329.92 -466.46 -324.94 -415.71 -529.69 -560.63
3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70
3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8
614.89 643.28 657.02 672.16 700.13 727.12 760.41 706.80 655.39 507.06 527.00 638.39 391.78 249.36 82.58 200.17 115.96 177.70 223.54 227.61 197.60 82.94 -26.27 102.43 26.50 -53.26 -130.52 -267.03 -125.49 -216.17 -330.13 -361.04
565.04 593.43 607.16 622.29 650.24 677.23 710.51 656.89 605.48 457.13 477.06 588.44 341.82 199.41 32.60 150.19 65.97 127.70 173.77 177.82 147.81 33.14 -76.07 52.61 -23.34 -103.11 -180.37 -316.89 -175.36 -266.06 -380.02 -410.94
515.20 543.58 557.30 572.43 600.36 627.34 660.61 606.99 555.57 407.19 427.12 538.50 291.87 149.45 -17.38 100.20 15.97 77.70 124.00 128.04 98.01 -16.66 -125.88 2.79 -73.17 -152.95 -230.22 -366.75 -225.22 -315.94 -429.91 -460.84
57
15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
-216.65 -112.5 -89.3 -175.3 -92.05 -19.55 38.25 43.6 -69.1 -19.05 -17.1 1.8 51.1 61.8 50.9 95.15 65.85 -11.4 55.6 33.05 101 71.05 29.65 -55.05 -60.35 -106 -23.9 -78.85 -37 -7.75 27.4 52.65
-195.45 -104.31 -78.99 -135.00 -73.26 -2.37 45.16 51.94 -55.57 -16.73 -18.49 -2.10 139.28 160.80 148.09 206.13 165.02 84.06 148.98 122.72 202.06 175.05 128.69 11.66 -2.65 -63.96 25.93 -52.54 -12.92 41.32 110.56 156.15
216.2021 147.4623 123.9432 157.0536 94.81413 40.42467 8.38526 2.656615 69.41738 34.07819 26.93907 2.6 18.8246 -4.84682 -3.08718 -26.6275 -25.0177 8.142071 -11.7282 -2.81814 -29.2581 -38.5979 -30.4377 31.19322 38.00365 80.41413 12.52467 64.28526 28.66738 -12.6218 -43.8109 -53.1
-245.36 -154.22 -128.92 -184.94 -123.21 -52.33 -4.79 1.97 -105.55 -66.71 -68.48 -52.10 89.46 110.96 98.24 156.28 115.16 34.19 99.09 72.83 152.16 125.14 78.78 -38.27 -52.59 -113.91 -24.03 -102.49 -62.90 -8.66 60.57 106.15
-199.952 -116.712 -91.9932 -140.354 -79.9641 -16.8247 25.51474 29.99339 -61.1174 -25.1282 -23.6891 -2.4 108.6754 130.1968 119.3372 168.7275 144.8677 61.70793 119.0782 95.61814 161.8081 144.0479 103.4377 -3.24322 -15.8036 -70.1641 10.02533 -57.5353 -19.9174 23.97181 73.46093 105.8
-295.26 -204.13 -178.86 -234.88 -173.15 -102.28 -54.75 -48.00 -155.53 -116.70 -118.48 -102.10 39.64 61.13 48.40 106.43 65.30 -15.67 49.21 22.94 102.26 75.24 28.87 -88.21 -102.53 -163.85 -73.98 -152.45 -112.88 -58.65 10.57 56.15
253.9563 170.6733 143.9248 193.542 130.2094 62.42674 15.54418 10.82922 109.2468 69.2645 69.08222 52.35 -30.5254 -55.2968 -53.2872 -88.2775 -77.0677 -26.2579 -62.8282 -46.9681 -91.7581 -90.5479 -69.9377 14.44322 24.75365 75.06413 -4.77533 59.53526 22.81738 -22.2218 -71.2609 -105.7
-395.07 -303.96 -278.72 -334.76 -273.05 -202.18 -154.67 -147.95 -255.49 -216.67 -218.46 -202.10 -59.99 -38.55 -51.28 6.73 -34.41 -115.39 -50.56 -76.84 2.47 -24.57 -70.96 -188.07 -202.41 -263.75 -173.88 -252.37 -212.84 -158.62 -89.41 -43.85
Property distribution of a stock price: Probability distribution of the stock price St, for time T is given by : With mean and Standard deviation as follows: In St ~? { In St + (?-?2) * (T-t) , ? ? ( T-t) } 58
Where St is the Stock Price ? is the expected return per annum ? is the Volatility. T-t is the time period. Expected value of the Stock price at the end of t Time period is given by E(St) = S e ? (T-t). And the variance of the St is given by: Var(St )= S2 e2?( T-t) { e ?2 ( T-t) -1}. The Distribution of the Rate of Return: with Mean and Standard deviation of { ?- ?2/2, ?/ ?T-t}
59
PRICING OF OPTIONS BLACK SCHOLES MODEL:
Value of Call Option:
C= SN (d1)- X e –r(T-t) N (d2) Or C= e- r (T-t) { SN (d1) e r(T-t) - XN (d2)
Where D1 = In (S/X) +( r + ?2/2 )( T-t) / ? (?T-t) D2 = In (S/X) +( r -?2/2 )( T-t) / ? (?T-t) = Interpretation of the above model: N(d1) = Change in Option price due to change in the Stock Price.(Delta). Probability that the option will be in-the-money. N (d2) = Probability that the Option will be exercised. XN (d2) = Strike times the Probability. SN (d1) e r(T-t) = Expected Value of a Variable that equals St , if St > X and Zero otherwise in a Risk Neutral World. Since C= c , the Value of American Call Option will be Equal to that of European Call Optio D1- ?(?T-t).
60
Value of Put :
C= X e- r (T-t) N (-d2)- SN (-d1). By replacing S by S .e-q (T-t) we can find the price of an Option with known dividend yield q. If dividends are known then present value of dividends are subtracted from S. BLACK SCHOLES MODEL Input Variables: Stock Price Exercise Price Current date Expiration date Risk free Interest rate Volatility Dividend yield Time Price of Stock Option Theoretical Parameters of Option Delta Gamma Theta 3605.45 3000.00 2-May-06 25-May-06 5.00% 16.52% 2.00% 0.0630137 Call 610.3463 Call 0.9987371 1.071E-07 -77.52858 Put 0.0001 Put -3.41E-06 1.07E-07 -0.018618
61
Vega Rho
0.0144885 -188.4456
0.014488 -0.000781
62
THEORETICAL PRICE OF CALL ACTUAL PRICE OF CALL OPTION S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 3000 600 617 628.7 650.8 683.1 714.7 746 698.1 635.1 471.45 520 635 389.75 240 122.7 212.4 117.15 176.8 243.1 236.85 196.65 152.45 96.95 176.9 120.15 89.5 70.25 39.95 56.25 25.65 FOR NEAR MONTH EXERCISE PRICE 3050 555 576.9 576.9 580.2 580.2 603.2 680 680 615 615 615 544.5 544.5 544.5 99.55 173.35 63.65 131.5 228 170.2 152.05 125.85 78.35 141.55 98.85 70.05 53.2 25.25 43.65 17.7 3100 510 501 540 558.5 575 582 657.8 634.95 595.25 426 391.95 540 339.25 185.15 76.4 141.55 44.75 82 174.8 170.15 132.7 102.8 64.35 119.8 77 56.7 39.2 22.1 31.95 13.15 3200 400.2 413 426.2 421 485 519.5 550 503.1 490 280.5 288.85 448.85 188.8 121.55 49.8 82.35 17.15 3 126 121.8 87.05 67.15 40.6 74.6 47.8 32.95 20.95 13.05 20.35 8.45 223.35 226.63 198.77 103.67 40.25 116.80 62.78 25.70 7.67 0.32 7.22 0.61 179.31 181.77 155.59 71.94 23.60 82.23 38.64 13.32 3.21 0.09 2.89 0.16 139.02 140.51 116.80 47.03 12.82 54.46 21.91 6.26 1.21 0.02 1.02 0.03 73.92 73.60 56.80 16.53 2.99 19.48 5.41 1.02 0.12 0.00 0.09 0.00 3000 610.35 638.90 652.82 668.14 696.69 723.86 757.32 703.96 652.79 505.14 525.26 636.79 390.48 248.30 82.72 199.82 115.79 OPTION FOR NEAR MONTH EXERCISE PRICE 3050 560.50 589.05 602.97 618.28 646.81 673.97 707.43 654.06 602.88 455.21 475.32 586.85 340.52 198.37 38.66 149.84 65.86 3100 510.66 539.20 553.11 568.42 596.92 624.08 657.53 604.15 552.97 405.27 425.38 536.90 290.57 148.70 10.88 99.91 20.42 3200 411.05 439.53 453.41 468.70 497.16 524.30 557.73 504.34 453.14 305.42 325.51 437.01 190.80 58.04 0.09 15.54 0.01
63
13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
19.2 16 31.15 61.65 62.85 27.4 38.35 57.3 77.5 81.9 25.75 33.25 24.55 5.85 127.5 125.35 116.25 142.1 119.85 69.85 107.35 92.8 132.55 105.45 73 27.95 22.2 10.25 22.55 6.75 8.75 11.35 29.65 52.7
12.8 10.65 20.75 43.15 44.95 22.05 21.55 38.05 53.55 54.6 13.85 17.35 8.45 0.5 158.1 155.95 145 179.5 140 92.2 137.25 119.9 172.8 136.45 98.25 42.85 35.35 16.45 38.45 11.75 15.75 28.7 66.75 103.05
11.25 9.8 16.25 30.75 31.95 16.7 14.85 23.6 33.9 32.65 8.3 8.95 3.25 0.2 127.5 125.35 116.25 142.1 119.85 69.85 107.35 92.8 132.55 105.45 73 27.95 22.2 10.25 22.55 6.75 8.75 11.35 29.65 52.7
6.7 5.7 8.6 16.45 15 8.6 7 10.1 10.75 12.8 3.7 2.55 0.6 0.25 78.15 74.9 66.05 80.45 67.8 35.45 56.25 48.65 70.05 53.5 33.5 11.2 8.95 4.9 5.25 2 2.9 1.75 2.2 0.1
0.01 0.00 0.59 5.58 6.77 1.09 5.69 25.61 53.45 55.80 2.20 7.62 3.56 146.51 163.86 152.26 205.10 166.63 97.78 150.66 126.73 200.50 174.30 130.56 37.98 28.97 7.28 41.61 6.92 11.97 43.47 110.39
0.00 0.00 0.13 1.73 1.89 0.19 1.32 8.69 22.93 21.69 0.14 0.50 0.03 107.70 122.15 111.48 159.43 123.65 64.17 107.80 86.41 153.10 128.10 88.18 16.82 11.37 1.80 16.90 1.37 1.65 10.79 60.50
0.00 0.00 0.02 0.44 0.41 0.02 0.22 2.11 7.05 5.19 0.00 0.01 0.00 74.92 86.01 76.74 117.76 86.20 38.63 71.25 53.68 109.34 86.82 53.43 5.99 3.47 0.32 5.06 0.17 0.09 0.93 16.71
0.00 0.00 0.00 0.02 0.01 0.00 0.00 0.04 0.20 0.05 0.00 0.00 0.00 30.03 34.88 29.27 53.09 33.40 10.46 23.25 14.81 42.58 28.95 13.06 0.37 0.14 0.00 0.16 0.00 0.00 0.00 0.00
64
Technical Analysis of Option Parameters
Delta Delta is the rate of change of the option Price with respect to underlying asset. Delta hedging keeps the total wealth of an investor as close to unchanged as possible. Suppose the delta of a stock is .60. This means that when stock price changes by some amount the option price changes by 60% of that of underlying. If the call price is Rs 10 and the stock price is Rs 100 and investor has written 20 Call Option’s (Lot of 100 each) in order to hedge the investor can buy 1200 shares( 2000*.60).In this case gain(loss) in the option position will tend to setoff by loss(gain) in the stock position. The scheme generally involves selling the stock just after the price has gone down and buying the stock just after the price have gone up(delta will increase so to maintain the portfolio as delta neutral more of the underlying stock must be purchased). It might be termed as- Buy High- sell low scheme. Delta of the underlying stock is always 1.
Delta of European Call on Non-dividend paying stock: Delta of European Put on Non-Dividend paying stock Delta of European Call on stock paying a dividend yield q : Delta of European Put on stock paying a dividend yield q:
? = N. d 1. ?= N .d1 – 1 ?= e –q (T-t) . N. d 1 ?= e –q (T-t) . (N. d 1 -1).
Since the underlying stock always has delta of 1.00 ,each 100 deltas in an option represents a theoretical position in the underlying stock. (i.e.) if person is having options with delta of 500 this is equivalent to holding 5 underlying stocks.
65
If we ignore the sign of delta (for Put ) then Delta also shows the probability that the Option will be in-the-money. An Option with delta greater than 50 is in the money , equal to 50 is at the money and delta less than 50 is out of the money. Thus there are 4 important interpretation of Delta:
Hedge Ratio
Rate of change wrt to Underlying Probability of Option in the money Equivalent underlying position
66
Delta
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 0.92 0.93 0.91 0.72 0.42 0.77 0.58 0.33 0.13 0.01 0.13 0.02 0.00 0.00 0.02 0.13 0.86 0.88 0.84 0.59 0.29 0.64 0.42 0.20 0.06 0.00 0.06 0.01 0.00 0.00 0.00 0.05 0.78 0.80 0.74 0.45 0.18 0.50 0.28 0.11 0.03 0.00 0.02 0.00 0.00 0.00 0.00 0.01 0.55 0.57 0.49 0.21 0.05 0.24 0.09 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3000 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.76 1.00 0.99 EXERCISE PRICE 3050 3100 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.35 1.00 0.72 3200 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.76 0.01 0.50 0.00
67
19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
0.16 0.04 0.15 0.48 0.76 0.84 0.11 0.32 0.24 0.84 0.89 0.88 0.95 0.91 0.76 0.91 0.87 0.97 0.96 0.91 0.55 0.48 0.19 0.64 0.20 0.39 0.87 1.00
0.06 0.01 0.05 0.22 0.47 0.51 0.01 0.03 0.00 0.74 0.80 0.77 0.89 0.82 0.61 0.81 0.75 0.93 0.89 0.79 0.32 0.25 0.06 0.36 0.05 0.08 0.41 0.99
0.01 0.00 0.01 0.07 0.20 0.18 0.00 0.00 0.00 0.61 0.67 0.64 0.79 0.70 0.44 0.67 0.58 0.83 0.77 0.61 0.14 0.10 0.01 0.14 0.01 0.01 0.06 0.65
0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.33 0.38 0.34 0.52 0.39 0.17 0.32 0.24 0.51 0.40 0.23 0.01 0.01 0.00 0.01 0.00 0.00 0.00 0.00
68
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
3000 3050 3100 3200
0.10
0.00 2700.00
2900.00
3100.00
3300.00
3500.00
3700.00
69
0.0000
delta of put
-0.1000
-0.2000
-0.3000
-0.4000 delta
-0.5000
-0.6000
-0.7000
-0.8000
-0.9000
-1.0000 3000 3050 3100 3200
16 -M ay
23 -M ay
30 -M ay
2M ay
9M ay
un
n
27 -J un
20 -J u
11 -J ul
18 -J ul
6Ju n
4Ju l
13 -J
25 -J
ul
70
71
Delta of Call Option
1.00 0.90 0.80 0.70 0.60 Delta 0.50 0.40 0.30 0.20 0.10 0.00
ay ay ay -J un -J un -J un l 11 -J ul ay 16 -M 23 -M 30 -M 13 20 27 25 -J ul ay 18 -J ul 6Ju n 2M 9M 4Ju
3000
Date 3050
3100
3200
72
Delta Hedging strategies: Long Position in Call Option : Short position of N.d1 shares. Short position in Call Option : Long Position of N.d1 shares. Long position in Put Option : Long position in the underlying stock. Short position in Put Option : Short position in the underlying stock. DELTA HEDGING Portfolio= "-C1+N(d1)S"
In order to create delta neutral position a person should take Opposite position to that of Call Option so that the value of the Portfolio remains the same if there is any change in the value of Stock Price.
The amount of shares that have to be purchased in order to make the above portfolio delta neutral is given by N(d1). That is for every Option that is purchased Nd1 shares of the underlying must be bought so that the changes in the value of Stock will not affect the value of Portfolio.
Delta Hedging Strategies Long Position in Call Option : Short position of N.d1 shares Short position in Call Option : Long Position of N.d1 shares Long position in Put Option : Long position in the underlying stock Short position in Put Option : Short position in the underlying stock
73
If the call Price is Rs 7.97 and the Put Price is Rs 8.91 for a stock which has exercise price of 105 and strike price of 100.
The various parameters of the Option are Parameters of Option Delta Gamma Theta Vega Rho Call 0.52430 0.01889 -12.06104 27.95787 -27.92 Put -0.47570 0.01889 -3.98600 27.95787 -27.85
In the above case if the call price is 7.67 with the delta of .5243 then for every option that is purchased .5243 shares of the Underlying stock must be kept. If a person buys 100 calls for 79.70 then he should have short of roughly 53 shares so that he is delta neutral.
His portfolio will be Long 100 calls short 53 shares Portfolio -767 5243 4476
Now if the stock price changes to Rs 105 then the value of call option will be Rs 10.82 His portfolio now will be
74
Long 100 calls Short 53 calls Portfolio
-1082 5505.15 4423.15
Thus with help of delta hedging his portfolio has been hedged against the loss in value.
Gamma Gamma is the rate at which an Option’s Delta changes as the price of underlying changes. It is a measure that how fast an Option change sits directional characteristics. If the gamma is extremely large then Delta is highly sensitive to the price of underlying asset. Both the calls and puts have positive gammas. Gamma is greatest for an option that is at the money and becomes progressively small as the Option moves in the money or out of the money. Gamma of the underlying is always 0 because the delta is 1. Measurement of Gamma: N d1 / S ? ? (T-t). Making Portfolio Gamma neutral Since the underlying stock has zero gamma only way by which the portfolio can be made Gamma neutral is taking a position in the traded option. But by taking a position in the traded option will result in changing the delta so again a position must be taken in the underlying stock as a result of change in delta. The position that must be taken in the traded option to make it Gamma neutral : -?/ ?
75
GAMMA
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 0.00090 0.00082 0.00107 0.00236 0.00288 0.00218 0.00306 0.00296 0.00186 0.00022 0.00193 0.00043 0.00001 0.00000 0.00049 0.00230 0.00135 0.00130 0.00161 0.00272 0.00251 0.00268 0.00306 0.00230 0.00109 0.00008 0.00109 0.00015 0.00000 0.00000 0.00015 0.00109 0.00183 0.00182 0.00214 0.00276 0.00192 0.00287 0.00264 0.00153 0.00055 0.00002 0.00052 0.00004 0.00000 0.00000 0.00004 0.00040 0.00217 0.00226 0.00233 0.00171 0.00066 0.00193 0.00108 0.00036 0.00007 0.00000 0.00006 0.00000 0.00000 0.00000 0.00000 0.00002 EXERCISE PRICE 3000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00168 0.00000 0.00000 3050 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00007 0.00673 0.00000 0.00070 3100 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00049 0.00804 0.00035 0.01242 3200 0.00004 0.00002 0.00001 0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00000 0.00000 0.00019 0.00403 0.00033 0.00905 0.00011
76
19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
0.00308 0.00110 0.00332 0.00581 0.00484 0.00463 0.00413 0.00984 0.01196 0.00171 0.00141 0.00157 0.00081 0.00129 0.00261 0.00142 0.00190 0.00056 0.00084 0.00166 0.00480 0.00513 0.00375 0.00538 0.00449 0.00855 0.00575 0.00000
0.00142 0.00029 0.00133 0.00435 0.00617 0.00756 0.00056 0.00212 0.00049 0.00232 0.00210 0.00230 0.00145 0.00207 0.00322 0.00239 0.00294 0.00130 0.00181 0.00294 0.00434 0.00408 0.00164 0.00542 0.00172 0.00337 0.01043 0.00112
0.00046 0.00005 0.00035 0.00197 0.00432 0.00501 0.00002 0.00008 0.00000 0.00273 0.00269 0.00286 0.00219 0.00278 0.00332 0.00324 0.00362 0.00234 0.00297 0.00392 0.00275 0.00219 0.00046 0.00328 0.00037 0.00041 0.00315 0.01373
0.00002 0.00000 0.00001 0.00008 0.00033 0.00015 0.00000 0.00000 0.00000 0.00224 0.00250 0.00246 0.00272 0.00268 0.00180 0.00279 0.00248 0.00330 0.00331 0.00272 0.00034 0.00017 0.00001 0.00024 0.00000 0.00000 0.00000 0.00006
77
-0.00100 Gamma 0.00700 0.00900 0.01100 0.01300 0.00100 0.00300 0.00500
2-May 4-May 6-May 8-May 10-May 12-May 14-May 16-May 18-May 20-May 22-May 24-May 26-May 28-May 30-May 1-Jun 3-Jun 5-Jun 7-Jun
0.01500
3000
3050
9-Jun 11-Jun
Gamma of Put and Call
date
13-Jun 15-Jun 17-Jun 19-Jun 21-Jun 23-Jun 25-Jun 27-Jun 29-Jun 1-Jul 3-Jul 5-Jul 7-Jul 9-Jul 11-Jul 13-Jul 15-Jul 17-Jul 19-Jul 21-Jul 23-Jul 25-Jul
3100 3200
78
Analysis of Option parameters:
Methodology: The entire project deals with analysis of Option price and its technical parameters for three month period starting from 2nd May 2006 to 27th July 2006. Actual Nifty closing prices have been taken for the above period along with Call and Put prices for four series 3000, 3050, 3100 and 3200. These actual prices are then compared with theoretical Option price using black scholes model along with Option parameters Delta, Gamma, Vega, Theta and Rho.
NIFTY Movements for the three month period since May has been generally volatile as can be compared from the historical volatility .The historical volatility from 1st Jan to 30th april is 14.30% while historical volatility from 2nd may to 27th july was 43.45%. This volatility is attributable to general market perception regarding the future price movements as many investors were perceiving Indian market to be too highly priced compared with other markets with price multiple of 25.This along with high oil price, uncertainty regarding US interest rates and meltdown of metal prices lead to downfall of nifty from 3605.45 on 2nd may to 3156.15 on 27th july (High – 3754.25 / Low – 2632.80). Delta and Gamma: If we analyze the May series, NIFTY was trading at 3605.45 on 2nd may and all the given option series (i.e.) 3000, 3050, 3100 and 3200 were considerably deep in-the-money Call Options as they were expected to be exercised by the holder of call option on the day of expiry.
The Delta for 3200 series was 1.00 till 18th may along with other series of lower exercise price, but sudden collapse of NIFTY from 3635.10 on 17th may to 3081.35 on 22nd may, 79
changed the entire scenario. The options which were deep in the money till 18th may suddenly changed to out-of-the money, thereby declining the probability that they will yield positive returns as reflected by change in Delta from 0.99 to 0.33 and 0.79 to 0.00 for 3100 and 3200 series respectively as can been seen from the chart above in the month of may for the given series.
Also analyzing the above chart, it can be seen that Options with higher exercise price have lower delta when compared to Options with lower exercise price, as they are considered more volatile since they have higher probability that they will be exercised on the date of maturity. Since these options have higher delta, they are also expected to show significant fluctuations to change in strike price when compared to options of lower exercise price.
The reverse of the Call option is applicable in case of Put Options. All the series were out-of the money in the month of May with 0 Delta, as Put options were expected to go unexercised on the date of expiry but due to downward movement of NIFTY, these options turned out to be in in-the-money, 3200 series and 3100 series as NIFTY was in the range of 3100-3200 during the last trading days of may. The rest of the series with exercise price of 3000 and 3050 continued to be out-of money. The fall of delta on 22nd may can be explained by fall in NIFTY to 3081.35 from 3635.10 on 17th may.
Theta : Theta of a portfolio of derivatives, ? is the rate of change of the value of the portfolio with respect to time. Theta is negative for an Option because as the time to maturity decreases the Option becomes less valuable. Its expressed as points per day.
80
For European Call Option: ? = - SN (d1) ? – r X e-r (T-t) N (d 2) / 2 ? (T-t )
For European Put Option : ? = - SN (d1) ? + r X e-r (T-t) N (d 2) / 2 ? (T-t )
Vega (?) : Vega is the rate of change of the value of the Portfolio with respect to the volatility of the underlying asset. If Vega is high then the portfolio is highly sensitive to the small changes in the volatility. Since all the options gain value when the volatility increase , the Vegas for both Calls and Puts is positive. At the money option has always greater Vega than in the money or out of the money option .Vega of all the Options decline as the expiration approaches because less time to expiration means any change in volatility will only have minor effect on the options value. For Non-dividend paying stock: ? = S ?( T- t) N (d1) For stock that pays divided with annual yield of q ? = S ?( T- t) N (d1) e –q (T-t )
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 SPOT 3605.45 3634.25 3648.40 3663.95 EXERCISE PRICE 3000 0.01 0.00 0.00 0.00 3050 0.08 0.02 0.01 0.00 3100 0.37 0.13 0.06 0.02 3200 4.74 2.11 1.18 0.60
81
8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06
3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.14 21.64 142.29 118.59 147.93 291.84 320.04 254.76 302.13 266.27 151.16 15.74 143.24 25.73 0.72 0.13 24.39 112.95 118.65 36.53 102.80 165.22 121.65 78.07 48.58 79.20 48.13 204.87
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.91 86.78 214.79 188.01 222.28 336.32 278.57 312.52 302.52 206.13 88.51 5.37 81.10 8.68 0.13 0.02 7.35 53.50 54.54 9.57 41.12 123.64 155.06 127.27 6.63 17.05 1.97 276.93
0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.08 14.13 103.69 290.00 263.71 294.61 341.95 213.96 334.84 261.08 137.23 44.46 1.57 38.78 2.42 0.02 0.00 1.75 19.50 17.77 1.72 10.69 55.86 108.67 84.40 0.28 0.63 0.00 326.42
0.08 0.02 0.00 0.01 0.03 0.84 0.19 0.00 7.37 128.01 4.91 386.19 367.49 363.56 248.55 88.81 262.66 128.07 39.81 7.29 0.09 5.51 0.11 0.00 0.00 0.05 1.24 0.72 0.02 0.22 2.76 9.93 2.96 0.00 0.00 0.00 308.50
82
28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
151.68 160.93 82.32 121.94 223.35 108.02 133.66 39.15 53.64 95.44 196.63 187.26 116.71 155.81 105.82 103.46 48.15 0.01 0.00 0.00
226.85 235.63 147.44 195.96 275.83 181.75 206.94 90.39 115.01 168.95 177.80 148.99 50.97 156.93 40.53 40.78 87.31 4.91 0.04 3.06
290.52 293.62 222.44 263.71 284.05 245.87 254.57 162.35 188.82 225.23 112.73 80.06 14.45 94.96 8.70 4.97 26.37 60.13 3.22 54.57
307.97 289.67 312.41 289.81 180.71 243.53 201.73 258.17 240.00 180.28 16.71 7.67 0.34 8.30 0.08 0.00 0.02 0.30 94.45 0.57
83
Vega of Put
400.00
350.00
300.00
250.00 Vega
200.00
150.00
100.00
50.00
0.00
2M ay
9M ay
23 -M ay
16 -M ay
30 -M ay
27 -J un
4Ju l
un
un
13 -J
date 3000 3050 3100 3200
Analysis of Vega of Call and Put Options
A high vega implies that the Option price highly sensitive to the small changes in the volatility. In the above scenario for the may series, vega was quite low during the initial 18 days when the market was range bound, but as the may series reached close to expiry, Vega also fluctuated contrary to the general practice according to which Vega of an Option declines as expiration approaches , due to the fact that less time to expiration means any change in volatility will only have minor effect on the options value. But since the market was highly volatile during the ending period of may, Vega of may series increased to reflect those changes in volatility. As far as June and July series is concerned, we can see than Vega of all the four series have declined steadily towards the end of expiry.
20 -J
11 -J ul
18 -J ul
25 -J ul
6Ju n
84
Within the june and july series also towards the end of expiry, Vega was particulary lower for the series which had higher exercise price when compared to those series which had lower exercise price. RHO : Rho of a portfolio is the change in value of portfolio with respect to change in interest rate. It measures the sensitivity of the value of the portfolio with respect to interest rates. For Call Options: Rho = X (T-t) e- r (T-t) N (d 2) For Put Options: Rho = - X (T-t) e- r (T-t) N (-d 2) Elasticity: Elasticity is the percentage change in the Options value to the percentage change in the underlying. Elasticity of an Option is also referred as Leverage. Greater the Options Elasticity more leveraged the Option is. Elasticity = (Underlying Price * Delta )/ Theoretical Value.
85
Comparison of theoretical and actual price of Option: In the given model, we have assumed interest rate which is risk free interest rate of 5% and dividend yield of 2%. The Volatility used for the calculation purpose is 14.68% which is historical volatility for six month period beginning 1st January 2006.If we look at the above chart, it clearly shows that the Call Options of 3000 to 3200 were generally under priced in the month of may when the market was all the options were over priced in the month of June when the market was bearish. In the month of July when the market was volatile and range bound, all the series were under priced except 3000 which was overpriced.
Comparison of theoretical edge of Put option for the above series show that Put options were over priced for all the four series for entire three months since May 2006. In the month of May, where call were under priced, Put options were overpriced and in the month of June when Call option were also overpriced, Put options were too overpriced but they were comparatively higher priced than Call options. Similarly the above explanation also holds true for the month of July where Put options were comparatively overpriced than the Call Options. One reason for the above mismatch between Call and Put price can be attributed to the fact that writer of Put option in bearish market might expect more premium from the buyer in order to mitigate himself from further fall in the market.
86
THEORETICAL EDGE FOR CALL
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 -19.75 -10.22 2.12 -48.78 -56.70 -60.10 -57.37 -63.80 -62.58 -39.63 -49.03 -25.04 -19.19 -16.00 -30.56 -56.07 -48.69 11.57 3.54 -53.91 -54.75 -59.32 -60.21 -56.73 -49.99 -25.16 -40.76 -17.54 -12.80 -10.65 -20.62 -41.42 -35.78 -29.64 -15.90 -55.77 -51.53 -65.34 -55.09 -50.44 -37.99 -22.08 -30.93 -13.12 -11.25 -9.80 -16.23 -30.31 -52.08 -48.20 -30.25 -50.62 -37.61 -55.12 -42.39 -31.93 -20.83 -13.05 -20.26 -8.45 -6.70 -5.70 -8.60 -16.43 3000 10.35 21.90 24.12 17.34 13.59 9.16 11.32 5.86 17.69 33.69 5.26 1.79 0.73 8.30 -39.98 -12.58 -1.36 EXERCISE PRICE 3050 5.50 12.15 26.07 38.08 66.61 70.77 27.43 -25.94 -12.12 -159.79 -139.68 42.35 -203.98 -346.13 -60.89 -23.51 2.21 3100 0.66 38.20 13.11 9.92 21.92 42.08 -0.27 -30.80 -42.28 -20.73 33.43 -3.10 -48.68 -36.45 -65.52 -41.64 -24.33 3200 10.85 26.53 27.21 47.70 12.16 4.80 7.73 1.24 -36.86 24.92 36.66 -11.84 2.00 -63.51 -49.71 -66.81 -17.14
87
19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-July-06
2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
-56.08 -26.31 -32.66 -31.69 -24.05 -26.10 -23.55 -25.63 -20.99 -5.85 19.01 38.51 36.01 63.00 46.78 27.93 43.31 33.93 67.95 68.85 57.56 10.03 6.77 -2.97 19.06 0.17 3.22 32.12 80.74
-43.06 -21.86 -20.23 -29.36 -30.62 -32.91 -13.71 -16.85 -8.42 -0.50 -50.40 -33.80 -33.52 -20.07 -16.35 -28.03 -29.45 -33.49 -19.70 -8.35 -10.07 -26.03 -23.98 -14.65 -21.55 -10.38 -14.10 -17.91 -6.25
-31.54 -16.68 -14.63 -21.49 -26.85 -27.46 -8.30 -8.94 -3.25 -0.20 -52.58 -39.34 -39.51 -24.34 -33.65 -31.22 -36.10 -39.12 -23.21 -18.63 -19.57 -21.96 -18.73 -9.93 -17.49 -6.58 -8.66 -10.42 -12.94
-14.99 -8.60 -7.00 -10.06 -10.55 -12.75 -3.70 -2.55 -0.60 -0.25 -48.12 -40.02 -36.78 -27.36 -34.40 -24.99 -33.00 -33.84 -27.47 -24.55 -20.44 -10.83 -8.81 -4.90 -5.09 -2.00 -2.90 -1.75 -2.20
88
Comparison of Theoretical and Actual Price
100.00
50.00
Theoretical Edge
0.00
23 -M ay 16 -M ay 30 -M ay ay ay 13 -J un 20 -J un 27 -J un 6Ju n l l l 2M 9M 11 -J u 25 -J u 18 -J u 4Ju l
-50.00
-100.00
-150.00 3000 3050 3100 3200
THEORETICAL EDGE FOR CALL
S&P CNX NIFTY Date 2-May-06 3-May-06 4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 SPOT 3605.45 3634.25 3648.40 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.30 3635.10 3388.90 3246.90 3081.35 3199.35 3000 -1.50 -3.70 -1.55 -2.00 -1.50 -1.35 -5.00 -4.20 -3.10 -1.85 -2.65 -2.25 -10.35 -20.55 -97.70 -26.25 3050 -5.15 -5.15 -4.90 -4.00 -4.00 -3.50 -4.90 -4.90 -5.60 -5.80 -3.40 -3.70 -11.20 -36.37 -108.48 -39.55 Exercise Price 3100 -3.40 -3.00 -5.00 -5.00 -3.00 -3.00 -4.90 -4.90 -4.50 -5.50 -4.15 -3.00 -17.25 -46.88 -106.39 -50.74 3200 -6.28 -5.02 -5.44 -4.89 -3.15 -4.65 -3.50 -3.10 -4.70 -6.04 -6.45 -4.35 -31.21 -74.47 -111.97 -74.48
89
24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06 7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06 10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06
3115.55 3177.70 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3 2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85 3142 3116.15 3195.9 3169.3
-34.30 -61.57 -58.53 -64.45 -97.05 -133.65 -99.16 -124.35 -107.09 -87.92 -64.87 -92.20 -88.78 -47.83 -25.54 -49.61 -62.20 -64.79 -65.19 -50.16 -47.71 -29.97 -33.78 -36.59 -27.62 -19.44 -64.54 -56.34 -57.23 -44.13 -48.76 -64.16 -47.15 -53.01 -30.48 -32.72
-48.69 -70.49 -65.25 -73.44 -101.67 -130.44 -105.51 -119.85 -63.73 -58.57 -64.84 -36.62 50.80 30.06 80.10 -26.72 -61.99 -47.59 -24.46 -36.59 -52.83 -26.12 -38.36 -13.63 -17.51 -2.02 -71.94 -64.37 -67.11 -53.95 -58.83 -70.51 -54.67 -60.99 -36.38 -40.51
-55.78 -82.56 -79.62 -84.33 -104.33 -128.75 -103.57 -122.25 -92.50 -66.48 -55.55 -71.37 -73.44 -33.85 -24.30 -28.07 -42.87 -36.29 -28.69 -24.95 -42.66 -28.49 -32.39 -7.94 -12.71 7.04 -73.15 -68.17 -71.41 -58.27 -63.63 -70.98 -59.33 -64.43 -43.40 -49.14
-51.81 -94.58 -93.80 -97.59 -95.93 -122.92 -97.41 -109.93 -81.95 -51.71 -32.31 -56.33 -75.46 -33.47 -12.21 -27.63 -6.17 -10.67 -25.98 -17.47 -31.63 -11.57 -20.34 -8.23 -11.85 8.63 -63.66 -66.78 -67.70 -60.74 -62.72 -64.47 -56.07 -59.56 -48.86 -53.65
90
14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-July-06
3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
-39.25 -55.03 -49.46 -43.72 -29.61 -25.18 -20.37 -16.62 -2.25
-48.23 -56.56 -45.56 -37.36 -25.96 -17.82 -15.02 -18.02 -4.94
-54.07 -50.11 -41.18 -31.59 -23.30 -14.05 -7.44 -13.63 -12.45
-54.26 -39.71 -31.58 -23.92 -13.15 -8.31 -0.42 -2.29 -4.16
91
Theoretical edge 100.00 -150.00 50.00 -50.00 0.00 -100.00
2M ay
9M ay
16 -M
ay 23 -M
ay 30 -M
ay
6Ju n
Theoritical Egde Put
3000 3050 3100 3200
13 -J un 20 -J un 27 -J un
4Ju l 11 -J ul 18 -J ul 25 -J ul
92
Relative Strength Index (RSI)
Date Close 47.4 21.1 -4.6 14.2 -3.9 -39.3 -20.1 -0.1 -17.5 -4.0 -19.9 61.7 30.1 -16.9 23.9 32.3 42.4 -8.3 26.6 -29.5 -4.1 -26.8 59.8 19.7 -11.2 18.6 13.6 -23.6 4.6 -0.6 -40.1 24.3 29.7 24.3 29.7 4.6 0.6 40.1 18.6 13.6 23.6 59.8 19.7 11.2 26.6 29.5 4.1 26.8 23.9 32.3 42.4 8.3 61.7 30.1 16.9 12.45 13.27 14.64 16.62 15.43 16.23 15.07 13.99 13.00 16.34 16.58 15.39 15.62 15.48 14.37 13.68 12.70 11.79 12.69 13.90 9.02 1.38 58.00 8.37 1.59 61.32 7.78 1.88 65.31 7.22 2.30 69.71 7.29 2.12 67.91 6.77 2.40 70.56 8.40 1.79 64.21 8.09 1.73 63.36 9.43 1.38 57.94 8.76 1.87 65.11 8.13 2.04 67.09 8.35 1.84 64.84 7.75 2.02 66.84 7.20 2.15 68.26 8.37 1.72 63.20 7.77 1.76 63.77 7.26 1.75 63.63 9.61 1.23 55.11 8.92 1.42 58.73 8.28 1.68 62.67 14.2 3.9 39.3 20.1 0.1 17.5 4.0 19.9 Up 47.4 21.1 4.6 Down AvgGain AvgLoss RS RSI
2-Jan-06 2835.95 3-Jan-06 2883.35 4-Jan-06 2904.4
5-Jan-06 2899.85 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 2914 2910.1 2870.8 2850.7
13-Jan-06 2850.55 16-Jan-06 17-Jan-06 18-Jan-06 2833.1 2829.1 2809.2
19-Jan-06 2870.85 20-Jan-06 2900.95 23-Jan-06 2884.05 24-Jan-06 2908
25-Jan-06 2940.35 27-Jan-06 2982.75 30-Jan-06 31-Jan-06 2974.5 3001.1
1-Feb-06 2971.55 2-Feb-06 2967.45 3-Feb-06 2940.6
6-Feb-06 3000.45 7-Feb-06 3020.1
8-Feb-06 3008.95 10-Feb-06 3027.55 13-Feb-06 3041.15 14-Feb-06 3017.55 15-Feb-06 16-Feb-06 17-Feb-06 3022.2 3021.6 2981.5
20-Feb-06 3005.85 21-Feb-06 3035.5
93
22-Feb-06 23-Feb-06
3050.8 3062.1
15.3 11.3 -12.0 17.4 7.3 48.4 27.6 -3.3 43.1 -7.6 -66.1 12.4 54.8 18.8 -7.3 31.3 7.5 31.6 -3.3 -22.2 7.0 32.7 41.8 3.3 29.2 64.8 -16.4 70.8 9.8 27.8 -56.1 23.6 -98.4 -34.5 79.7 92.9 17.8
15.3 11.3 12.0 17.4 7.3 48.4 27.6 3.3 43.1 7.6 66.1 12.4 54.8 18.8 7.3 31.3 7.5 31.6 3.3 22.2 7.0 32.7 41.8 3.3 29.2 64.8 16.4 70.8 9.8 27.8 56.1 23.6 98.4 34.5 79.7 92.9 17.8
14.00 13.81 12.82 13.15 12.73 15.28 16.16 15.00 17.01 15.79 14.66 14.50 17.38 17.48 16.23 17.30 16.60 17.67 16.41 15.24 14.65 15.93 17.78 16.75 17.64 21.01 19.51 23.17 22.22 22.61 21.00 21.19 19.67 18.27 22.65 27.67 26.96
7.69 1.82 64.55 7.14 1.93 65.91 7.49 1.71 63.12 6.96 1.89 65.40 6.46 1.97 66.33 6.00 2.55 71.80 5.57 2.90 74.36 5.41 2.77 73.49 5.02 3.38 77.19 5.21 3.03 75.20 9.56 1.53 60.54 8.88 1.63 62.03 8.24 2.11 67.83 7.65 2.28 69.55 7.63 2.13 68.03 7.08 2.44 70.95 6.58 2.52 71.62 6.11 2.89 74.32 5.91 2.78 73.52 7.07 2.15 68.30 6.57 2.23 69.05 6.10 2.61 72.33 5.66 3.14 75.86 5.26 3.19 76.12 4.88 3.61 78.33 4.53 4.64 82.25 5.38 3.63 78.38 5.00 4.64 82.26 4.64 4.79 82.73 4.31 5.25 84.00 8.01 2.62 72.39 7.44 2.85 74.02 13.94 1.41 58.53 15.40 1.19 54.25 14.30 1.58 61.29 13.28 2.08 67.57 12.33 2.19 68.61
24-Feb-06 3050.05 27-Feb-06 3067.45 28-Feb-06 1-Mar-06 2-Mar-06 3074.7 3123.1 3150.7
3-Mar-06 3147.35 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 3190.4 3182.8 3116.7 3129.1 3183.9
13-Mar-06 3202.65 14-Mar-06 3195.35 16-Mar-06 3226.6
17-Mar-06 3234.05 20-Mar-06 3265.65 21-Mar-06 3262.3
22-Mar-06 3240.15 23-Mar-06 3247.15 24-Mar-06 3279.8
27-Mar-06 3321.65 28-Mar-06 29-Mar-06 3325 3354.2
30-Mar-06 3418.95 31-Mar-06 3402.55 3-Apr-06 3473.3
4-Apr-06 3483.15 5-Apr-06 7-Apr-06 3510.9 3454.8
10-Apr-06 3478.45 12-Apr-06 13-Apr-06 3380 3345.5
17-Apr-06 3425.15 18-Apr-06 3518.1
19-Apr-06 3535.85
94
20-Apr-06
3573.5
37.7 -0.4 -24.2 -86.3 93.1 -47.7 0.3 49.3 47.8 28.8 14.2 15.5 29.2 27.4 33.7 -53.2 -51.0
37.7 0.4 24.2 86.3 93.1 47.7 0.3 49.3 47.8 28.8 14.2 15.5 29.2 27.4 33.7 53.2 51.0 147.1 20.4
27.73 25.75 23.91 22.20 27.26 25.32 23.53 25.36 26.97 27.10 26.18 25.42 25.69 25.81 26.37 24.49 22.74 21.12 21.06 27.54 246.2 142.0 165.6 25.58 23.75 22.05 28.91 83.8 26.84 29.36 29.54 27.81 29.6 114.3 108.8 25.83 23.98 22.27 29.90 74.7 79.3 76.9 136.1 27.76 25.78 23.94 22.23 30.78
11.45 2.42 70.77 10.67 2.41 70.71 11.63 2.06 67.27 16.96 1.31 56.69 15.75 1.73 63.39 18.03 1.40 58.41 16.74 1.41 58.43 15.54 1.63 62.00 14.43 1.87 65.14 13.40 2.02 66.91 12.45 2.10 67.78 11.56 2.20 68.74 10.73 2.39 70.53 9.96 2.59 72.15 9.25 2.85 74.03 12.39 1.98 66.40 15.15 1.50 60.02 24.57 0.86 46.21 22.82 0.92 48.00 21.19 1.30 56.52 37.26 0.69 40.70 44.74 0.53 34.67 53.37 0.41 29.24 49.56 0.58 36.84 52.01 0.52 34.04 48.29 0.61 37.81 44.84 0.66 39.72 41.64 0.67 40.05 40.78 0.63 38.77 46.03 0.52 34.25 50.51 0.44 30.60 46.90 0.64 38.93 48.89 0.57 36.22 51.06 0.50 33.55 52.91 0.45 31.15 58.85 0.38 27.42 54.64 0.56 36.03
21-Apr-06 3573.05 24-Apr-06 3548.9
25-Apr-06 3462.65 26-Apr-06 3555.75 27-Apr-06 3508.1
28-Apr-06 3508.35 29-Apr-06 3557.6
2-May-06 3605.45 3-May-06 3634.25 4-May-06 3648.4
5-May-06 3663.95 8-May-06 3693.15 9-May-06 3720.55 10-May-06 3754.25 11-May-06 3701.05 12-May-06 3650.05
15-May-06 3502.95 -147.1 16-May-06 17-May-06 18-May-06 19-May-06 3523.3 20.4
3635.1 111.8 111.8 3388.9 -246.2 3246.9 -142.0
22-May-06 3081.35 -165.6 23-May-06 3199.35 118.0 118.0 24-May-06 3115.55 25-May-06 26-May-06 29-May-06 30-May-06 3177.7 3209.6 3214.9 3185.3 -83.8 62.1 31.9 5.3 -29.6 62.1 31.9 5.3
31-May-06 3071.05 -114.3 1-Jun-06 2962.25 -108.8 2-Jun-06 3091.35 129.1 129.1 5-Jun-06 3016.65 6-Jun-06 2937.3 -74.7 -79.3 -76.9
7-Jun-06 2860.45
8-Jun-06 2724.35 -136.1 9-Jun-06 2866.3 142.0 142.0
95
12-Jun-06 2776.85 13-Jun-06 14-Jun-06 15-Jun-06
-89.5
89.5 113.6 30.5
28.58 26.54 24.64 34.74 38.80 37.92
57.13 0.50 33.35 61.16 0.43 30.26 58.97 0.42 29.47 54.76 0.63 38.82 50.85 0.76 43.28 47.22 0.80 44.54 47.81 0.74 42.41 44.40 0.84 45.55 41.23 0.96 48.98 38.28 1.05 51.21 35.55 1.06 51.57 40.66 0.86 46.36 37.75 0.94 48.42 35.15 0.94 48.35 32.64 0.97 49.31 30.31 1.28 56.14 28.15 1.34 57.22 27.01 1.29 56.41 25.09 1.46 59.36 26.20 1.30 56.49 30.08 1.05 51.22 27.93 1.22 54.94 27.78 1.14 53.23 25.80 1.36 57.61 25.86 1.26 55.74 27.29 1.11 52.56 33.61 0.84 45.51 32.21 0.81 44.73 34.26 0.71 41.41 31.81 0.91 47.63 35.11 0.77 43.34 32.60 0.85 46.08 30.28 0.98 49.58 28.11 1.16 53.71 26.10 1.29 56.26 26.05 1.20 54.48 24.19 1.23 55.23
2663.3 -113.6 2632.8 -30.5
2798.8 166.0 166.0 91.5 26.6 -55.6 62.1 71.3 47.9 7.6 62.1 71.3 47.9 7.6 107.1 39.3 1.3 16.8 91.5 26.6 55.6
16-Jun-06 2890.35 19-Jun-06 20-Jun-06 2916.9 2861.3
35.22 37.14 39.58 40.18 37.85 35.15 35.44 32.91 31.76 38.80 37.65
21-Jun-06 2923.45 22-Jun-06 2994.75 23-Jun-06 25-Jun-06 26-Jun-06 3042.7 3050.3
2943.2 -107.1 39.3 -1.3 16.8
27-Jun-06 2982.45 28-Jun-06 29-Jun-06 30-Jun-06 2981.1 2997.9
3128.2 130.3 130.3 22.8 -12.3 58.4 -40.7 -80.6 66.2 -25.8 79.8 -26.6 -46.0 79.8 26.6 46.0 115.8 13.9 60.9 90.3 78.1 40.8 54.7 69.7 46.0 25.3 12.4 66.2 25.8 58.4 40.7 80.6 22.8 12.3
3-Jul-06 3150.95 4-Jul-06 3138.65 5-Jul-06 6-Jul-06 3197.1 3156.4
34.96 36.64 34.02 31.59 34.06 31.63 35.06 32.56 30.23 28.07 26.07 24.21 28.93 26.86 27.86 29.77 32.62 33.58 31.18 29.84
7-Jul-06 3075.85 10-Jul-06 3142
11-Jul-06 3116.15 12-Jul-06 13-Jul-06 3195.9 3169.3
14-Jul-06 3123.35
17-Jul-06 3007.55 -115.8 18-Jul-06 2993.65 19-Jul-06 2932.75 20-Jul-06 3023.05 21-Jul-06 2945 -13.9 -60.9 90.3 -78.1 40.8 54.7 69.7 46.0 -25.3 12.4
24-Jul-06 2985.85 25-Jul-06 3040.5
26-Jul-06 3110.15 27-Jul-06 3156.15 28-Jul-06 31-Jul-06 3130.8 3143.2
96
1-Aug-06 2-Aug-06 3-Aug-06
3147.8 3182.1 3190
4.6 34.3 7.9 -13.3 -25.7 61.3 42.2 5.5 14.3 38.8 43.0 -2.2 2.8 9.3 -1.4
4.6 34.3 7.9 13.3 25.7 61.3 42.2 5.5 14.3 38.8 43.0 2.2 2.8 9.3 1.4
28.04 28.48 27.01 25.08 23.29 26.01 27.16 25.62 24.80 25.80 27.03 25.09 23.51 22.49 20.88 19.39
22.46 1.25 55.52 20.86 1.37 57.73 19.37 1.39 58.24 18.93 1.33 56.99 19.41 1.20 54.54 18.02 1.44 59.06 16.74 1.62 61.88 15.54 1.65 62.24 14.43 1.72 63.22 13.40 1.93 65.82 12.44 2.17 68.47 11.71 2.14 68.19 10.87 2.16 68.38 10.10 2.23 69.02 9.47 2.20 68.79 8.80 2.20 68.79
4-Aug-06 3176.75 7-Aug-06 8-Aug-06 9-Aug-06 10-Aug-06 3151.1 3212.4 3254.6 3260.1
11-Aug-06 3274.35 14-Aug-06 3313.1
16-Aug-06 3356.05 17-Aug-06 3353.9
18-Aug-06 3356.75 21-Aug-06 22-Aug-06 3366 3364.6
97
100.00
SNP Nifty
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 0.00 23-Jan 30-Jan 6-Feb 13-Feb 20-Feb 27-Feb 6-Mar 13-Mar 20-Mar 27-Mar 3-Apr 10-Apr 17-Apr 24-Apr
2500
1-May 8-May 15-May 22-May 29-May 5-Jun 12-Jun 19-Jun 26-Jun 3-Jul 10-Jul 17-Jul 24-Jul 31-Jul 7-Aug 14-Aug 21-Aug RSI
2700
2900
3100
3300
3500
3700
3900
RSI
NIFTY
Date
Close
23 -J 30 an -J a 6- n F 13 eb -F 20 eb -F 27 eb -F e 6- b M 13 ar -M 20 ar -M 27 ar -M a 3- r Ap 10 r -A 17 pr -A 24 pr -A 1- pr M a 8- y M 15 ay -M 22 ay -M 29 ay -M a 5- y Ju 12 n -J 19 un -J 26 un -J un 3Ju 10 l -J 17 ul -J 24 ul -J 31 ul -J 7- ul A 14 ug -A 21 ug -A ug
98
RSI RSI = 100 - [100/(1 + RS)] where: RS = (Avg. of n-day up closes)/(Avg. of n-day down closes) n= days (9 - 15 day RSI)
The RSI ranges from 0 to 100. At around the 70 level, a stock is considered overbought and one should expect fall in the price of stock. Levels below 30 refer to oversold position and one can expect upward movement in the price of stock from the current level. I
Methodology for RSI calculation For the calculation of RSI, 14 day moving average period is used.
In the above chart, three month NIFTY data is used starting since 2
nd
January till 22nd August.
Interpretation In the above RSI chart, RSI was hovering around the level of 60-70 in the month of JanuaryFebruary, suggesting the early indications that the market may heat up in the days to come. In the month of March and April and 1st 15 days of May ,when NIFTY was at its peak, RSI levels went further to 80 , thus giving a clear indication that market has heaten up and the bull phase is about to get over and one should expect the prices to cool down from the current levels of 3500-3600. In the end of may , after the bull phase as indicated by RSI, market went crashing down and the bear phase continued till mid June , where again RSI level turned to 30 , thus suggesting that market may gain in the near period. The end of bear phase after mid june paved the way for anpther bull phase which continued till end of august. Implications for Option traders
99
In January and February, since RSI was at 60 levels and increasing towards 70-80, once could have expected NIFTY to go up and thus a Long Call/ Short put would have been appropriate strategy.
In April and May RSI was at 80 levels, indicating at bearish market, one should have taken short call/ long put.
In mid June as the RSI was at 30 levels, indicating another bull phase, Long Call and Short put should have been appropriate strategy to take.
100
Trading Strategy using Options:
Using Single Option and the stock: Long Position in the stock + Short Position in the Call Option. Short Position in the stock + Long Position in the call Option. Long Position in the stock +Long Position in the Put option Short Position in the stock + Short Position in the Put option Bull Spread: Buying the call option with a strike price and selling the call option on the same stock with a higher strike price. In the Bull Spread if the Stock price does well then the payoff for the investor will be the difference between 2 exercise price. If on the expiration date the stock price lies in between the two exercise price then the payoff will be Strike Price less the Lower exercise price( Long Call). If the stock price is less than both the exercise price then both the calls remain unexercised and investor will lose the initial cost of the spread. In Bull spread the loss as well as the maximum payoff is limited. In return for giving upside potential investor reduces the Spread cost by initial outlay from writing the call option. 3 types of Bull spreads can be distinguished: Both the calls initially out of the money – Most Aggressive One call in the money and other call out of money- Less aggressive Both the calls in the money- Conservative
101
Bull Spread with Calls:
Long Call -Lower Strike Price Short Call -Higher Strike Price
Bull spreads with Puts:
In Bull spread with Put one put is written with higher strike price and investor buys one put with lower exercise price. Because Put that is written with higher strike price in involves an initial cash inflows. If on the expiration date , the strike price is higher than both the Exercise price , then both the Put will exercise worthless and investor will gain an amount equal to initial cash inflow. If on the expiation date , the strike price is lower than both the exercise price then both the Put will be exercised and there will be loss equal to difference between both the exercise price. If on the expiration date, the strike price is between two exercise price ,then the Put that is written (i.e.) with higher strike price will be exercised and the Put that is bought will expire worthless. The resulting loss in this case will be Higher exercise price less the strike price.
Bull spread with put
Long Put - Lower Strike Price. Short Put – Higher Strike Price
BULL SPREAD WITH PUT
102
On 2nd may when the index was at 1916.75 and if investor is bullish about the market but at the same time he wants to reduce his risk he can use Bull Spread. Suppose an investor buys 2050 Put and at the same time sells 2100 Put then initial inflow will be:
Proceeds from writing a Put Initial outlay from Long Put Initial Inflow 195.00 147.65 47.35
His position as on 26th may when the index was at 2074.70 will be Put that is written for 2100 will be exercised resulting in loss of Rs 25.30 and Put that is bought will expire worthless Thus investor has earned Rs 22.05(47.35-25.30).
Payoff Structure from Bull Spread with Puts: Short Put with exercise Spot Price 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 price of 2100 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 Long Put with exercise price of 2050 10 5 0 0 0 0 0 0 0 0 0 0 Payoff -50 -50 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 Initial Inflow 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 47.35 Total Payoff -2.65 -2.65 -2.65 2.35 7.35 12.35 17.35 22.35 27.35 32.35 37.35 42.35
103
2100 2105 2110 2115
0 0 0 0
0 0 0 0
0 0 0 0
47.35 47.35 47.35 47.35
47.35 47.35 47.35 47.35
Pay off Bull -Put
50.00
40.00
30.00
Payoff
20.00
Pay off Bull -Put
10.00
0.00 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 2100 2105 2110 2115
-10.00 Spot Pricd
BULL SPREAD WITH CALL
On 2nd may when the index was at 1916.75 and if investor is bullish about the market but at the same time he wants to reduce his risk he can buy Spread.Suppose an investor buys 2050 call and at the same time sells 2100 call then the total investment will be: Proceeds from writing a call Initial outlay from Long Call Initial Cost of Spread 1.90 3.80 1.90
His position as on 26th may when the index was at 2074.70 will be 104
Short Call of 2100 will be unexercised Long Call of 2050 will be exercised resulting in pay off of 24.70 Thus investor has earned Rs24.70 against initail investment of just Rs 1.90
Payoff Structure from Bull Spread with Calls: Long call with Short Call with exercise Spot Price 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 2100 2105 2110 2115 price of 2100 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 -10 -15 exercise price of 2050 0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Payoff 0 0 0 5 10 15 20 25 30 35 40 45 50 50 50 50 Cost 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 Total Payoff -1.90 -1.90 -1.90 3.10 8.10 13.10 18.10 23.10 28.10 33.10 38.10 43.10 48.10 48.10 48.10 48.10
105
60.00
50.00
40.00
30.00 Payoff 20.00 10.00 0.00 2040 2045 2050 2055 2060 2065 2070 2075 2080 2085 2090 2095 2100 2105 2110 2115 -10.00 Spot price Bull -Put
Bear spread :
Bear spread with Call :
Buying a call Option with one strike price and selling a call with another strike price with lower strike price. Long Call -Higher Strike Price. Short Call -Lower Strike Price.
Bear Spread with Put :
Long Put - Higher Strike Price. Short Put Volatility Spread: Backspread Ratio Vertical Spread Straddle - Lower Strike Price
106
Strangle Butterfly
Back spread:
Back spread is a delta neutral position which consists of more long Options than short Options where all the Options expire at the same time. In order to achieve this Options with smaller deltas must be purchased and Option with larger deltas must be sold. The primary consideration of a Backspread is that some movement will occur. A trader will go for Call Backspread if he expects market to go up and will take Put Backspread if he expects market to go down. Call Back Spread : Long Calls - Higher exercise price Short Calls - Lower exercise price. Put Back spread : Long Puts - Lower exercise price Short Puts - Higher exercise price.
(Long calls should be more than short calls to make it delta neutral).
Ratio Vertical Spread:
In this trader takes opposite position of backspread , and is short more contracts than long with all the options expiring on the same date. Ratio vertical spread realizes its maximum value when stock price finishes right at the exercise price. Its taken by someone who expects the market to be quite stable.
107
Call ratio vertical Spread : Long calls - Lower exercise price Short calls - Higher exercise price. Put ratio vertical spread : Long put - Higher exercise price Short put - Lower exercise price. ( short calls will be more to make it delta neutral). Backspread will gain if the market moves outside the limits and will lose if the stock price remains with the range of Higher and lower strike price.
Ratio Vertical Spread will gain if the market is within the range of lower and higher exercise price and will lose if the stock price is outside this range.
108
Butterfly spread:
Long Butterfly :
Buying a call Option with higher and lower strike price and selling two call options with strike price average of the above two strike price. This strategy is suited for an investor who feels that the large price changes are unlikely. Long Butterfly acts like a ratio vertical spread. If the strike price is less than Lowest strike price all the calls will not be exercised and will result in loss to the amount of initial investment. If Strike price is higher than H then all the calls will be exercised and it will result in the loss because gains from buying call will be equalized by loss from writing call option. If on the expiration date if the spot price is between H and L then the strategy will result in a profit with maximum profit when the strike price is in the mid way between the H and L.
Short Butterfly:
Write 2 calls with higher and lower strike price and buy 2 calls with the exercise price in between H and L. This strategy works like backspread and is undertaken by the trader when he expects the market to move sharply in either direction. If the market remains within H and L range then Short butterfly results in loss to the trader. Straddle : Investors buys(sells) Call and Put with same expiration date with same strike price. If both Call and Put Option are purchased then it is Long Straddle ( Bottom Straddle)and if both Call and Put Option are sold then it is Short Straddle. Trader’s buy Straddles and Strangles when they believe that the underlying asset will be volatile but do not have any belief about the direction of the underlying. They will benefit from Put option when the market turns bearish and they will benefit from Call Option when the market turns Bullish..
109
With a Long straddle , the trader’s potential profit is unlimited if market moves in either direction. A loss will be incurred if the market does not move away from the exercise price since in that case both Call and Put will not be exercised. Buying a straddle is an appropriate strategy when large price changes are expected in the stock. A short Straddle( Top Straddle) will realize maximum profit if the market stays close to the call and put exercise price. The writer of straddle benefits from the price stability. They buy a straddle when they believe that the market will remain stable. Strangle: Buying a call and Put with same strike price and maturity date but with different strike price. In case of Long Strangle again the investor is not sure about the direction of the stock price but is expecting volatility. In case of Strangle the stock price has to move further away than the Straddle for an investor to make profit but at the same time downward risk in Strangle is less when compared to straddle when the stock ends up at the Central value. Thus the volatility spreads can be distinguished into 2 categories. Helped by the fluctuations in the Underlying Asset and those that are hurt by changes in the underlying asset. Strategies which are helped by changes in the underlying asset ( market is volatile) will have Positive Gamma and Positive Vega. So if the volatility increases then these strategies will bring positive payoff. The strategies which are helped by changes in the underlying price( direction immaterial ) movements are : Backspread Long straddle Long Strangle 110
Short Butterfly. Strategies which bring positive payoffs when the market is quite stable , have negative Gamma and Negative Vega. If the volatility decreases then the payoff from these strategies will increase. The strategies which come under this type are: Ratio vertical spread Short straddle Short Strangle Long Butterfly If an option is under priced (low implied volatility) then one should look for spreads with positive Vega (i.e.) Backspreads/Long Straddle /Long Strangle/ Short Butterfly. If an option is overpriced (high implied volatility) then one should look for spreads with negative Vega (i.e.) Ratio vertical Spread / Short Straddle / Short Strangle / Long Butterfly.
111
Calendar spread: Selling a call option and buying a longer maturity call option with the same strike price. Diagonal Spread : Where both the expiration date and strike price differ. Strap : Long Position in two calls and one put all with same strike price and expiration date. In this case investor is expecting sharp movement in the price of stock but is expecting strong intuition for upward movement so he buys 2 calls . Strips: Long Position in one call and two puts all with same strike price and expiration date. In the case of strips investor is expecting sharp movement in the stock price with greater expectation for downward movement in the stock price hence he buys 2 puts . Long Strangle If the Index on 1st April is at 2067.65 and investor is expecting Volatility and at the same time he wants to minimize the downward risk that occurs from straddle he can buy a strangle.If he buys a 2100 call and 1900 put for april then the total cost for him will be Long Call Long Put 2100 2050 3.00 37.95
Total Cost
40.95
Position at expiration (28th April) 1941.3
112
Call Option Put Option
2100 2050
0 108.7
Net returns
67.75
Individual Pay off Call Spot Price 1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 Put Call 2100 Put 2050 Payoff Cost of Straddle 175 150 125 100 75 50 25 0 0 0 25 50 75 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 40.95 Total Payoff 134.05 109.05 84.05 59.05 34.05 9.05 -15.95 -40.95 -40.95 -40.95 -15.95 9.05 34.05 Strategy Pay off
2100 2050 0 0 0 0 0 0 0 0 0 0 25 50 75 175 150 125 100 75 50 25 0 0 0 0 0 0
-3.00 137.05 -3.00 112.05 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 22.00 47.00 72.00 87.05 62.05 37.05 12.05 -12.95 -37.95 -37.95 -37.95 -37.95 -37.95 -37.95
113
2200 2225 2250 2275
100 125 150 175
0
97.00
-37.95 -37.95 -37.95 -37.95
100 125 150 175
40.95 40.95 40.95 40.95
59.05 84.05 109.05 134.05
0 122.00 0 147.00 0 172.00
200
Long Strangle
Long Strangle 150 Call 2100 Put 2050
100
Payoff
50
0 1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225 2250 2275
-50
-100 Spot
114
Short Strangle On 6th May when index was at 1977.50, if an investor shorts 100 2050 Calls and 100 2100 puts for May month with exercise price 2050 having an expiration date on 26th may, then the total credit to the investor will be: Short Call Short Put Initail Inflow Position on expiration date (may 26th) 2050 2100 8.30 139.75 148.05 2074.7
Call
Put
Short Call
Short Put Initial Total Payoff -79.20 -54.20 -29.20 -4.20 20.80 45.80 70.80 95.80 95.80
Spot Price 1875 1900 1925 1950 1975 2000 2025 2050 2075
2050 0 0 0 0 0 0 0 0 -25
2100 -225 -200 -175 -150 -125 -100 -75 -50 -25
2050 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 -16.70
2100 Payoff -85.25 -60.25 -35.25 -10.25 14.75 39.75 64.75 89.75 114.75 -225 -200 -175 -150 -125 -100 -75 -50 -50
Credit 145.80 145.80 145.80 145.80 145.80 145.80 145.80 145.80 145.80
115
2100 2125 2150 2175 2200 2225 2250 2275
-50 -75 -100 -125 -150 -175 -200 -225
0 0 0 0 0 0 0 0
-41.70 -66.70 -91.70 -116.70 -141.70 -166.70 -191.70 -216.70
139.75 139.75 139.75 139.75 139.75 139.75 139.75 139.75
-50 -75 -100 -125 -150 -175 -200 -225
145.80 145.80 145.80 145.80 145.80 145.80 145.80 145.80
95.80 70.80 45.80 20.80 -4.20 -29.20 -54.20 -79.20
200.00
Pay off from Short Strangle
150.00
100.00
50.00
Pay off
0.00 1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225 2250 2275
-50.00
-100.00
-150.00
Pay off from Short Straddle
Short Call 2050
Short Put 2100
Spot Price on expiry -200.00
-250.00
Long Strangle On 9th march when index was at 2160.80 ,if an investor buys 100 calls and 100 puts
116
for January month with exercise price 2100 having an expiration date on 31st march, then the total cost to the investor will be:
Long Call Long Put Total cost
2100 2100
400.20 17.80 418
Index on expiration date Call Option Put Option Net payoff 2100 2100 2030.65 0 69.35 -348.65
Payoff from Long Spot Price Call 2100 1925 1950 1975 2000 2025 2050 2075 2100 0 0 0 0 0 0 0 0 Put 2100 175 150 125 100 75 50 25 0 Individual Payoff Long Call 2100 -400.20 -400.20 -400.20 -400.20 -400.20 -400.20 -400.20 -400.20 Long Put 2100 157.20 132.20 107.20 82.20 57.20 32.20 7.20 -17.80 175 150 125 100 75 50 25 0 418 418 418 418 418 418 418 418 -243 -268 -293 -318 -343 -368 -393 -418 Total Payoff Cost of Straddle Net Pay off
117
2125 2150 2175 2200 2225 2250 2275
25 50 75 100 125 150 175
0 0 0 0 0 0 0
-375.20 -350.20 -325.20 -300.20 -275.20 -250.20 -225.20
-17.80 -17.80 -17.80 -17.80 -17.80 -17.80 -17.80
25 50 75 100 125 150 175
418 418 418 418 418 418 418
-393 -368 -343 -318 -293 -268 -243
200
Long Straddle
100
Long Straddle Long Call 2100 Long Put 2100
0 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225 2250 2275
-100 Payoff -200 -300 -400
-500
Spot
Short Straddle On 6th May when index was at 1977.50, if an investor shorts 100 calls and 100 puts for May month with exercise price 2050 having an expiration date on 26th may, then the total
118
credit to the investor will be:
Short Call Short Put Initial Credit
2050 2050
8.30 80.65 88.95 2074.70 -24.70 0.00 64.25
Position At expiration date. Short Call Short Put Net Position 2050 2050
Example: Short Stradle
On 6th May when index was at 1977.50, if an investor shorts 100 calls and 100 puts for May month with exercise price 2050 having an expiration date on 26th may, then the total credit to the investor will be:
Short Call Short Put Initial Credit
2050 2050
8.30 80.65 88.95 2074.70 -24.70 0.00 64.25
Position At expiration date. Short Call Short Put Net Position 2050 2050
119
loss from short
Individual Strategies
Total
Income from Net Pay
Spot Price
Call 2050
Put 2050 -175 -150 -125 -100 -75 -50 -25 0 0 0 0 0 0 0 0
Call 2050 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 -16.70 -41.70 -66.70 -91.70 -116.70 -141.70 -166.70
Put 2050 -94.35 -69.35 -44.35 -19.35 5.65 30.65 55.65 80.65 80.65 80.65 80.65 80.65 80.65 80.65 80.65
loss
straddle off
1875 1900 1925 1950 1975 2000 2025 2050 2075 2100 2125 2150 2175 2200 2225
0 0 0 0 0 0 0 0 -25 -50 -75 -100 -125 -150 -175
-175 -150 -125 -100 -75 -50 -25 0 -25 -50 -75 -100 -125 -150 -175
88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95 88.95
-86.05 -61.05 -36.05 -11.05 13.95 38.95 63.95 88.95 63.95 38.95 13.95 -11.05 -36.05 -61.05 -86.05
120
150.00
Short Straddle
100.00
50.00
0.00 Pay off 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 -16.70 -41.70 -66.70 -91.70 -116.70 -141.70 -166.70
-50.00
-100.00
-150.00
Pay off from Short Straddle Call 2050 Put 2050
Spot Price on expiration -200.00
Volatility Spot Date Nifty Daily returns Date Spot Nifty Daily returns
2-Jan-06 2835.95 3-Jan-06 2883.35 4-Jan-06 2904.4 0.0166 0.0073 -0.0016 0.0049 -0.0013 -0.0136 -0.0070 -0.0001
21-Apr-06 24-Apr-06 25-Apr-06 26-Apr-06 27-Apr-06 28-Apr-06 29-Apr-06 2-May-06 3-May-06
3573.05 3548.9 3462.65 3555.75 3508.1 3508.35 3557.6 3605.45 3634.25
-0.0001 -0.0068 -0.0246 0.0265 -0.0135 0.0001 0.0139 0.0134 0.0080
5-Jan-06 2899.85 6-Jan-06 9-Jan-06 10-Jan-06 12-Jan-06 2914 2910.1 2870.8 2850.7
13-Jan-06 2850.55
121
16-Jan-06 17-Jan-06 18-Jan-06
2833.1 2829.1 2809.2
-0.0061 -0.0014 -0.0071 0.0217 0.0104 -0.0058 0.0083 0.0111 0.0143 -0.0028 0.0089 -0.0099 -0.0014 -0.0091 0.0201 0.0065 -0.0037 0.0062 0.0045 -0.0078 0.0015 -0.0002 -0.0134 0.0081
4-May-06 5-May-06 8-May-06 9-May-06 10-May-06 11-May-06 12-May-06 15-May-06 16-May-06 17-May-06 18-May-06 19-May-06 22-May-06 23-May-06 24-May-06 25-May-06 26-May-06 29-May-06 30-May-06 31-May-06 1-Jun-06 2-Jun-06 5-Jun-06 6-Jun-06
3648.4 3663.95 3693.15 3720.55 3754.25 3701.05 3650.05 3502.95 3523.3 3635.1 3388.9 3246.9 3081.35 3199.35 3115.55 3177.7 3209.6 3214.9 3185.3 3071.05 2962.25 3091.35 3016.65 2937.3
0.0039 0.0043 0.0079 0.0074 0.0090 -0.0143 -0.0139 -0.0411 0.0058 0.0312 -0.0701 -0.0428 -0.0523 0.0376 -0.0265 0.0198 0.0100 0.0016 -0.0092 -0.0365 -0.0361 0.0427 -0.0245 -0.0267
19-Jan-06 2870.85 20-Jan-06 2900.95 23-Jan-06 2884.05 24-Jan-06 2908
25-Jan-06 2940.35 27-Jan-06 2982.75 30-Jan-06 31-Jan-06 2974.5 3001.1
1-Feb-06 2971.55 2-Feb-06 2967.45 3-Feb-06 2940.6
6-Feb-06 3000.45 7-Feb-06 3020.1
8-Feb-06 3008.95 10-Feb-06 3027.55 13-Feb-06 3041.15 14-Feb-06 3017.55 15-Feb-06 16-Feb-06 17-Feb-06 3022.2 3021.6 2981.5
20-Feb-06 3005.85
122
21-Feb-06 22-Feb-06 23-Feb-06
3035.5 3050.8 3062.1
0.0098 0.0050 0.0037 -0.0039 0.0057 0.0024 0.0156 0.0088 -0.0011 0.0136 -0.0024 -0.0210 0.0040 0.0174 0.0059 -0.0023 0.0097 0.0023 0.0097 -0.0010 -0.0068 0.0022 0.0100 0.0127
7-Jun-06 8-Jun-06 9-Jun-06 12-Jun-06 13-Jun-06 14-Jun-06 15-Jun-06 16-Jun-06 19-Jun-06 20-Jun-06 21-Jun-06 22-Jun-06 23-Jun-06 25-Jun-06 26-Jun-06 27-Jun-06 28-Jun-06 29-Jun-06 30-Jun-06 3-Jul-06 4-Jul-06 5-Jul-06 6-Jul-06 7-Jul-06
2860.45 2724.35 2866.3 2776.85 2663.3 2632.8 2798.8 2890.35 2916.9 2861.3 2923.45 2994.75 3042.7 3050.3 2943.2 2982.45 2981.1 2997.9 3128.2 3150.95 3138.65 3197.1 3156.4 3075.85
-0.0265 -0.0487 0.0508 -0.0317 -0.0418 -0.0115 0.0611 0.0322 0.0091 -0.0192 0.0215 0.0241 0.0159 0.0025 -0.0357 0.0132 -0.0005 0.0056 0.0425 0.0072 -0.0039 0.0185 -0.0128 -0.0259
24-Feb-06 3050.05 27-Feb-06 3067.45 28-Feb-06 1-Mar-06 2-Mar-06 3074.7 3123.1 3150.7
3-Mar-06 3147.35 6-Mar-06 7-Mar-06 8-Mar-06 9-Mar-06 10-Mar-06 3190.4 3182.8 3116.7 3129.1 3183.9
13-Mar-06 3202.65 14-Mar-06 3195.35 16-Mar-06 3226.6
17-Mar-06 3234.05 20-Mar-06 3265.65 21-Mar-06 3262.3
22-Mar-06 3240.15 23-Mar-06 3247.15 24-Mar-06 3279.8
27-Mar-06 3321.65
123
28-Mar-06 29-Mar-06
3325 3354.2
0.0010 0.0087 0.0191 -0.0048 0.0206 0.0028 0.0079 -0.0161 0.0068 -0.0287 -0.0103 0.0235 0.0268 0.0050 0.0106
10-Jul-06 11-Jul-06 12-Jul-06 13-Jul-06 14-Jul-06 17-Jul-06 18-Jul-06 19-Jul-06 20-Jul-06 21-Jul-06 24-Jul-06 25-Jul-06 26-Jul-06 27-Jul-06
3142 3116.15 3195.9 3169.3 3123.35 3007.55 2993.65 2932.75 3023.05 2945 2985.85 3040.5 3110.15 3156.15
0.0213 -0.0083 0.0253 -0.0084 -0.0146 -0.0378 -0.0046 -0.0206 0.0303 -0.0262 0.0138 0.0181 0.0226 0.0147
30-Mar-06 3418.95 31-Mar-06 3402.55 3-Apr-06 3473.3
4-Apr-06 3483.15 5-Apr-06 7-Apr-06 3510.9 3454.8
10-Apr-06 3478.45 12-Apr-06 13-Apr-06 3380 3345.5
17-Apr-06 3425.15 18-Apr-06 3518.1
19-Apr-06 3535.85 20-Apr-06 3573.5
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CALCULATION OF HISTORICAL VOLATILITY: Standard deveation of daily Historical Volatility = No of Days return * ? No of days 252 Trading days
Average NIFTY
3119.44
STANDARD DEVEATION
210.85
Average daily returns
0.003256
Annual Returns
82.05%
Standard deveation of daily return
0.010450
Historical Volatility
16.52%
Calculation of Implied Volatility
Input Variables: Stock Price Exercise Price 2724.35 3000.00
125
Current date Expiration date Risk free Interest rate Dividend yield
8-Jun-06 29-Jun-06 5.00% 2.00%
Time
0.057534247 years Call 39.95 Put 335.35
Theorotical Price of Stock Option
Parameters of Option Delta Gamma Theta Vega Rho
Call 0.2276 0.00094 -856.45 197.10 -33.37
Put -0.7713 0.00094 -761.30 197.10 -138.74
Actual Option Price
39.95
335.35
Implied Volatility of Call Implied Volatility of Put
49.03% 61.04%
126
In order to Calculate Implied Volatility of Call and Put Option when all other inputs of the Black scholes model are given, we can do it by solving using Corrado Miller Approach or Newton Raphson Technique. The Implied Volatility for Call and Put Option obtained is 47.03% and 53.07% when strike price is 20 for Stock selling at 17.5 having Call Price in Market at 3.5 and Put price as 0.85.
127
OBJECTIVE BEHIND THE RESEARCH:
Investment Decision Making Factors in STOCK & DERIVATIVE form of Investment:
1) To determine the important macro-economic factors that determines the investment decision. 2) To find out which of the important factors influence investor to choose a particular company and particular sector while making investment decisions. 3) Cluster the respondents according to their according to the factors that determine their investment decisions. 4) To construct a perceptual map to find out the perception of each sector according to various factors. 5) To find out the investment behavior of respondents (speculative, long term, hedger or arbitrager) using discriminant analysis. 6) To determine the most ideal strategy considered by investors and brokers • • When market is bullish When market is bearish
7) To find out which option strategy can command the maximum premium.
SAMPLE SIZE: 30 respondents.
128
EXECUTIVE SUMMARY: The objective of this research is to determine the factors that determine the investing decision for an investor for a particular Company as well as particular firm. It also determines the perception of some of the industrial sectors based on the attributes give by the respondents. In addition to that the investors have been segregated based on the cluster analysis into groups so that investors can be segregated into groups for better understanding the motives for investment. Through Discriminate analysis, the behavior of investors is predicted so that investors could be classified into various groups based on their investing activity by getting score on the factors that they consider while investing in a stock. The research also determines the most optimal strategy while investing in Options through use of Conjoint analysis for both the market conditions (Bullish and Bearish.)
ADVANCE STATISTICAL METHODS:
129
Research Area Research Problem:
: Stocks and Derivatives.
Forecasting the future stock trends based on past movements.
Parameters reflecting on Index or Stock Movement
1. Financial performance of Company. 2. Daily volumes (Transactions of particular stock). 3. Exchange rate movement. 4. GDP growth rate. 5. Interest rate movements. 6. FII inflows and outflows. 7. Volatility. 8. Inflation. 9. Dividends, Bonus shares, right issue, and IPO’s. Analyzing the impact of the above macro-economic variables on sector performance. Clustering of Shares based on their annualized returns and determination of cause of inter-relationship between shares within each groups and explanation of inter and intra group effects.
Analyzing the impact of spot price on Future’s and Option price. Determination of inter-relationship between theoretical Call and Put price (using Black-Scholes pricing model) with actual market price of Call and Put.
130
Call Option and Put Option are influenced by the following 5 factors (Black- Schloes pricing model). Analyzing how much each of the factor is actually reflected in the Option Price. 1. Spot price. 2. Exercise price. 3. Volatility. 4. Time to expiry. 5. Interest rate.
131
EXHIBIT 1: Age profile of respondents
50
40
30
20
10
Percent
0 <24 24-35 36-45 >45
Age
Age Cumulative Percent 23.3 66.7 83.3 100.0
Valid
<24 24-35 36-45 >45 Total
Frequency 7 13 5 5 30
Percent 23.3 43.3 16.7 16.7 100.0
Valid Percent 23.3 43.3 16.7 16.7 100.0
132
Income Profile:
50
40
30
20
10
Percent
0 <3,00,000 6,00,000-10,00,000 3,00,000-6,00,000 >10,00,000
Income
Income Cumulative Percent 26.7 70.0 90.0 100.0
Valid
<3,00,000 3,00,000-6,00,000 6,00,000-10,00,000 >10,00,000 Total
Frequency 8 13 6 3 30
Percent 26.7 43.3 20.0 10.0 100.0
Valid Percent 26.7 43.3 20.0 10.0 100.0
133
40
30
20
10
Percent
0 50,000 1,50,000-3,00,000 50,000-1,50,000 3,00,000-7,00,000
Yearly volume
Yearly volume Cumulative Percent 26.7 63.3 90.0 100.0
Valid
50,000 50,000-1,50,000 1,50,000-3,00,000 3,00,000-7,00,000 Total
Frequency 8 11 8 3 30
Percent 26.7 36.7 26.7 10.0 100.0
Valid Percent 26.7 36.7 26.7 10.0 100.0
40
30
20
10
Percent
0 < 50,000 1,50,000-3,00,000 7,00,000=10,00,000 >10,00,000 50,000-1,50,000 3,00,000-7,00,000
Portfolio
134
Portfolio Cumulative Percent 3.3 16.7 46.7 73.3 90.0 100.0
Valid
< 50,000 50,000-1,50,000 1,50,000-3,00,000 3,00,000-7,00,000 7,00,000=10,00,000 >10,00,000 Total
Frequency 1 4 9 8 5 3 30
Percent 3.3 13.3 30.0 26.7 16.7 10.0 100.0
Valid Percent 3.3 13.3 30.0 26.7 16.7 10.0 100.0
Option
Spot
Futures
135
Arbitrage
Speculation
Hedging Long term investment
Motive for investment Cumulative Percent 20.0 46.7 80.0 100.0
Valid
Speculation Hedging Long term investment Arbitrage Total
Frequency 6 8 10 6 30
Percent 20.0 26.7 33.3 20.0 100.0
Valid Percent 20.0 26.7 33.3 20.0 100.0
136
Cluster Membership Case Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Cluster 3 2 3 2 3 3 3 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 Distance 5.316 3.929 4.481 4.054 2.314 2.795 6.134 4.823 3.502 3.410 5.734 3.942 2.968 5.334 4.207 4.484 3.401 3.656 2.763 3.826 4.021 3.711 5.601 5.413 7.557 4.806 3.221 3.373 6.616 4.677
137
STATISTICS FOR RESTONDENTS: For the purpose of research , a sample of 30 respondents were selected. Age Profile of respondents: Out of 30 respondents, 66.67% of them were under the age group of 35 and (20) and 10 respondents were above of the age 36 and above.
Income
profile of respondents: Of the 30,respondents were under the upper income
category 30% were with income category of Rs6,00,00 and above family income and 26.65 of them were under the income category of Rs3,00,00 and below. For the purpose of income, annual family income of the respondent was used to segregate them into the groups.
Investment Profile of Respondents: Most of the sample population studied for the purpose were actively trading in the stock market with 36.7% of sample size were having annual volume of transactions worth more than Rs1,50,000 an year and 36.65 of them had annual volume of transactions worth Rs50,00 to Rs 1,50,000. Only 26.75 of them traded thinly in the stock markets who had annual volume of transactions worth less than Rs50,000 an year.
83.4% of respondents had overall portfolio worth more than Rs3,00,00 invested in shares and futures over a period of time. Thus most of the respondents had invested huge amount of money in the shares market. Nature of respondents :33.335 of the sample size were long term investors ,20% speculators and arbitragers and 26.75 of them were hedgers. Thus the sample size was evenly distributed according to the nature of activity performed.
138
Trading instruments used: 46.75 of the sample size were active traders in the cash segment and 30% were actively involved in Options market.23.3% of them were primarily operating in the Futures segment.
Market awareness: Out of 30 respondents, 16 of them followed market on daily basis and only 4 of them followed on weekly basis. 10 respondents followed market on hourly basis. All the respondents who followed market on weekly basis were Long term investors and 83.35 of the arbitragers followed market on hourly basis.
Row and Column Points Symmetrical Normalization
1.0 .5 Speculation 0.0 Hourly Long term investment Motive for investmen weekly t How often makt follo -1.5 -1.5 -1.0 -.5 0.0 .5 1.0 1.5 2.0 wed -.5 Hedging Daily
Dimension 2
Arbitrage
-1.0
Dimension 1
The correspondence analysis conducted to get insight about the nature of investing activities and its relationship with following the market , concludes that Arbitragers follow market on Hourly basis, and long term investors follow market on less continuous basis. Most of the Hedgers and Speculators follow market on daily basis.
139
Market and Motive for investment :
Row and Column Points Symmetrical Normalization
1.0 Option .5 Long term investment Spot 0.0 Speculation -.5
Dimension 2
Hedging Futures Motive for investmen t
-1.0
-1.5 -1.5 -1.0 -.5 0.0 .5 1.0 1.5
Actively traded
Dimension 1
As seen by the above results of the correspondence analysis between nature of investing activity and Market actively traded, we can conclude that Long term investors invest in Spot market ,Hedgers in Futures market and Arbitragers in Option market. Speculators are in someway mid between Spot , Future and Options market concludes the fact that they tend to take a favorable position in any of the market according to the situation. These results can further be validate by the empirical studies and nature of these investors as Futures are the primary tool for taking hedged positions in order to minimize their overall risk of the portfolio. Also Long term investors operate in spot market as in India in Futures and Options market an investor can take a position only for maximum of 90 days which makes them short term investors.
140
Actively traded * Motive for investment Crosstabulation Count Motive for investment Long term Hedging investment 1 10 4 3 8 10
Actively traded Total
Spot Futures Option
Speculation 3 2 1 6
Arbitrage 1 5 6
Total 14 7 9 30
How often makt followed Count
How often makt followed Total
Hourly Daily weekly
Speculation 3 3
6
7
6
5
4
3
Motive for investmen
Speculation Hedging
2
1
C ount
Long term investment Arbitrage Hourly Daily w eekly
0
How often makt followed
Important Factors Determination While Choosing a Stock
FACTOR ANALYSIS In order to determine the important factors that investors consider while choosing a particular company over other provided three most important factors that together explained 77.935 of the total variance. 141
Total Variance Explained Initial Eigenvalues xtraction Sums of Squared Loading Rotation Sums of Squared Loadings Componen Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative % 1 5.387 53.866 53.866 5.387 53.866 53.866 3.213 32.133 32.133 2 1.388 13.883 67.749 1.388 13.883 67.749 2.526 25.263 57.395 3 1.018 10.181 77.930 1.018 10.181 77.930 2.053 20.534 77.930 4 .688 6.875 84.805 5 .510 5.098 89.903 6 .405 4.046 93.949 7 .220 2.204 96.154 8 .206 2.064 98.217 9 .131 1.312 99.530 10 704E-02 .470 100.000 Extraction Method: Principal Component Analysis.
Scree Plot
6
5
4
3
2
Eigenvalue
1
0 1 2 3 4 5 6 7 8 9 10
Component Number
142
Component Score Coefficient Matrix Component 2 -.121 -.088 .269 .360 .014 .217 .572 .240 .066 .201
1 Company Brand Name Sector of company Profits Dividends Mkt scenario Mkt share Promoters Management News Future price .068 .085 .103 .058 .303 .351 .203 .069 .361 .368
3 .496 .496 .150 -.008 .112 -.046 -.214 .159 .182 -.016
Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. Component Scores.
Three factors are identified based on Eigen Values one, are as follows:
Factor One:
Market Scenario, Market Share, News about the company and the price of
Company’s share in the Futures Market.
Factor two: Profits, Dividends, Promoters goodwill, Management.
Factor three: Company Brand name, Sector of the company,.
Factor 1 is termed as Current Market scenario that explains 32.13% of the variance, Factor 2 as Company’s profitability and goodwill that explains 25.62% of the variance and Factor 3 is named as Company’s reputation and sector which explains 20.53% of the variance. Thus the important factors that determine an investors decision to invest in a particular stock are :
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Current Market Scenario. Company’s Profitability. Company’s reputation and sector.
Factors Determining Investors Investment Decision (Macro economic factors that are taken into account before investing)
FACTOR ANALYSIS TO DETERMINE THE MOST IMPORTANT FACTORS THAT DETERMINE THE INVESTMENT DECISION: ( Macro level decisions)
KMO and Bartlett's Test Kaiser-Meyer-Olkin Measure of Sampling Adequacy. Bartlett's Test of Sphericity Approx. Chi-Square df Sig. .439 172.576 105 .000
Validity of test: Bartlett’s test of Sphericity indicates whether correlation matrix is an identity matrix, which would indicate that our variables are unrelated. Since the sig level is less than .05, it indicates that there are probably significant relationships among variables. Thus, Bartlett’s Test of Significance shows that our data is suitable for Factor analysis.
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Total Variance Explained Initial Eigenvalues % of Variance Cumulative % 22.449 22.449 15.339 37.788 13.286 51.074 9.358 60.432 8.610 69.042 6.887 75.929 5.931 81.860 4.500 86.360 3.945 90.305 3.311 93.617 2.303 95.920 1.715 97.635 1.213 98.848 .711 99.560 .440 100.000 Extraction Sums of Squared Loadings Total % of Variance Cumulative % 3.367 22.449 22.449 2.301 15.339 37.788 1.993 13.286 51.074 1.404 9.358 60.432 Rotation Sums of Squared Loadings Total % of Variance Cumulative % 3.268 21.784 21.784 2.200 14.664 36.449 2.013 13.420 49.869 1.585 10.563 60.432
Component Total 1 3.367 2 2.301 3 1.993 4 1.404 5 1.291 6 1.033 7 .890 8 .675 9 .592 10 .497 11 .346 12 .257 13 .182 14 .107 15 6.604E-02
Extraction Method: Principal Component Analysis.
Scree Plot
4
3
2
Eigenvalue
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Component Number
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Rotated Component Matrix
a
Component Bullish teand Bearish treand sensex movements Political factors- Internal Poliical factors -External Monsoon Sports Festival Govy policy statments RBI statments Interest rates FII movments Exchange rate Inflation rate Bank rate 1 -1.73E-02 -.156 -8.67E-02 .838 .815 -4.58E-02 .103 -.100 .891 .739 -1.19E-03 .219 .329 -.211 .553 2 -3.73E-02 .632 .637 -5.19E-02 -5.55E-02 .299 .157 -.172 -2.47E-02 -2.97E-02 .652 .763 -.215 .311 .306 3 .770 -8.53E-02 .307 -.208 .166 -1.63E-02 .667 -3.96E-02 -6.09E-02 .177 -7.48E-02 -9.07E-03 -.596 -.565 -.293 4 -9.30E-02 .209 -.210 1.214E-02 4.991E-02 .587 .559 .777 -.165 -.190 .207 -.141 -.170 .206 .170
Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 6 iterations.
The above analysis tells that there are four factors that have been identified to be significant while deciding the investment decision:
Factor one: Political Factors: (Political (Internal), Political (External), Government policy, RBI Statements, Bank rate.) which explains 21,74% of the variance, Factor two: Market Indicators (Bearish trend, Sensex movements, FII Movements. Interest rates) which explains 15.34% of the variance. Factor three: Economic Indicators: Bullish, Exchange rate, Inflation rate, which explains 13,26% of the variance. Factor four: External and Uncontrollable Factors: Monsoon, Sports, festival, which explains 9.36% of the total variance.
Overall these four factors explain 60.43% of the total variance.
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Thus based on the above two tests we can conclude following factors explain the overall investing decision while investing in general and investing in a particular company.
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CLUSTER ANALYSIS: CLUSTER ANALYSIS OF RESPONDENTS BASED ON THE FACTORS THAT THEY CONSIDER IMPORTANT WHILE INVESTING IN SHARE OF A PARTICULAR COMPANY.
Agglomeration Schedule Stage Cluster First Appears Cluster 1 Cluster 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 6 0 4 0 7 1 0 0 3 0 8 0 9 11 10 5 0 0 0 14 0 0 12 0 0 13 17 0 15 0 18 0 21 19 22 16 20 23 25 24 27 0 26 28
Stage 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Cluster Combined Cluster 1 Cluster 2 17 18 5 13 20 27 16 21 3 9 5 6 2 15 5 10 16 19 2 17 22 26 20 28 5 12 16 22 2 3 23 25 4 16 7 8 20 30 1 5 4 29 2 24 7 14 4 20 2 23 1 7 2 4 2 11 1 2
Coefficients 3.000 6.000 10.000 11.000 12.000 13.000 14.000 16.667 17.500 17.500 18.000 20.000 23.000 24.333 27.750 28.000 29.400 30.000 38.000 38.000 39.167 41.833 47.000 50.786 52.143 53.333 71.768 103.550 124.947
Next Stage 10 6 12 9 15 8 10 13 14 15 14 19 20 17 22 25 21 23 24 26 24 25 26 27 27 29 28 29 0
Since there is sudden jump in the co-efficient , from 71.78 to 103.55, there are three cluster solution.
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The three cluster analysis by using K-means Cluster show the following results.
The cluster analysis using K-means cluster for three clusters show that there are significant difference between the distances between the three clusters and number of cases in each cluster is 30.
Final Cluster Centers Cluster 2 6.80 5.60 3.40 2.20 8.80 7.70 3.80 3.00 8.50 8.40
1 Company Brand Name Sector of company Profits Dividends Mkt scenario Mkt share Promoters Management News Future price 8.30 6.60 7.50 8.00 5.10 5.70 6.90 8.20 5.20 4.90
3 6.60 6.70 5.80 5.70 7.30 6.40 4.80 4.90 7.30 7.40
Distances between Final Cluster Centers Cluster 1 2 3 1 11.453 6.509 2 11.453 5.500 3 6.509 5.500
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Number of Cases in each Cluster Cluster 1 2 3 4.000 15.000 11.000 30.000 .000
Valid Missing
Cluster Membership for each case The cluster analysis using K-means cluster for three clusters show that there are significant difference between the distances between the three clusters and number of cases in each cluster is 30.
THE RESPONDENT’S CHARACTERISTICS FOR THE CLUSTERS: Cluster one: The means for cluster one is maximum for these variables which show that for them Brand name, profits, Dividends, Promoters, and Management matter most while investing in shares. Respondent’s in cluster one tend to invest in mostly known companies who have reputable image in the public domain. Cluster two: The mean for cluster three is maximum for the variables Market scenario, Market share of the company, News and Price of stocks’ share in Futures market. This means that these investors take into account the current market situations as the most important variable while investing in shares of a particular company. Cluster three:
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Respondents in cluster three-show average mean of 5-6 in all the variables, these investors are mostly cautious investors who take into account all the relevant factors while investing in shares.
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PERCEPUAL MAPPING: BASED ON FACTOR SCORES: In order to get the perceptual map of different sectors based on the attributes, the mean score for each sector on different attributes was identified and factor analysis for these attributes was generated which resulted in two significant factors. Factor 1: Consistency, Profitability, Volume, and Growth - Returns Factor 2: Volatility and risk - Risk
Sector Auto Bank Cement Communication Construction Electronic FMCG Hotel Oil Pharma Power Technology
Consistency 5.77 7.27 4.33 4.97 3.97 6.07 6.13 4.67 7.7 6.23 4.87 5.3
Profitability 5.3 7.43 5.33 6.13 3.6 7.37 5.9 2.8 7.43 7.2 5.53 6.13
Volume 4.1 7.57 5.03 5.8 3.37 5.27 6.2 2.7 7.77 6.03 4.97 4.73
Growth 5.9 7.7 3.73 7.3 3.9 6.57 5.1 4.67 7.23 7.53 5.87 7.43
Volatility 3.87 5.83 4.43 6.17 5.6 6.07 4.3 6.3 4.17 6.63 5.73 5.9
Risk 4.6 4.03 4.1 5.7 4.8 5.2 4.57 6.3 5.67 6.93 4.7 6.9
fac1_1 -0.23938 1.409 -0.79594 0.15501 -1.56996 0.45415 0.21144 -1.59812 1.54364 0.72216 -0.34993 0.05794
fac2_1 -1.07003 -0.40675 -1.38829 0.79603 -0.26009 0.34647 -1.19855 0.96915 -0.5913 1.56529 -0.0877 1.32577
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Rotated Component Matrix Component 1 Consistency Profitability Volume Growth Volatility Risk .920 .945 .933 .822 -8.74E-02 3.902E-02
a
2 -9.08E-02 3.453E-02 -.181 .486 .868 .873
Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 3 iterations.
These factors were plotted in the two dimensional scale to get the perceptual map on the above two dimensions.
2.0 Oil 1.5 Bank
1.0 .5 FMCG 0.0 Auto Electronic
Pharma
Communication Technology Power
-.5 Cement -1.0 Construction Hotel
Return
-1.5 -2.0 -1.5 -1.0
-.5
0.0
.5
1.0
1.5
2.0
Risk
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INTERPRETATION OF THE PERCEPTUAL MAP: Dimensions for the perceptual map are Risk and Return. Following sectors are associated with high risk and high returns- Electronic, Communication, Technology, and Pharma. Hotel industry is the only sector that has highest risk and lowest returns. Cement, Automobile, Power, and Construction are the sectors that are perceived to have low risk and low returns and are more suitable for investors who have less risk appetite. Oil and Banking sector are the industries that are the least risky and provide the highest returns.
MULTI-DIMENSIONAL SCALING: Multi-dimensional scaling for each of the sectors, based on the Euclidean Distance Method provide similar results as obtained using the factor scores.
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Derived Stimulus Configuration Euclidean distance model
1.5 cement 1.0 oil banking .5 fmcg automobile construction power 0.0 electronic communication pharma -1.0 -1.5 -2 -1 0 1 2 3 hotel technology
Dimension 2
-.5
Dimension 1
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Derived Stimulus Configuration Euclidean distance model
1.5 cement volume fmcg consistency oil .5 banking automobile profitability construction 0.0 power electronic volatility communication growth pharma -1.0 -3 -2 -1 0 1 2 technology hotel 3 risk
1.0
Dimension 2
-.5
Dimension 1
Multidimensional scaling for different industrial sectors based on the six attributes is presented in the above two charts. These show the relative position of various industrial sector based on different attributes. The results of Multi-Dimensional scaling is summarized as follows:
Pharma, technology, Electronic and Communication industries stocks are perceived similar. Oil and Banking companies stock are perceived as similar in attributes. Automobile, Power, Construction and Cement are perceived similarly.
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Oil and Banking sector are considered to be the most Profitable sector. Pharma, technology, Electronic and Communication industries are considered to be the most growth oriented sector . FMCG stocks are considered to be most consistent in returns and have highest volumes in turnover in the market thereby providing most liquidity. Hotel industries stock are considered to be the least profitable and most dissimilar among the above mentioned sectors and are least favorable for investing.
CONJOINT ANALYSIS: For determining the most Optimal Strategy while choosing Option when the market is Bullish, In order to determine the most Optimum Strategy while choosing Options, respondents were given 9 combinations of strategy to choose from.
These combination were developed after conducting fractional factorial Orthogonal design.
The strategies were combination of four factors as follows: Strategy : Long Call or Short Put ( 2 levels) (Since under Bullish trend, a rational investor will only opt for Long call or short put and under Bearish scenario , he will opt for Short Call or Long Put) Premium( 3 levels) : In the money Option (In the money Options have Highest Premium), At the Money Option and Out of money Option (These kinds of Options have lowest premium). Time( 3 levels): Near month option, Next month Option and Far month Option.(Currently in India an Investor has only three dated options to choose from- one which expires on current
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month, those which expire next month and those which expire tow months later called as Far month) Symbol (2 levels) : Index Option( European Option) and Stock Option.( American Option).
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Conjoint Result
Summary Utilities
.1
0.0
Utility
-.1 Call put
STRATEGY
Summary Utilities
3
2
1
0
-1
-2
Utility
-3 in the money at the money out of the money
PREMIUM
159
Summary Utilities
1.5
1.0
.5
0.0
-.5
-1.0
Utility
-1.5 near month next month far month
TIME
Summary Utilities
.4
.2
0.0
-.2
Utility
-.4 stock index
SYMBOL
160
Importance summary
70 60
50
40
30
20
Importance
10 0 STRATEGY PREMIUM TIME SYMBOL
Factor
Based on the Utilities score for each variable we can conclude that , under Bullish Trend investors favor the following :
Put option over Call Option. In the money option , At the money Option and Out of the money option.( In the money options are the least risky )
Near month option over next month and far month. (Due to uncerainity in the future trend investors prefer option that expires in the immediate month as their expectations of market may not hold true for long period of time.)
Index Option as compared to Stock Option. (Index option are better representative of overall market scenario.) Thus the most optimal strategy based on the utility scores is :
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In the money – Index Put Option that expires on near month.
Most important criteria while determining an Option is the Premium which is to be paid for the option. Next most important factor is the time and symbol and the least important variable is the kind of Option that will be purchased (Long call or short put) as both of them provide returns if the market actually turns bullish.
CONJOINT ANALYSIS: When Market is Bearish In order to determine the most optimal strategy while selecting a Option , respondents were given 9 combinations of strategies that were developed after Orthogonal Design of four factors. Symbol ( 2 levels): Index Option and Stock Option Strategy (2 levels): Long Put and Short Call Premium (3 levels) : In the money Option, At the money option and Out of money Option Time (3 levels) : Near month, next month and Far month.
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Summary Utilities
.3
.2
.1
-.0
-.1
-.2
Utility
-.3 Short Calll Long Put
STRATEGY
Summary Utilities
1.0
.5
0.0
-.5
-1.0
Utility
-1.5 In the Money At the Money Out of the Money
PREMIUM
163
Summary Utilities
.6
.4
.2
0.0
-.2
Utility
-.4 Near Month Next Month Far Month
TIME
Importance summary
60
50
40
30
20
Importance
10
0 STRATEGY SYMBOL PREMIUM TIME
Factor
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Interpretation of the results : Based on the utility score for each of the above factors the following results emerge out.
Long Put has higher utility when compared to Short Put. In the money option has more utility when compared to out of money and at the money option. Index option is preferred over Stock Option and while deciding the time period of Option, Next month option is more preferred when compared to near month and far month. Thus on the basis of the above analysis, the most optimal strategy while choosing an Option is Index In the money Put Option which expires on next month.
The most important factor that is used while deciding a particular option strategy is Premium followed by time and symbol and the least most factor is the kind of Option and Long Put ). ………………………………………………………………………………………….. ( Short Call
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Annexure The annexure which has been prepared for this particular report required high involvement of excel sheets, where in I had to use huge data, then I had to apply complex formulas, where in if I would have given these annexure in my report, the formulas would not have made any sense.
So all the annexure, I am putting it separately on a C.D., if you wish you can have a look at it.
The primary research which was done for this particular report, I am enclosing the questionnaire prepared.
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Questionnaire.
1) How often do you follow market?
o o o o o o o o o
Hour by hour basis Daily basis Weekly basis
4) In which of the following are do you actively traded in? Spot market Futures Option
6) What is your primary motive behind investment? Speculation Hedging Long term investment
7) Please rate the following factors on a scale of one to seven, which you consider important while investing in a stock for a particular company?
1) Company brand name 2) Industrial Sector of the company 3) Profitability of Company 4) Dividends paid by the company 5) Current market scenario 6) Market share of company 7) Promoter’s goodwill
1
2
3
4
5
6
7 8 9 10
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8) Management strength 9) News about the company 10) Price in futures market for company 8) Please rate each of the following factors on a scale of one to ten, which decide/influence your investment decision?
1) Bullish trend 2) Bearish tread 3) BSE /NSE Sensex 4) Political factors Indian External
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
10 10 10
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
5) Non-Political factors Monsoon Sports news Festivals 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10
6) Govt Policy 7) RBI statements 8) Interest rate scenario 9) FII Movements 10) Exchange rate Movements 11) Inflation
1
2
3
4
5
6
7
8
9
10
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12) Bank rate
1
2
3
4
5
6
7
8
9
10
9) Please, rate each of the following sectors on a scale of one to ten in order of attractiveness for the following factors.
Sector/Attractiveness Consistency
Profit ability
Volumes
Growth
Volatility
risk
Auto Banking Cement Communication Construction Electronic FMCG Hotel Oil Pharmaceuticals Power Technology
10) Please rank the following sectors of stock that you consider as the most promising for the “next six months”?
o Auto
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o Banking o Cements o Communication o Construction o Electronic o FMCG o Hotel o Oil o Pharmaceuticals o Power o Technology/Software
11) While selecting a particular Option strategy please rank the particular strategy from one to nine? When outlook is -Bullish
Long call , index option,
in the money call,
next month
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Long call , stock option, Short put, stock option, Short put , index option, Long call , stock option, Long call , stock option, Long call , stock option, Short put , index option, Long call , index option ,
in the money call , in the money put, at the money put , at the money call , at the money call, out of the money call , out of the money put , out of the money call ,
near month far month near month next month far month near month next month far month
When outlook is –Bearish Short call , index option, Short call , stock option, Long Put, stock option, in the money call, in the money call , in the money put, at the money put , at the money call , at the money call, out of the money call , out of the money put , out of the money call , next month near month far month near month next month far month near month next month far month 2 3 8 1 5 6 7 4 9
Long Put , index option, Short call , stock option, Short call , stock option, Short call , stock option, Long Put , index option, Short call , index option ,
12) What is your annual family income?
o o o
<3,00,000 3,00,000-6,00,000 6,00,000-10,00,000 171
o o o o o o o o o
>10,00,000
13) Age less than 24 24-35 36-45 >45
2) What is your yearly volume of transactions? <1,50,000 Rs 1,50,000 – Rs 5,00,000 Rs 5,00,000 – Rs 10,00,000 >Rs 10,00,000
3) What is your overall portfolio of investments in trading at a particular point of time?
o o o o
<1,50,000 Rs 1,50,000 – Rs 5,00,000 Rs 5,00,000 – Rs 10,00,000 >Rs 10,00,000
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Bibliography
John.C.Hull Shelden Nattenberg NSE Website
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