Description
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.
Derivative Based Risk Management
Group Project
October 17, 2008
Team Members
Cris Benavides Warren Choi Tatyana Litvak Wei Sun
Project Assignment 1 1. Group Members Cris Benavides Warren Choi Tatyana Litvak Wei Sun 2. (From the WSJ) The Hoya Index Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn’t find a job) to start an index fund. Since they had done poorly in finance classes, they figured an index fund was a heck of a lot easier to manage than an actively managed fund where they would actually have to pick stocks. Fortunately for them, so many mutual funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 100 million in assets, and the founders realized that if they suffered big losses, they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $100M invested in S&P 500 index futures. Long exposure of +FSP $100,000,000 and a loss of 10% or more with only a 1/100 chance. +FSP 3. Futures market situation and evolution:
Underlying ? SS = S&P 500 ? SP
Current date __10/08/08_____ Settle (Close) Price Actual Maturity date Symbol Subsequent (next maturity) date 10/10/08 Settle (Close) Price Subsequent (next maturity) date mark?to ?market
Dec?08
981.00 12/19/2008 SPZ8 891.00 ($90.00)
Mar?09
981.40 3/20/2009 SPH9 890.80 ($90.60)
Jun?09
981.40 6/19/2009 SPM9 890.80 ($90.60)
Sep?09
980.60 9/18/2009 SPU9 889.70 ($90.90)
Each contract represents: 250 x 981 = $245,250 for December 2008. Last trade as of 10/10/2008: $891
4. Brief overview of market outlook for the S&P 500: As we know with the recent events in the US economy, the market has become extremely volatile while stock prices have reach historical lows. Looking at the S&P chart 6 month chart, stock prices have decreased almost 20%, with the DOW dropping a whopping 800 points in one day this month. It is obvious to state that the economy, with all of its fluctuations have begun to show some signs of improvement once again, with all of the government aid to banks, and the hype of the new presidential hopeful in the next month. Warren Buffet's recently released statements about his belief that the economy can only rebound and that longing stocks is the wise thing to do. We believe that as the S&P is at historical lows, and the air surrounding the market is so fickle according to its immediate environment, we believe the S&P will go up. So we are bullish on direction. With volatility at historical highs due to uncertain future outlook on the economy, we believe that the volatility will more or less remain where it is without increasing to higher levels. In fact, we would expect in the long run for the volatility to decrease and revert back to pre-September times, but not until well into next year.
S&P 500 6-mo
Project Assignment 2 A. Price risk management as of 10/08/08. 1. We seek to manage the business risk of an S&P 500 Index Portfolio. 2. Our exposure is long, owning a $100,062,000 portfolio. a. (From the WSJ) The Hoya Follow-The-Herd Index Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn’t find a job) to start an index fund. Since they had done poorly in finance classes, they figured an index fund was a heck of a lot easier to manage than an actively managed fund where they would actually have to pick stocks. Fortunately for them, so many mutual funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 100 million in assets, and the founders realized that if they suffered big losses, they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $100M invested in S&P 500 index futures. 3. IF OUR EXPOSURE WERE SHORT: a. (From the WSJ) The Hoya Follow-The-Herd Hedge Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn’t find a job) to start this new hedge fund. They had done poorly in finance classes, but they figured shorting the S&P 500 index was a no-brainer since the markets continued to fall. Fortunately for them, so many hedge funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 100 million in assets with which to short the S&P 500. The founders realized that if the markets moved up, they’d suffer big losses, and they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $100M invested in S&P 500 index futures. 4. The risk management problem we will address is a long exposure. 5. To set our business context we must determine our total exposure and a dollar loss limit. The dollar loss limit should be a reasonable fraction of our total exposure. 6. Total exposure value is $100.062M. 7. A dollar and percentage loss limit for our exposure is $10M and 10%. 8. We want only a 1% chance of losing more than $10M and 10%. # of standard deviations from current futures price: 2.33 Associated loss probability: 1% # of times out of n that loss limit is exceeded: 1 out of 100 For the S&P 500 underlying 12/19/2008 maturity date and 72 (10/8/2008 - 12/19/2008) day futures contract:
0Ft
= 981 with R = 2% and RP = 5%
Our 10% loss limit critical price level is calculated relative to a measure of a consensus market expectation: Expected future price = 990.64 and based on an annualized standard deviation estimate of 53.26% (from Riskmetrics 30-day monthly estimate of 15.27%?(365/30)) For a long exposure, the lower critical price level = 570.87 For a short exposure, the upper critical price level = 1719.05 B. If we had a Long Exposure From the calculation above, there is a 1% chance that the underlying price will be at or below 570.87 in a year. The associated loss relative to selling the underlying at the current futures price of 981 equals the “loss at the lower critical price level” = -41.81% Therefore, we determine how much of our long exposure may be retained: loss limit / loss at lower critical price level = -10%/-41.81% = 23.90% Roughly, we must decrease our exposure by 1 – (loss limit/loss at critical price level) = 1-23.9% = 76.1% For the underlying position of $100.062M, we must sell $76.095M or 76.1%. Our underlying exposure equals 408 contracts ($100,000,000/($250*$981)). We must sell 311 futures contracts to meet our risk targets. C. If we had a Short Exposure From the calculation above, there is a 1% chance that the underlying price will be at or above 1719.05 in a year. The associated loss relative to buying the underlying at the current futures price of 981 equals the “loss at the upper critical price level” = -75.23% Therefore, we determine how much of our long exposure may be retained: loss limit / loss at lower critical price level = -10%/-41.81% = 23.90% Roughly, we must decrease our exposure by 1 – (loss limit/loss at critical price level) = 1-13.3% = 86.7% For the underlying position of $100M, we must sell $86.717M or 86.72%. Our underlying exposure equals 408 contracts ($100,000,000/($250*$981)). We must buy 354 futures contracts to meet our risk targets. D. Spreadsheet analysis Long Position
Price Value at Risk (V@R) Today 10/8/2008 Futures price
Underlying
SP500
981 Monthly price volatility (stan. dev.)
250
$100,062,000
15.27
For Volatility - standard deviation information,
Notes Quick & Dirty Check
Target Loss
Risk Limit -10,000,000 # of contract underlying # s.d. V@R (e.g. 1.00) 2.33 Exposure (+/-Contracts) Exposure (maturity) Date 12/19/2008 $ underlying For risk premium-adjusted V@R Adjustment (+/-Contracts) Funding Rate
Risk Premium Estimate
408 /riskmetrics.com/clients/data/cde/index.cgi
-311
OK@ 97
user is guriskmetrics password is riskmetrics
2.00% Monthly Estimates (optional) 5.00% Riskmetrics
weight last 150 obs.
Standard deviations (s.d.
E.g. 1% as 1.0)
15.2700 690.1272 -7,053,666
1405.9351 10,304,676
V@R Center and Confidence Interval
Own estimate 15.2700 690.1272 -7,053,666
1405.9351 10,304,676
T>30 days= 72 Riskmetrics inferred (optional) mo nthly vo l*sqrt(72/30) Own estimate 23.6562 23.6562
Loss % Keep Hedge
-9.99% Simple Log -41.81% -54.14% 23.9% 18.5% -76.1% -81.5%
23.9% with 4.9% loss 6.1% loss 6.7% loss 7.6% loss Probability 1 out of 6 10 13 20
Set no hedge & To Match "Keep"
Long V@R @ price*exp(-#*sd) $ V@R
Long upside @ price*exp(+#*sd) $ profit
50% 40% 30% 20% 10% 0% 0.00 200.00 400.0 0
570.8690
-9,945,677
1719.0684 17,898,160
570.8690
for 1.00 s.d for 1.28 s.d for 1.44 s.d for 1.65 s.d for 2.00 s.d for 2.33 s.d for 3.09 s.d Check # s.d.
15.87% 10.03% 7.49% 4.95% 2.28% 1.00% 0.100% 2.3
-9,945,677
1719.0684 17,898,160
Probability of doing worse than -2.33 standard deviation (or 570.8690) is 0.99%
Note: Riskmetrics assumes a zero risk premium. If the graph doesn't plot, click the X-axis and format axis "scale" to bra cket price range.
44 8.9% loss 100 10.0% loss 1000 12.3% loss
570.8690
60 0.00 800.00
990.6376
100 0.00 1200.00 1400.00
1719.0684
1600.00 1800 .00 2000.00
Short Position
Price Value at Risk (V@R) Today 10/8/2008 Futures price Underlying SP500
981 Monthly price volatility (stan. dev.)
250
-$100,062,000
15.27
For Volatility - standard deviation information,
Notes Quick & Dirty Check
Target Loss
Risk Limit -10,000,000 # of contract underlying # s.d. V@R (e.g. 1.00) 2.33 Exposure (+/-Contracts) Exposure (maturity) Date 12/19/2008 $ underlying For risk premium-adjusted V@R Adjustment (+/-Contracts) Funding Rate
Risk Premium Estimate
-408 /riskmetrics.com/clients/data/cde/index.cgi
354
OK@ -54
user is guriskmetrics password is riskmetrics
2.00% Monthly Estimates (optional) 5.00% Riskmetrics
weight last 150 obs.
Standard deviations (s.d.
E.g. 1% as 1.0)
15.2700 1405.9351 -5,736,624
690.1272 3,926,783
V@R Center and Confidence Interval
T>30 days= 72 Riskmetrics inferred (optional) mo nthly vo l*sqrt(72/30) Own estimate Own estimate 15.2700 23.6562 23.6562 1405.9351 -5,736,624
690.1272 3,926,783
Loss % Keep Hedge
-9.99% Simple Log -75.24% -56.10% 13.3% 17.8% 86.7% 82.2%
186.7% with Probability 1 out of
Set no hedge & To Match "Keep"
Short V@R @ price*exp(+#*sd) $ V@R
Short upside @ price*exp(-#*sd) $ profit
50% 40% 30% 20% 10% 0% 0.00 200.00 400.0 0
1719.0684
-9,963,924
570.8690 5,536,769
1719.0684
for 1.00 s.d for 1.28 s.d for 1.44 s.d for 1.65 s.d for 2.00 s.d for 2.33 s.d for 3.09 s.d Check # s.d.
15.87% 10.03% 7.49% 4.95% 2.28% 1.00% 0.100% 5.9
6 52.2% loss 10 68.5% loss 13 78.4% loss 20 91.9% loss 44 ######### 100 ######### 1000 #########
-9,963,924
570.8690 5,536,769
Probability of doing worse than +2.33 standard deviation (or 1719.0684) is 0.99%
Note: Riskmetrics assumes a zero risk premium. If the graph doesn't plot, click the X-axis and format axis "scale" to bra cket price range.
570.8690
60 0.00 800.00
990.6376
100 0.00 1200.00 1400.00
1719.0684
1600.00 1800 .00 2000.00
Project Assignment 3 1. Business problem and risk: The Hoya Index Fund has a portfolio with $100M invested in S&P 500 index futures. This is equivalent to 408 S&P 500 futures contracts. We want only a 1% chance of losing more than $10M. 2. See Project Assignment 2. 3. Market outlook: Our view for December futures is up and stable. We expect the market to move up. Even though volatility is high, we expect it will remain at these levels for the foreseeable future. 4. Closest to maturity futures price and maturity date is December 2008 futures price of $981.
Strikes 800.0 960.0 980.0 1150.0 1250.0
Calls ATM 204.1 ATM 91.5 ATM 80.2 OTM 17.6 OTM 5
Puts OTM 23.8 OTM 70.6 ATM 79.2 ATM 186 ATM 273.2
Direction View Direction Up No Direction Direction Down
Volatility Up
+408F+408P (S#3) +408F+408Potm (S#4) +250F+500P (S#5) -250F+500C (S#6) -408F+408Cotm (S#8) -408F+408C (S#7)
Volatility View Volatility Stable
+97F+48P (S#16) +408F-408Cotm+408Potm (S#9) Preferred Practice for +F: Bull Spread (S#9) -408F+408Cotm-408Potm (S#10) -54F+27C (S#15)
Volatility Down
+97F (S#1) +97F+48P-49C (S#14) +66F-132C (S#11) -66F-132P (S#12) -54F-27Potm+27Cotm (S#13) -54F (S#2)
Note: Positions are in black font if we start with long exposure, red font with short exposure. The S# indicates the number of scenario that contains the detail description for the corresponding position in the following section.
Scenario #1
View Up/Sure
Purpose Trade
Position +97F
Description: Based on our risk control requirement specified in Project Assignment #2, we must sell 311 future contracts. The remaining long exposure is 408-311=97 contracts. This position has 1 out of 100 chance of losing more than $10M.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
l f 981.0 0.00 97 Calculated Profit of a Long Forward Position Underlying per Contract 250 Total Gain(Loss) (13,095,000) (10,912,500) (8,730,000) (6,547,500) (4,365,000) (2,182,500) 0 2,182,500 4,365,000 6,547,500 8,730,000 10,912,500 13,095,000
Prices at Maturity Step size 90.00 Input futures price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+97f (52,380.00) (43,650.00) (34,920.00) (26,190.00) (17,460.00) (8,730.00) 0.00 8,730.00 17,460.00 26,190.00 34,920.00 43,650.00 52,380.00
+97F V@R up-sure/trade
60,000 40,000 20,000 0 (20,000) (40,000) (60,000) 441.0
621.0
801.0
981.0
1161.0 1341.0 1521.0
Price at Contract Maturity
Scenario #2
View Down/Sure
Purpose Trade
Position -54F
Description: Based on our risk control requirement specified in Project Assignment #2, we must buy 354 future contracts. The remaining short exposure is 408-354=54 contracts. This position has 1 out of 100 chance of losing more than $10M.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Short Forward Position -54F 29,160.00 24,300.00 19,440.00 14,580.00 9,720.00 4,860.00 0.00 (4,860.00) (9,720.00) (14,580.00) (19,440.00) (24,300.00) (29,160.00) Underlying per Contract 250 Total Gain (Loss) 7,290,000.00 6,075,000.00 4,860,000.00 3,645,000.00 2,430,000.00 1,215,000.00 0.00 (1,215,000.00) (2,430,000.00) (3,645,000.00) (4,860,000.00) (6,075,000.00) (7,290,000.00)
Prices at Maturity Step size 90.00 Input futures price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
-54F V@R down-sure/trade
40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) 441
621
801
981
1161
1341
1521
Price at Contract Maturity
Scenario #3
View Up/Unsure
Purpose Trade, Insure
Position +408F+408P (Syn +408C)
Description: The maximum loss for this position is $8.18M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 408 Calculated Profit of a Combined +408F+408P Position +408F (220,320) (183,600) (146,880) (110,160) (73,440) (36,720) 0 36,720 73,440 110,160 146,880 183,600 220,320
L P 980.0 79.20 408 Underlying per Contract 250 Total Gain(Loss) (8,180,400) (8,180,400) (8,180,400) (8,180,400) (8,180,400) (8,180,400) (8,078,400) 1,101,600 10,281,600 19,461,600 28,641,600 37,821,600 47,001,600
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408P 187,598 150,878 114,158 77,438 40,718 3,998 (32,314) (32,314) (32,314) (32,314) (32,314) (32,314) (32,314)
+408F+408P (32,722) (32,722) (32,722) (32,722) (32,722) (32,722) (32,314) 4,406 41,126 77,846 114,566 151,286 188,006
+F Insure up-unsure/trade-insure +408F+408P Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario
View
Purpose
Position
#4
Up/Unsure
Trade, Insure
+408F+408Potm
Description: The maximum loss for this position is $9.34M, which meets our risk control requirement. When compared with +F+Pitm, this position’s maximum loss is bigger and its potential gain on the up side is also bigger.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 408 Calculated Profit of a Combined +408F+408Potmotm Position
L P 960.0 70.60 408 Underlying per Contract 250 Total (Gain/Loss) (9,343,200) (9,343,200) (9,343,200) (9,343,200) (9,343,200) (9,343,200) (7,201,200) 1,978,800 11,158,800 20,338,800 29,518,800 38,698,800 47,878,800
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408F (220,320) (183,600) (146,880) (110,160) (73,440) (36,720) 0 36,720 73,440 110,160 146,880 183,600 220,320
+408Potm 182,947 146,227 109,507 72,787 36,067 (653) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805)
+408F+408Potm (37,373) (37,373) (37,373) (37,373) (37,373) (37,373) (28,805) 7,915 44,635 81,355 118,075 154,795 191,515
+F Insure OTM up-unsure/trade-insure +408F+408Potm Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario
View
Purpose
Position
#5
No Direction/Volatile
Trade, Insure
+250F+500P (Syn Long Straddle)
Description: The maximum loss for this position is $9.9M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 250 Calculated Profit of a Combined +250F+500P Position +250F (135,000) (112,500) (90,000) (67,500) (45,000) (22,500) 0 22,500 45,000 67,500 90,000 112,500 135,000
L P 980.0 79.20 500 Underlying per Contract 250 Total Gain(Loss) 23,725,000 18,100,000 12,475,000 6,850,000 1,225,000 (4,400,000) (9,900,000) (4,275,000) 1,350,000 6,975,000 12,600,000 18,225,000 23,850,000
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+500P 229,900 184,900 139,900 94,900 49,900 4,900 (39,600) (39,600) (39,600) (39,600) (39,600) (39,600) (39,600)
+250F+500P 94,900 72,400 49,900 27,400 4,900 (17,600) (39,600) (17,100) 5,400 27,900 50,400 72,900 95,400
+F Vol volative/trade(vol)-insure +250F+500P Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #6
View No Direction/Volatile
Purpose Trade, Insure
Position -250F+500C (Syn Long Straddle)
Description: The maximum loss for this position is $9.9M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 250 Calculated Profit of a Combined -250F+500C Position -250F 135,000 112,500 90,000 67,500 45,000 22,500 0 (22,500) (45,000) (67,500) (90,000) (112,500) (135,000)
L C 980.0 80.20 500 Underlying per Contract 250 Total Gain(Loss) 23,725,000 18,100,000 12,475,000 6,850,000 1,225,000 (4,400,000) (9,900,000) (4,275,000) 1,350,000 6,975,000 12,600,000 18,225,000 23,850,000
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+500C (40,100) (40,100) (40,100) (40,100) (40,100) (40,100) (39,600) 5,400 50,400 95,400 140,400 185,400 230,400
-250F+500C 94,900 72,400 49,900 27,400 4,900 (17,600) (39,600) (17,100) 5,400 27,900 50,400 72,900 95,400
-F Vol unsure/trade(vol)-insure -250F+500C Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #7
View Down/Unsure
Purpose Trade, Insure
Position -408F+408C (Syn +408P)
Description: The maximum loss for this position is $8.08M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 408 Calculated Profit of a Combined -408F+408C Position -408F 220,320 183,600 146,880 110,160 73,440 36,720 0 (36,720) (73,440) (110,160) (146,880) (183,600) (220,320)
L C 980.0 80.20 408 Underlying per Contract 250 Total Gain(Loss) 46,899,600 37,719,600 28,539,600 19,359,600 10,179,600 999,600 (8,078,400) (8,078,400) (8,078,400) (8,078,400) (8,078,400) (8,078,400) (8,078,400)
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408C (32,722) (32,722) (32,722) (32,722) (32,722) (32,722) (32,314) 4,406 41,126 77,846 114,566 151,286 188,006
-408F+408C 187,598 150,878 114,158 77,438 40,718 3,998 (32,314) (32,314) (32,314) (32,314) (32,314) (32,314) (32,314)
-F Insure down-unsure/trade-insure -408F+408C
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #8
View Down/Unsure
Purpose Trade, Insure
Position -408F+408Cotm
Description: The maximum loss for this position is $2.05M, which meets our risk control requirement. When compared with -F+Citm, this position’s maximum loss is smaller and its potential gain on the down side is also smaller.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 408 Calculated Profit of a Combined -408F+408Cotm Position -408F 220,320 183,600 146,880 110,160 73,440 36,720 0 (36,720) (73,440) (110,160) (146,880) (183,600) (220,320)
L C 800.0 201.10 408
FV 0 days <-@ 0.00% Underlying per Contract 250 Total 34,567,800 25,387,800 16,207,800 7,027,800 (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200)
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408Cotm (82,049) (82,049) (82,049) (82,049) (81,641) (44,921) (8,201) 28,519 65,239 101,959 138,679 175,399 212,119
-408F+408Cotm 138,271 101,551 64,831 28,111 (8,201) (8,201) (8,201) (8,201) (8,201) (8,201) (8,201) (8,201) (8,201)
-F Insure otm down-unsure(<atm)/trade-insure(<atm) -408F+408Co
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #9
View Limited Up/Volatility Stable
Purpose Trade, Insure, Income
Position +408F-408Cotm+408Potm (Syn Bull Spread)
Description: The maximum loss for this position is $7.55M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 408 Calculated Profit of a Combined +408F+408Potm408Cotm Position
L P 960.0 70.60 408
S C 1150.0 17.60 408 Underlying per Contract 250 Total Gain(Loss) (7,548,000) (7,548,000) (7,548,000) (7,548,000) (7,548,000) (7,548,000) (5,406,000) 3,774,000 11,832,000 11,832,000 11,832,000 11,832,000 11,832,000
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408F (220,320) (183,600) (146,880) (110,160) (73,440) (36,720) 0 36,720 73,440 110,160 146,880 183,600 220,320
+408Potm 182,947 146,227 109,507 72,787 36,067 (653) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805)
408Cotm 7,181 7,181 7,181 7,181 7,181 7,181 7,181 7,181 2,693 (34,027) (70,747) (107,467) (144,187)
+408F+408Potm408Cotm (30,192) (30,192) (30,192) (30,192) (30,192) (30,192) (21,624) 15,096 47,328 47,328 47,328 47,328 47,328
Syn. Bull Spread limited up-worry big down/T-Inc-Ins +408F+408Potm-408Cotm 250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
+ 408F -408Cotm + 408Potm + 408F+ 408Potm-408Cotm
Scenario # 10
View Limited Down / Volatility Stable
Purpose Trade, Insure, Income
Position -408F+408Cotm-408Potm (Syn Bear Spread)
Description: The maximum loss for this position is $9.45M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 408 Calculated Profit of a Combined -408F408Potm+408Cotm Position
S P 800.0 23.80 408
L C 1050.0 47.40 408 Underlying per Contract 250 Total Gain(Loss) 16,054,800 16,054,800 16,054,800 16,054,800 15,952,800 6,772,800 (2,407,200) (9,445,200) (9,445,200) (9,445,200) (9,445,200) (9,445,200) (9,445,200)
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
-408F 220,320 183,600 146,880 110,160 73,440 36,720 0 (36,720) (73,440) (110,160) (146,880) (183,600) (220,320)
-408Potm (136,762) (100,042) (63,322) (26,602) 9,710 9,710 9,710 9,710 9,710 9,710 9,710 9,710 9,710
+408Cotm (19,339) (19,339) (19,339) (19,339) (19,339) (19,339) (19,339) (10,771) 25,949 62,669 99,389 136,109 172,829
-408F408Potm+408Cotm 64,219 64,219 64,219 64,219 63,811 27,091 (9,629) (37,781) (37,781) (37,781) (37,781) (37,781) (37,781)
Syn. Bear Spread Limited down-Worry big up/T-Ins-Inc -408F-408Potm+408Cotm 250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
-408F + 408Cotm -408Potm -408F-408Potm+ 408Cotm
Scenario # 11
View No Direction/Sure
Purpose Trade, Income
Position +66F-132C (Syn Short Straddle)
Description: The loss of this position is greater than $10M when future price is below $219 or above $1,743. This price range corresponds to below -6.39*Sigma and above +2.39*Sigma around the expected future price. The probability is 0.83%, which meets our risk control (less than 1%).
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 66 Calculated Profit of a Combined +66F-132C Position +66F (50,292) (41,910) (33,528) (25,146) (16,764) (8,382) 0 8,382 16,764 25,146 33,528 41,910 50,292
S C 980.0 80.20 132 Underlying per Contract 250 Total Gain(Loss) (9,926,400) (7,830,900) (5,735,400) (3,639,900) (1,544,400) 551,100 2,613,600 518,100 (1,577,400) (3,672,900) (5,768,400) (7,863,900) (9,959,400)
Prices at Maturity Step size 127.00 Input Futures=> Price
219.0 346.0 473.0 600.0 727.0 854.0 981.0 1108.0 1235.0 1362.0 1489.0 1616.0 1743.0
-132C 10,586 10,586 10,586 10,586 10,586 10,586 10,454 (6,310) (23,074) (39,838) (56,602) (73,366) (90,130)
+66F-132C (39,706) (31,324) (22,942) (14,560) (6,178) 2,204 10,454 2,072 (6,310) (14,692) (23,074) (31,456) (39,838)
+F Stable stable/trade(vol)-income +66F-132C Position
60,000 40,000 20,000 0 (20,000) (40,000) (60,000) (80,000) (100,000) 219.0
473.0
727.0
981.0
1235.0
1489.0
1743.0
Price at Contract Maturity
Scenario # 12
View No Direction/Sure
Purpose Trade, Income
Position -66F-132P (Syn Short Straddle)
Description: The loss of this position is greater than $10M when future price is below $219 or above $1,743. This price range corresponds to below -6.39*Sigma and above +2.39*Sigma around the expected future price. The probability is 0.83%, which meets our risk control (less than 1%).
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 66 Calculated Profit of a Combined -66F-132P Position -66F 50,292 41,910 33,528 25,146 16,764 8,382 0 (8,382) (16,764) (25,146) (33,528) (41,910) (50,292)
S P 980.0 80.20 132 Underlying per Contract 250 Total Gain(Loss) (9,893,400) (7,797,900) (5,702,400) (3,606,900) (1,511,400) 584,100 2,646,600 551,100 (1,544,400) (3,639,900) (5,735,400) (7,830,900) (9,926,400)
Prices at Maturity Step size 127.00 Input Futures=> Price
219.0 346.0 473.0 600.0 727.0 854.0 981.0 1108.0 1235.0 1362.0 1489.0 1616.0 1743.0
-132P (89,866) (73,102) (56,338) (39,574) (22,810) (6,046) 10,586 10,586 10,586 10,586 10,586 10,586 10,586
-66F-132P (39,574) (31,192) (22,810) (14,428) (6,046) 2,336 10,586 2,204 (6,178) (14,560) (22,942) (31,324) (39,706)
-F Stable stable/trade(vol)-income -66F-132P Position
60,000 40,000 20,000 0 (20,000) (40,000) (60,000) (80,000) (100,000) 219.0
473.0
727.0
981.0
1235.0
1489.0
1743.0
Price at Contract Maturity
Scenario # 13
View Down/Sure
Purpose Trade, Insure
Position -54F-27Potm+27Cotm
Description: This position is benchmarked by the –F only position (-54F). The loss will be smaller on the upside, and the gain will be smaller on the downside.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Combined -54F27Potm+27Cotm Position
S P 800.0 23.80 27
L C 1050.0 47.40 27 Underlying per Contract 250 Total Gain(Loss) 6,043,950 5,213,700 4,383,450 3,553,200 2,722,950 1,501,200 (159,300) (1,455,300) (2,285,550) (3,115,800) (3,946,050) (4,776,300) (5,606,550)
Prices at Maturity Step size 123.00 Input Futures=> Price
243.0 366.0 489.0 612.0 735.0 858.0 981.0 1104.0 1227.0 1350.0 1473.0 1596.0 1719.0
-54F 39,852 33,210 26,568 19,926 13,284 6,642 0 (6,642) (13,284) (19,926) (26,568) (33,210) (39,852)
-27Potm (14,396) (11,075) (7,754) (4,433) (1,112) 643 643 643 643 643 643 643 643
+27Cotm (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) 178 3,499 6,820 10,141 13,462 16,783
-54F27Potm+27Cotm 24,176 20,855 17,534 14,213 10,892 6,005 (637) (5,821) (9,142) (12,463) (15,784) (19,105) (22,426)
Down-Sure/T-Ins -54F-27Potm+27Cotm 50,000 40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) (50,000) 243.0
489.0
735.0
981.0
1227.0
1473.0
1719.0
Price at Contract Maturity
-54F -27Potm + 27Cotm -54F-27Potm+ 27Cotm
Scenario # 14
View Up/Sure
Purpose Trade, Insure
Position +97F+48Potm-49Cotm
Description: This position is benchmarked by the +F only position (+97F). The loss will be smaller on the downside, and the gain will be smaller on the upside.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Combined -54F27Potm+27Cotm Position
S P 800.0 23.80 27
L C 1050.0 47.40 27 Underlying per Contract 250 Total Gain(Loss) 6,043,950 5,213,700 4,383,450 3,553,200 2,722,950 1,501,200 (159,300) (1,455,300) (2,285,550) (3,115,800) (3,946,050) (4,776,300) (5,606,550)
Prices at Maturity Step size 123.00 Input Futures=> Price
243.0 366.0 489.0 612.0 735.0 858.0 981.0 1104.0 1227.0 1350.0 1473.0 1596.0 1719.0
-54F 39,852 33,210 26,568 19,926 13,284 6,642 0 (6,642) (13,284) (19,926) (26,568) (33,210) (39,852)
-27Potm (14,396) (11,075) (7,754) (4,433) (1,112) 643 643 643 643 643 643 643 643
+27Cotm (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) 178 3,499 6,820 10,141 13,462 16,783
-54F27Potm+27Cotm 24,176 20,855 17,534 14,213 10,892 6,005 (637) (5,821) (9,142) (12,463) (15,784) (19,105) (22,426)
Down-Sure/T-Ins -54F-27Potm+27Cotm 50,000 40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) (50,000) 243.0
489.0
735.0
981.0
1227.0
1473.0
1719.0
Price at Contract Maturity
-54F -27Potm + 27Cotm -54F-27Potm+ 27Cotm
Scenario # 15
View Down/Stable
Purpose Trade, Insure
Position -54F+27C
Description: This position is benchmarked by the -F only position (-54F). The loss will be smaller on the upside, and the gain will be almost the same on the downside.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Combined -54F+27C Position -54F 39,852 33,210 26,568 19,926 13,284 6,642 0 (6,642) (13,284) (19,926) (26,568) (33,210) (39,852)
L C 980.0 80.20 27 Underlying per Contract 250 Total Gain(Loss) 9,421,650 7,761,150 6,100,650 4,440,150 2,779,650 1,119,150 (534,600) (1,364,850) (2,195,100) (3,025,350) (3,855,600) (4,685,850) (5,516,100)
Prices at Maturity Step size 123.00 Input Futures=> Price
243.0 366.0 489.0 612.0 735.0 858.0 981.0 1104.0 1227.0 1350.0 1473.0 1596.0 1719.0
+27C (2,165) (2,165) (2,165) (2,165) (2,165) (2,165) (2,138) 1,183 4,504 7,825 11,146 14,467 17,788
-54F+27C 37,687 31,045 24,403 17,761 11,119 4,477 (2,138) (5,459) (8,780) (12,101) (15,422) (18,743) (22,064)
down-stable/trade-insure -54F+27C Position
50,000 40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) (50,000) 243.0
489.0
735.0
981.0
1227.0
1473.0
1719.0
Price at Contract Maturity
Scenario # 16
View Up/Stable
Purpose Trade, Insure
Position +97F+48P
Description: This position is benchmarked by the +F only position (+97F). The loss will be smaller on the downside, and the gain will be almost the same on the upside.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 97 Calculated Profit of a Combined +97F+48P Position +97F (52,380) (43,650) (34,920) (26,190) (17,460) (8,730) 0 8,730 17,460 26,190 34,920 43,650 52,380
L P 980.0 79.20 48 Underlying per Contract 250 Total Gain(Loss) (7,577,400) (6,474,900) (5,372,400) (4,269,900) (3,167,400) (2,064,900) (950,400) 1,232,100 3,414,600 5,597,100 7,779,600 9,962,100 12,144,600
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+48P 22,070 17,750 13,430 9,110 4,790 470 (3,802) (3,802) (3,802) (3,802) (3,802) (3,802) (3,802)
+97F+48P (30,310) (25,900) (21,490) (17,080) (12,670) (8,260) (3,802) 4,928 13,658 22,388 31,118 39,848 48,578
up-stable/trade-insure +97F+48P Position
60,000 40,000 20,000
0 (20,000) (40,000) (60,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
5. We recommend hedging our long position in 408 futures contracts by selling 408 Cotm (out of money) call options with a strike price of $1150 and a premium of $17.60, and buying 408 Potm (out of money) put options with a strike price of $960 and a premium of $70.60. This limits our loss in case of a market downturn to $7.55M. (This is Scenario #9 in the charts above). Especially with the current volatility of the market, with this bull spread it will greatly reduce our position cost due to the fact that we are selling calls and buying puts out of money.
doc_681453575.pdf
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.
Derivative Based Risk Management
Group Project
October 17, 2008
Team Members
Cris Benavides Warren Choi Tatyana Litvak Wei Sun
Project Assignment 1 1. Group Members Cris Benavides Warren Choi Tatyana Litvak Wei Sun 2. (From the WSJ) The Hoya Index Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn’t find a job) to start an index fund. Since they had done poorly in finance classes, they figured an index fund was a heck of a lot easier to manage than an actively managed fund where they would actually have to pick stocks. Fortunately for them, so many mutual funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 100 million in assets, and the founders realized that if they suffered big losses, they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $100M invested in S&P 500 index futures. Long exposure of +FSP $100,000,000 and a loss of 10% or more with only a 1/100 chance. +FSP 3. Futures market situation and evolution:
Underlying ? SS = S&P 500 ? SP
Current date __10/08/08_____ Settle (Close) Price Actual Maturity date Symbol Subsequent (next maturity) date 10/10/08 Settle (Close) Price Subsequent (next maturity) date mark?to ?market
Dec?08
981.00 12/19/2008 SPZ8 891.00 ($90.00)
Mar?09
981.40 3/20/2009 SPH9 890.80 ($90.60)
Jun?09
981.40 6/19/2009 SPM9 890.80 ($90.60)
Sep?09
980.60 9/18/2009 SPU9 889.70 ($90.90)
Each contract represents: 250 x 981 = $245,250 for December 2008. Last trade as of 10/10/2008: $891
4. Brief overview of market outlook for the S&P 500: As we know with the recent events in the US economy, the market has become extremely volatile while stock prices have reach historical lows. Looking at the S&P chart 6 month chart, stock prices have decreased almost 20%, with the DOW dropping a whopping 800 points in one day this month. It is obvious to state that the economy, with all of its fluctuations have begun to show some signs of improvement once again, with all of the government aid to banks, and the hype of the new presidential hopeful in the next month. Warren Buffet's recently released statements about his belief that the economy can only rebound and that longing stocks is the wise thing to do. We believe that as the S&P is at historical lows, and the air surrounding the market is so fickle according to its immediate environment, we believe the S&P will go up. So we are bullish on direction. With volatility at historical highs due to uncertain future outlook on the economy, we believe that the volatility will more or less remain where it is without increasing to higher levels. In fact, we would expect in the long run for the volatility to decrease and revert back to pre-September times, but not until well into next year.
S&P 500 6-mo
Project Assignment 2 A. Price risk management as of 10/08/08. 1. We seek to manage the business risk of an S&P 500 Index Portfolio. 2. Our exposure is long, owning a $100,062,000 portfolio. a. (From the WSJ) The Hoya Follow-The-Herd Index Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn’t find a job) to start an index fund. Since they had done poorly in finance classes, they figured an index fund was a heck of a lot easier to manage than an actively managed fund where they would actually have to pick stocks. Fortunately for them, so many mutual funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 100 million in assets, and the founders realized that if they suffered big losses, they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $100M invested in S&P 500 index futures. 3. IF OUR EXPOSURE WERE SHORT: a. (From the WSJ) The Hoya Follow-The-Herd Hedge Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn’t find a job) to start this new hedge fund. They had done poorly in finance classes, but they figured shorting the S&P 500 index was a no-brainer since the markets continued to fall. Fortunately for them, so many hedge funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 100 million in assets with which to short the S&P 500. The founders realized that if the markets moved up, they’d suffer big losses, and they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $100M invested in S&P 500 index futures. 4. The risk management problem we will address is a long exposure. 5. To set our business context we must determine our total exposure and a dollar loss limit. The dollar loss limit should be a reasonable fraction of our total exposure. 6. Total exposure value is $100.062M. 7. A dollar and percentage loss limit for our exposure is $10M and 10%. 8. We want only a 1% chance of losing more than $10M and 10%. # of standard deviations from current futures price: 2.33 Associated loss probability: 1% # of times out of n that loss limit is exceeded: 1 out of 100 For the S&P 500 underlying 12/19/2008 maturity date and 72 (10/8/2008 - 12/19/2008) day futures contract:
0Ft
= 981 with R = 2% and RP = 5%
Our 10% loss limit critical price level is calculated relative to a measure of a consensus market expectation: Expected future price = 990.64 and based on an annualized standard deviation estimate of 53.26% (from Riskmetrics 30-day monthly estimate of 15.27%?(365/30)) For a long exposure, the lower critical price level = 570.87 For a short exposure, the upper critical price level = 1719.05 B. If we had a Long Exposure From the calculation above, there is a 1% chance that the underlying price will be at or below 570.87 in a year. The associated loss relative to selling the underlying at the current futures price of 981 equals the “loss at the lower critical price level” = -41.81% Therefore, we determine how much of our long exposure may be retained: loss limit / loss at lower critical price level = -10%/-41.81% = 23.90% Roughly, we must decrease our exposure by 1 – (loss limit/loss at critical price level) = 1-23.9% = 76.1% For the underlying position of $100.062M, we must sell $76.095M or 76.1%. Our underlying exposure equals 408 contracts ($100,000,000/($250*$981)). We must sell 311 futures contracts to meet our risk targets. C. If we had a Short Exposure From the calculation above, there is a 1% chance that the underlying price will be at or above 1719.05 in a year. The associated loss relative to buying the underlying at the current futures price of 981 equals the “loss at the upper critical price level” = -75.23% Therefore, we determine how much of our long exposure may be retained: loss limit / loss at lower critical price level = -10%/-41.81% = 23.90% Roughly, we must decrease our exposure by 1 – (loss limit/loss at critical price level) = 1-13.3% = 86.7% For the underlying position of $100M, we must sell $86.717M or 86.72%. Our underlying exposure equals 408 contracts ($100,000,000/($250*$981)). We must buy 354 futures contracts to meet our risk targets. D. Spreadsheet analysis Long Position
Price Value at Risk (V@R) Today 10/8/2008 Futures price
Underlying
SP500
981 Monthly price volatility (stan. dev.)
250
$100,062,000
15.27
For Volatility - standard deviation information,
Notes Quick & Dirty Check
Target Loss
Risk Limit -10,000,000 # of contract underlying # s.d. V@R (e.g. 1.00) 2.33 Exposure (+/-Contracts) Exposure (maturity) Date 12/19/2008 $ underlying For risk premium-adjusted V@R Adjustment (+/-Contracts) Funding Rate
Risk Premium Estimate
408 /riskmetrics.com/clients/data/cde/index.cgi
-311
OK@ 97
user is guriskmetrics password is riskmetrics
2.00% Monthly Estimates (optional) 5.00% Riskmetrics
weight last 150 obs.
Standard deviations (s.d.
E.g. 1% as 1.0)
15.2700 690.1272 -7,053,666
1405.9351 10,304,676
V@R Center and Confidence Interval
Own estimate 15.2700 690.1272 -7,053,666
1405.9351 10,304,676
T>30 days= 72 Riskmetrics inferred (optional) mo nthly vo l*sqrt(72/30) Own estimate 23.6562 23.6562
Loss % Keep Hedge
-9.99% Simple Log -41.81% -54.14% 23.9% 18.5% -76.1% -81.5%
23.9% with 4.9% loss 6.1% loss 6.7% loss 7.6% loss Probability 1 out of 6 10 13 20
Set no hedge & To Match "Keep"
Long V@R @ price*exp(-#*sd) $ V@R
Long upside @ price*exp(+#*sd) $ profit
50% 40% 30% 20% 10% 0% 0.00 200.00 400.0 0
570.8690
-9,945,677
1719.0684 17,898,160
570.8690
for 1.00 s.d for 1.28 s.d for 1.44 s.d for 1.65 s.d for 2.00 s.d for 2.33 s.d for 3.09 s.d Check # s.d.
15.87% 10.03% 7.49% 4.95% 2.28% 1.00% 0.100% 2.3
-9,945,677
1719.0684 17,898,160
Probability of doing worse than -2.33 standard deviation (or 570.8690) is 0.99%
Note: Riskmetrics assumes a zero risk premium. If the graph doesn't plot, click the X-axis and format axis "scale" to bra cket price range.
44 8.9% loss 100 10.0% loss 1000 12.3% loss
570.8690
60 0.00 800.00
990.6376
100 0.00 1200.00 1400.00
1719.0684
1600.00 1800 .00 2000.00
Short Position
Price Value at Risk (V@R) Today 10/8/2008 Futures price Underlying SP500
981 Monthly price volatility (stan. dev.)
250
-$100,062,000
15.27
For Volatility - standard deviation information,
Notes Quick & Dirty Check
Target Loss
Risk Limit -10,000,000 # of contract underlying # s.d. V@R (e.g. 1.00) 2.33 Exposure (+/-Contracts) Exposure (maturity) Date 12/19/2008 $ underlying For risk premium-adjusted V@R Adjustment (+/-Contracts) Funding Rate
Risk Premium Estimate
-408 /riskmetrics.com/clients/data/cde/index.cgi
354
OK@ -54
user is guriskmetrics password is riskmetrics
2.00% Monthly Estimates (optional) 5.00% Riskmetrics
weight last 150 obs.
Standard deviations (s.d.
E.g. 1% as 1.0)
15.2700 1405.9351 -5,736,624
690.1272 3,926,783
V@R Center and Confidence Interval
T>30 days= 72 Riskmetrics inferred (optional) mo nthly vo l*sqrt(72/30) Own estimate Own estimate 15.2700 23.6562 23.6562 1405.9351 -5,736,624
690.1272 3,926,783
Loss % Keep Hedge
-9.99% Simple Log -75.24% -56.10% 13.3% 17.8% 86.7% 82.2%
186.7% with Probability 1 out of
Set no hedge & To Match "Keep"
Short V@R @ price*exp(+#*sd) $ V@R
Short upside @ price*exp(-#*sd) $ profit
50% 40% 30% 20% 10% 0% 0.00 200.00 400.0 0
1719.0684
-9,963,924
570.8690 5,536,769
1719.0684
for 1.00 s.d for 1.28 s.d for 1.44 s.d for 1.65 s.d for 2.00 s.d for 2.33 s.d for 3.09 s.d Check # s.d.
15.87% 10.03% 7.49% 4.95% 2.28% 1.00% 0.100% 5.9
6 52.2% loss 10 68.5% loss 13 78.4% loss 20 91.9% loss 44 ######### 100 ######### 1000 #########
-9,963,924
570.8690 5,536,769
Probability of doing worse than +2.33 standard deviation (or 1719.0684) is 0.99%
Note: Riskmetrics assumes a zero risk premium. If the graph doesn't plot, click the X-axis and format axis "scale" to bra cket price range.
570.8690
60 0.00 800.00
990.6376
100 0.00 1200.00 1400.00
1719.0684
1600.00 1800 .00 2000.00
Project Assignment 3 1. Business problem and risk: The Hoya Index Fund has a portfolio with $100M invested in S&P 500 index futures. This is equivalent to 408 S&P 500 futures contracts. We want only a 1% chance of losing more than $10M. 2. See Project Assignment 2. 3. Market outlook: Our view for December futures is up and stable. We expect the market to move up. Even though volatility is high, we expect it will remain at these levels for the foreseeable future. 4. Closest to maturity futures price and maturity date is December 2008 futures price of $981.
Strikes 800.0 960.0 980.0 1150.0 1250.0
Calls ATM 204.1 ATM 91.5 ATM 80.2 OTM 17.6 OTM 5
Puts OTM 23.8 OTM 70.6 ATM 79.2 ATM 186 ATM 273.2
Direction View Direction Up No Direction Direction Down
Volatility Up
+408F+408P (S#3) +408F+408Potm (S#4) +250F+500P (S#5) -250F+500C (S#6) -408F+408Cotm (S#8) -408F+408C (S#7)
Volatility View Volatility Stable
+97F+48P (S#16) +408F-408Cotm+408Potm (S#9) Preferred Practice for +F: Bull Spread (S#9) -408F+408Cotm-408Potm (S#10) -54F+27C (S#15)
Volatility Down
+97F (S#1) +97F+48P-49C (S#14) +66F-132C (S#11) -66F-132P (S#12) -54F-27Potm+27Cotm (S#13) -54F (S#2)
Note: Positions are in black font if we start with long exposure, red font with short exposure. The S# indicates the number of scenario that contains the detail description for the corresponding position in the following section.
Scenario #1
View Up/Sure
Purpose Trade
Position +97F
Description: Based on our risk control requirement specified in Project Assignment #2, we must sell 311 future contracts. The remaining long exposure is 408-311=97 contracts. This position has 1 out of 100 chance of losing more than $10M.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
l f 981.0 0.00 97 Calculated Profit of a Long Forward Position Underlying per Contract 250 Total Gain(Loss) (13,095,000) (10,912,500) (8,730,000) (6,547,500) (4,365,000) (2,182,500) 0 2,182,500 4,365,000 6,547,500 8,730,000 10,912,500 13,095,000
Prices at Maturity Step size 90.00 Input futures price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+97f (52,380.00) (43,650.00) (34,920.00) (26,190.00) (17,460.00) (8,730.00) 0.00 8,730.00 17,460.00 26,190.00 34,920.00 43,650.00 52,380.00
+97F V@R up-sure/trade
60,000 40,000 20,000 0 (20,000) (40,000) (60,000) 441.0
621.0
801.0
981.0
1161.0 1341.0 1521.0
Price at Contract Maturity
Scenario #2
View Down/Sure
Purpose Trade
Position -54F
Description: Based on our risk control requirement specified in Project Assignment #2, we must buy 354 future contracts. The remaining short exposure is 408-354=54 contracts. This position has 1 out of 100 chance of losing more than $10M.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Short Forward Position -54F 29,160.00 24,300.00 19,440.00 14,580.00 9,720.00 4,860.00 0.00 (4,860.00) (9,720.00) (14,580.00) (19,440.00) (24,300.00) (29,160.00) Underlying per Contract 250 Total Gain (Loss) 7,290,000.00 6,075,000.00 4,860,000.00 3,645,000.00 2,430,000.00 1,215,000.00 0.00 (1,215,000.00) (2,430,000.00) (3,645,000.00) (4,860,000.00) (6,075,000.00) (7,290,000.00)
Prices at Maturity Step size 90.00 Input futures price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
-54F V@R down-sure/trade
40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) 441
621
801
981
1161
1341
1521
Price at Contract Maturity
Scenario #3
View Up/Unsure
Purpose Trade, Insure
Position +408F+408P (Syn +408C)
Description: The maximum loss for this position is $8.18M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 408 Calculated Profit of a Combined +408F+408P Position +408F (220,320) (183,600) (146,880) (110,160) (73,440) (36,720) 0 36,720 73,440 110,160 146,880 183,600 220,320
L P 980.0 79.20 408 Underlying per Contract 250 Total Gain(Loss) (8,180,400) (8,180,400) (8,180,400) (8,180,400) (8,180,400) (8,180,400) (8,078,400) 1,101,600 10,281,600 19,461,600 28,641,600 37,821,600 47,001,600
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408P 187,598 150,878 114,158 77,438 40,718 3,998 (32,314) (32,314) (32,314) (32,314) (32,314) (32,314) (32,314)
+408F+408P (32,722) (32,722) (32,722) (32,722) (32,722) (32,722) (32,314) 4,406 41,126 77,846 114,566 151,286 188,006
+F Insure up-unsure/trade-insure +408F+408P Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario
View
Purpose
Position
#4
Up/Unsure
Trade, Insure
+408F+408Potm
Description: The maximum loss for this position is $9.34M, which meets our risk control requirement. When compared with +F+Pitm, this position’s maximum loss is bigger and its potential gain on the up side is also bigger.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 408 Calculated Profit of a Combined +408F+408Potmotm Position
L P 960.0 70.60 408 Underlying per Contract 250 Total (Gain/Loss) (9,343,200) (9,343,200) (9,343,200) (9,343,200) (9,343,200) (9,343,200) (7,201,200) 1,978,800 11,158,800 20,338,800 29,518,800 38,698,800 47,878,800
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408F (220,320) (183,600) (146,880) (110,160) (73,440) (36,720) 0 36,720 73,440 110,160 146,880 183,600 220,320
+408Potm 182,947 146,227 109,507 72,787 36,067 (653) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805)
+408F+408Potm (37,373) (37,373) (37,373) (37,373) (37,373) (37,373) (28,805) 7,915 44,635 81,355 118,075 154,795 191,515
+F Insure OTM up-unsure/trade-insure +408F+408Potm Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario
View
Purpose
Position
#5
No Direction/Volatile
Trade, Insure
+250F+500P (Syn Long Straddle)
Description: The maximum loss for this position is $9.9M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 250 Calculated Profit of a Combined +250F+500P Position +250F (135,000) (112,500) (90,000) (67,500) (45,000) (22,500) 0 22,500 45,000 67,500 90,000 112,500 135,000
L P 980.0 79.20 500 Underlying per Contract 250 Total Gain(Loss) 23,725,000 18,100,000 12,475,000 6,850,000 1,225,000 (4,400,000) (9,900,000) (4,275,000) 1,350,000 6,975,000 12,600,000 18,225,000 23,850,000
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+500P 229,900 184,900 139,900 94,900 49,900 4,900 (39,600) (39,600) (39,600) (39,600) (39,600) (39,600) (39,600)
+250F+500P 94,900 72,400 49,900 27,400 4,900 (17,600) (39,600) (17,100) 5,400 27,900 50,400 72,900 95,400
+F Vol volative/trade(vol)-insure +250F+500P Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #6
View No Direction/Volatile
Purpose Trade, Insure
Position -250F+500C (Syn Long Straddle)
Description: The maximum loss for this position is $9.9M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 250 Calculated Profit of a Combined -250F+500C Position -250F 135,000 112,500 90,000 67,500 45,000 22,500 0 (22,500) (45,000) (67,500) (90,000) (112,500) (135,000)
L C 980.0 80.20 500 Underlying per Contract 250 Total Gain(Loss) 23,725,000 18,100,000 12,475,000 6,850,000 1,225,000 (4,400,000) (9,900,000) (4,275,000) 1,350,000 6,975,000 12,600,000 18,225,000 23,850,000
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+500C (40,100) (40,100) (40,100) (40,100) (40,100) (40,100) (39,600) 5,400 50,400 95,400 140,400 185,400 230,400
-250F+500C 94,900 72,400 49,900 27,400 4,900 (17,600) (39,600) (17,100) 5,400 27,900 50,400 72,900 95,400
-F Vol unsure/trade(vol)-insure -250F+500C Position
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #7
View Down/Unsure
Purpose Trade, Insure
Position -408F+408C (Syn +408P)
Description: The maximum loss for this position is $8.08M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 408 Calculated Profit of a Combined -408F+408C Position -408F 220,320 183,600 146,880 110,160 73,440 36,720 0 (36,720) (73,440) (110,160) (146,880) (183,600) (220,320)
L C 980.0 80.20 408 Underlying per Contract 250 Total Gain(Loss) 46,899,600 37,719,600 28,539,600 19,359,600 10,179,600 999,600 (8,078,400) (8,078,400) (8,078,400) (8,078,400) (8,078,400) (8,078,400) (8,078,400)
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408C (32,722) (32,722) (32,722) (32,722) (32,722) (32,722) (32,314) 4,406 41,126 77,846 114,566 151,286 188,006
-408F+408C 187,598 150,878 114,158 77,438 40,718 3,998 (32,314) (32,314) (32,314) (32,314) (32,314) (32,314) (32,314)
-F Insure down-unsure/trade-insure -408F+408C
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #8
View Down/Unsure
Purpose Trade, Insure
Position -408F+408Cotm
Description: The maximum loss for this position is $2.05M, which meets our risk control requirement. When compared with -F+Citm, this position’s maximum loss is smaller and its potential gain on the down side is also smaller.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 408 Calculated Profit of a Combined -408F+408Cotm Position -408F 220,320 183,600 146,880 110,160 73,440 36,720 0 (36,720) (73,440) (110,160) (146,880) (183,600) (220,320)
L C 800.0 201.10 408
FV 0 days <-@ 0.00% Underlying per Contract 250 Total 34,567,800 25,387,800 16,207,800 7,027,800 (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200) (2,050,200)
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408Cotm (82,049) (82,049) (82,049) (82,049) (81,641) (44,921) (8,201) 28,519 65,239 101,959 138,679 175,399 212,119
-408F+408Cotm 138,271 101,551 64,831 28,111 (8,201) (8,201) (8,201) (8,201) (8,201) (8,201) (8,201) (8,201) (8,201)
-F Insure otm down-unsure(<atm)/trade-insure(<atm) -408F+408Co
250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
Scenario #9
View Limited Up/Volatility Stable
Purpose Trade, Insure, Income
Position +408F-408Cotm+408Potm (Syn Bull Spread)
Description: The maximum loss for this position is $7.55M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 408 Calculated Profit of a Combined +408F+408Potm408Cotm Position
L P 960.0 70.60 408
S C 1150.0 17.60 408 Underlying per Contract 250 Total Gain(Loss) (7,548,000) (7,548,000) (7,548,000) (7,548,000) (7,548,000) (7,548,000) (5,406,000) 3,774,000 11,832,000 11,832,000 11,832,000 11,832,000 11,832,000
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+408F (220,320) (183,600) (146,880) (110,160) (73,440) (36,720) 0 36,720 73,440 110,160 146,880 183,600 220,320
+408Potm 182,947 146,227 109,507 72,787 36,067 (653) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805) (28,805)
408Cotm 7,181 7,181 7,181 7,181 7,181 7,181 7,181 7,181 2,693 (34,027) (70,747) (107,467) (144,187)
+408F+408Potm408Cotm (30,192) (30,192) (30,192) (30,192) (30,192) (30,192) (21,624) 15,096 47,328 47,328 47,328 47,328 47,328
Syn. Bull Spread limited up-worry big down/T-Inc-Ins +408F+408Potm-408Cotm 250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
+ 408F -408Cotm + 408Potm + 408F+ 408Potm-408Cotm
Scenario # 10
View Limited Down / Volatility Stable
Purpose Trade, Insure, Income
Position -408F+408Cotm-408Potm (Syn Bear Spread)
Description: The maximum loss for this position is $9.45M, which meets our risk control requirement.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 408 Calculated Profit of a Combined -408F408Potm+408Cotm Position
S P 800.0 23.80 408
L C 1050.0 47.40 408 Underlying per Contract 250 Total Gain(Loss) 16,054,800 16,054,800 16,054,800 16,054,800 15,952,800 6,772,800 (2,407,200) (9,445,200) (9,445,200) (9,445,200) (9,445,200) (9,445,200) (9,445,200)
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
-408F 220,320 183,600 146,880 110,160 73,440 36,720 0 (36,720) (73,440) (110,160) (146,880) (183,600) (220,320)
-408Potm (136,762) (100,042) (63,322) (26,602) 9,710 9,710 9,710 9,710 9,710 9,710 9,710 9,710 9,710
+408Cotm (19,339) (19,339) (19,339) (19,339) (19,339) (19,339) (19,339) (10,771) 25,949 62,669 99,389 136,109 172,829
-408F408Potm+408Cotm 64,219 64,219 64,219 64,219 63,811 27,091 (9,629) (37,781) (37,781) (37,781) (37,781) (37,781) (37,781)
Syn. Bear Spread Limited down-Worry big up/T-Ins-Inc -408F-408Potm+408Cotm 250,000 200,000 150,000 100,000 50,000 0 (50,000) (100,000) (150,000) (200,000) (250,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
-408F + 408Cotm -408Potm -408F-408Potm+ 408Cotm
Scenario # 11
View No Direction/Sure
Purpose Trade, Income
Position +66F-132C (Syn Short Straddle)
Description: The loss of this position is greater than $10M when future price is below $219 or above $1,743. This price range corresponds to below -6.39*Sigma and above +2.39*Sigma around the expected future price. The probability is 0.83%, which meets our risk control (less than 1%).
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 66 Calculated Profit of a Combined +66F-132C Position +66F (50,292) (41,910) (33,528) (25,146) (16,764) (8,382) 0 8,382 16,764 25,146 33,528 41,910 50,292
S C 980.0 80.20 132 Underlying per Contract 250 Total Gain(Loss) (9,926,400) (7,830,900) (5,735,400) (3,639,900) (1,544,400) 551,100 2,613,600 518,100 (1,577,400) (3,672,900) (5,768,400) (7,863,900) (9,959,400)
Prices at Maturity Step size 127.00 Input Futures=> Price
219.0 346.0 473.0 600.0 727.0 854.0 981.0 1108.0 1235.0 1362.0 1489.0 1616.0 1743.0
-132C 10,586 10,586 10,586 10,586 10,586 10,586 10,454 (6,310) (23,074) (39,838) (56,602) (73,366) (90,130)
+66F-132C (39,706) (31,324) (22,942) (14,560) (6,178) 2,204 10,454 2,072 (6,310) (14,692) (23,074) (31,456) (39,838)
+F Stable stable/trade(vol)-income +66F-132C Position
60,000 40,000 20,000 0 (20,000) (40,000) (60,000) (80,000) (100,000) 219.0
473.0
727.0
981.0
1235.0
1489.0
1743.0
Price at Contract Maturity
Scenario # 12
View No Direction/Sure
Purpose Trade, Income
Position -66F-132P (Syn Short Straddle)
Description: The loss of this position is greater than $10M when future price is below $219 or above $1,743. This price range corresponds to below -6.39*Sigma and above +2.39*Sigma around the expected future price. The probability is 0.83%, which meets our risk control (less than 1%).
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 66 Calculated Profit of a Combined -66F-132P Position -66F 50,292 41,910 33,528 25,146 16,764 8,382 0 (8,382) (16,764) (25,146) (33,528) (41,910) (50,292)
S P 980.0 80.20 132 Underlying per Contract 250 Total Gain(Loss) (9,893,400) (7,797,900) (5,702,400) (3,606,900) (1,511,400) 584,100 2,646,600 551,100 (1,544,400) (3,639,900) (5,735,400) (7,830,900) (9,926,400)
Prices at Maturity Step size 127.00 Input Futures=> Price
219.0 346.0 473.0 600.0 727.0 854.0 981.0 1108.0 1235.0 1362.0 1489.0 1616.0 1743.0
-132P (89,866) (73,102) (56,338) (39,574) (22,810) (6,046) 10,586 10,586 10,586 10,586 10,586 10,586 10,586
-66F-132P (39,574) (31,192) (22,810) (14,428) (6,046) 2,336 10,586 2,204 (6,178) (14,560) (22,942) (31,324) (39,706)
-F Stable stable/trade(vol)-income -66F-132P Position
60,000 40,000 20,000 0 (20,000) (40,000) (60,000) (80,000) (100,000) 219.0
473.0
727.0
981.0
1235.0
1489.0
1743.0
Price at Contract Maturity
Scenario # 13
View Down/Sure
Purpose Trade, Insure
Position -54F-27Potm+27Cotm
Description: This position is benchmarked by the –F only position (-54F). The loss will be smaller on the upside, and the gain will be smaller on the downside.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Combined -54F27Potm+27Cotm Position
S P 800.0 23.80 27
L C 1050.0 47.40 27 Underlying per Contract 250 Total Gain(Loss) 6,043,950 5,213,700 4,383,450 3,553,200 2,722,950 1,501,200 (159,300) (1,455,300) (2,285,550) (3,115,800) (3,946,050) (4,776,300) (5,606,550)
Prices at Maturity Step size 123.00 Input Futures=> Price
243.0 366.0 489.0 612.0 735.0 858.0 981.0 1104.0 1227.0 1350.0 1473.0 1596.0 1719.0
-54F 39,852 33,210 26,568 19,926 13,284 6,642 0 (6,642) (13,284) (19,926) (26,568) (33,210) (39,852)
-27Potm (14,396) (11,075) (7,754) (4,433) (1,112) 643 643 643 643 643 643 643 643
+27Cotm (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) 178 3,499 6,820 10,141 13,462 16,783
-54F27Potm+27Cotm 24,176 20,855 17,534 14,213 10,892 6,005 (637) (5,821) (9,142) (12,463) (15,784) (19,105) (22,426)
Down-Sure/T-Ins -54F-27Potm+27Cotm 50,000 40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) (50,000) 243.0
489.0
735.0
981.0
1227.0
1473.0
1719.0
Price at Contract Maturity
-54F -27Potm + 27Cotm -54F-27Potm+ 27Cotm
Scenario # 14
View Up/Sure
Purpose Trade, Insure
Position +97F+48Potm-49Cotm
Description: This position is benchmarked by the +F only position (+97F). The loss will be smaller on the downside, and the gain will be smaller on the upside.
L or S (Long/Short) F, C, or P Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Combined -54F27Potm+27Cotm Position
S P 800.0 23.80 27
L C 1050.0 47.40 27 Underlying per Contract 250 Total Gain(Loss) 6,043,950 5,213,700 4,383,450 3,553,200 2,722,950 1,501,200 (159,300) (1,455,300) (2,285,550) (3,115,800) (3,946,050) (4,776,300) (5,606,550)
Prices at Maturity Step size 123.00 Input Futures=> Price
243.0 366.0 489.0 612.0 735.0 858.0 981.0 1104.0 1227.0 1350.0 1473.0 1596.0 1719.0
-54F 39,852 33,210 26,568 19,926 13,284 6,642 0 (6,642) (13,284) (19,926) (26,568) (33,210) (39,852)
-27Potm (14,396) (11,075) (7,754) (4,433) (1,112) 643 643 643 643 643 643 643 643
+27Cotm (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) (1,280) 178 3,499 6,820 10,141 13,462 16,783
-54F27Potm+27Cotm 24,176 20,855 17,534 14,213 10,892 6,005 (637) (5,821) (9,142) (12,463) (15,784) (19,105) (22,426)
Down-Sure/T-Ins -54F-27Potm+27Cotm 50,000 40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) (50,000) 243.0
489.0
735.0
981.0
1227.0
1473.0
1719.0
Price at Contract Maturity
-54F -27Potm + 27Cotm -54F-27Potm+ 27Cotm
Scenario # 15
View Down/Stable
Purpose Trade, Insure
Position -54F+27C
Description: This position is benchmarked by the -F only position (-54F). The loss will be smaller on the upside, and the gain will be almost the same on the downside.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
S F 981.0 0.00 54 Calculated Profit of a Combined -54F+27C Position -54F 39,852 33,210 26,568 19,926 13,284 6,642 0 (6,642) (13,284) (19,926) (26,568) (33,210) (39,852)
L C 980.0 80.20 27 Underlying per Contract 250 Total Gain(Loss) 9,421,650 7,761,150 6,100,650 4,440,150 2,779,650 1,119,150 (534,600) (1,364,850) (2,195,100) (3,025,350) (3,855,600) (4,685,850) (5,516,100)
Prices at Maturity Step size 123.00 Input Futures=> Price
243.0 366.0 489.0 612.0 735.0 858.0 981.0 1104.0 1227.0 1350.0 1473.0 1596.0 1719.0
+27C (2,165) (2,165) (2,165) (2,165) (2,165) (2,165) (2,138) 1,183 4,504 7,825 11,146 14,467 17,788
-54F+27C 37,687 31,045 24,403 17,761 11,119 4,477 (2,138) (5,459) (8,780) (12,101) (15,422) (18,743) (22,064)
down-stable/trade-insure -54F+27C Position
50,000 40,000 30,000 20,000 10,000 0 (10,000) (20,000) (30,000) (40,000) (50,000) 243.0
489.0
735.0
981.0
1227.0
1473.0
1719.0
Price at Contract Maturity
Scenario # 16
View Up/Stable
Purpose Trade, Insure
Position +97F+48P
Description: This position is benchmarked by the +F only position (+97F). The loss will be smaller on the downside, and the gain will be almost the same on the upside.
L or S (Long/Short) F, C, or P (Forward, Call, Put) Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts
L F 981.0 0.00 97 Calculated Profit of a Combined +97F+48P Position +97F (52,380) (43,650) (34,920) (26,190) (17,460) (8,730) 0 8,730 17,460 26,190 34,920 43,650 52,380
L P 980.0 79.20 48 Underlying per Contract 250 Total Gain(Loss) (7,577,400) (6,474,900) (5,372,400) (4,269,900) (3,167,400) (2,064,900) (950,400) 1,232,100 3,414,600 5,597,100 7,779,600 9,962,100 12,144,600
Prices at Maturity Step size 90.00 Input Futures=> Price
441.0 531.0 621.0 711.0 801.0 891.0 981.0 1071.0 1161.0 1251.0 1341.0 1431.0 1521.0
+48P 22,070 17,750 13,430 9,110 4,790 470 (3,802) (3,802) (3,802) (3,802) (3,802) (3,802) (3,802)
+97F+48P (30,310) (25,900) (21,490) (17,080) (12,670) (8,260) (3,802) 4,928 13,658 22,388 31,118 39,848 48,578
up-stable/trade-insure +97F+48P Position
60,000 40,000 20,000
0 (20,000) (40,000) (60,000) 441.0
621.0
801.0
981.0
1161.0
1341.0
1521.0
Price at Contract Maturity
5. We recommend hedging our long position in 408 futures contracts by selling 408 Cotm (out of money) call options with a strike price of $1150 and a premium of $17.60, and buying 408 Potm (out of money) put options with a strike price of $960 and a premium of $70.60. This limits our loss in case of a market downturn to $7.55M. (This is Scenario #9 in the charts above). Especially with the current volatility of the market, with this bull spread it will greatly reduce our position cost due to the fact that we are selling calls and buying puts out of money.
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