Description
ctcm
Futures
? October Groundnut oil futures are selling at 19.44 cents per lb. The standard size of the contract is 60,000 lbs. Initial Margin is $3000 while the maintenance margin is $1500. If a trader goes long in two October futures contracts and the prices on the subsequent four days are 19, 19.4, 19.6 and 19.8 cents/lb, explain how the margin account changes. Assume that money in excess of the initial margin is withdrawn immediately.
Futures
Ans:
Initial Margin Requirement per contract = $3000 Maintenance Margin per contract = $1500
Day Change in Price cents/lb Change in contract value 0.44/100* 60000*2 = 528 0.40/100* 60000*2 = 480 240 240 Margin Call Margin withdarwal Balance amount $6000 19.00-19.44 = -0.44 5472
0 1
2
19.40-19.00 = 0.40
-
-
5952
3 4
19.60-19.40 = 0.20 19.80-19.60 = 0.20
-
192 240
6000 6000
?
Today, September 1, the jeweler is setting the price of jewelry to be sold in December through the catalog he is printing. His major input expense is the cost of gold, which changes from day to day in the market. Today, the jeweler sees the following prices: Spot gold, $375 per ounce Gold futures for December delivery, $380 per ounce.
? ?
Required : i. What is the effective cost to the jeweler if the futures price in December is $400 per ounce ii. What is the effective cost to the jeweler if the futures price in December is $350 per ounce Note : At the expiration of a futures contract, the spot and futures price normally converge, i.e., become the same
PRICING OF FUTURES
So in general, through the forces of arbitrage, we say that the futures price is the spot price compounded at the risk-free rate: f0 (T) = S0 (1 + r) Therefore, to compound the asset price over the life of the futures, let r equal an annual rate and specify the life of the futures as T years. Then the futures price is found as f0 (T) = S0 (1 + r)T
As an example, consider a futures contract that has a life of 182 days; the annual interest rate is 5 percent. Then T = 182/365 and r = 0.05. If the spot price is $100, the futures price would then be: f0 (T) = S0 (1 + r)T = 100(1.05)182/365 = 102.46
PRICING FUTURES WHEN THERE ARE STORAGE COSTS Let us specify this cost with the variable FV(SC,O,T), which denotes the value at time T (expiration) of the storage costs (excluding opportunity costs) associated with holding the asset over the period 0 to T. We would buy the asset at So, sell a futures contract at fo(T), store the asset and accumulate costs of FV(SC,O,T), and deliver the asset at expiration to receive the futures price. The total payoff is fo(T) - FV(SC,O,T). This amount is risk free. To avoid an arbitrage opportunity, its present value should equal the initial outlay, So, required to establish the position. Thus, [fo(T) - FV(SC,O,T)] / (1 + r) T = S0 Solving for the futures price gives fo(T) = S0 (1 + r)T + FV(SC,O,T) This result says that the futures price equals the spot price compounded over the life of the futures contract at the risk-free rate, plus the future value of the storage costs over the life of the contract.
Q. The price of Silver was $ 7.511 per ounce in the New York on April 15, 2005. At the end of the trading day the settlement price of the December Futures contract price was $8.456. The rate of lending is 11% p.a. on Eurodollars. The cost of storing silver is negligible. Find: 1. The cost-of-carry price relationship between the cash price of silver and the Silver futures price. 2. Is there any arbitrage opportunity based on your answer above.
Ans. The fair price of the Futures can be calculated as follows: fo(T) = S0 (1 + r)T + FV(SC,O,T) Therefore Fair price of Futures is = 7.511 *(1+0.11)^8/12 + 0 = $ 8.061 per ounce 2. Futures are now priced at $8.456 but the fair price is $ 8.061, thus the futures is overpriced.
So the strategy should be to sell the futures and buy the silver in spot market. April, 2005 Cash Silver : $7.511 per ounce December 2005 Futures price is $ 8.061 per ounce.
Actions 1. On April 2005 Sell Dec Futures Borrow $ 7.511 Buy Cash Silver
0 +7.511 -7.511 0 +8.456 -8.061 0.395 per ounce
On December 2005 1. Deliver cash silver against futures 2. Payback borrowed amount with principal 3. Net Arbitrage Profit
Example: An asset is selling for $225. A futures contract expires in 150 days (T = 150/365 = 0.41 1). The risk-free rate is 7.5 percent, and the net cost of carry is $5.75. The futures price will be?
Ans: fo(T) = fo(O.411) = $225(1.075)0.411+$5.75 = $237.54 Sometimes the opportunity cost of interest is converted to dollars and imbedded in the cost of carry. Then we say that fo(T) = So + FV(CB,0,T); the futures price is the spot price plus the cost of carry,
doc_526035102.pptx
ctcm
Futures
? October Groundnut oil futures are selling at 19.44 cents per lb. The standard size of the contract is 60,000 lbs. Initial Margin is $3000 while the maintenance margin is $1500. If a trader goes long in two October futures contracts and the prices on the subsequent four days are 19, 19.4, 19.6 and 19.8 cents/lb, explain how the margin account changes. Assume that money in excess of the initial margin is withdrawn immediately.
Futures
Ans:
Initial Margin Requirement per contract = $3000 Maintenance Margin per contract = $1500
Day Change in Price cents/lb Change in contract value 0.44/100* 60000*2 = 528 0.40/100* 60000*2 = 480 240 240 Margin Call Margin withdarwal Balance amount $6000 19.00-19.44 = -0.44 5472
0 1
2
19.40-19.00 = 0.40
-
-
5952
3 4
19.60-19.40 = 0.20 19.80-19.60 = 0.20
-
192 240
6000 6000
?
Today, September 1, the jeweler is setting the price of jewelry to be sold in December through the catalog he is printing. His major input expense is the cost of gold, which changes from day to day in the market. Today, the jeweler sees the following prices: Spot gold, $375 per ounce Gold futures for December delivery, $380 per ounce.
? ?
Required : i. What is the effective cost to the jeweler if the futures price in December is $400 per ounce ii. What is the effective cost to the jeweler if the futures price in December is $350 per ounce Note : At the expiration of a futures contract, the spot and futures price normally converge, i.e., become the same
PRICING OF FUTURES
So in general, through the forces of arbitrage, we say that the futures price is the spot price compounded at the risk-free rate: f0 (T) = S0 (1 + r) Therefore, to compound the asset price over the life of the futures, let r equal an annual rate and specify the life of the futures as T years. Then the futures price is found as f0 (T) = S0 (1 + r)T
As an example, consider a futures contract that has a life of 182 days; the annual interest rate is 5 percent. Then T = 182/365 and r = 0.05. If the spot price is $100, the futures price would then be: f0 (T) = S0 (1 + r)T = 100(1.05)182/365 = 102.46
PRICING FUTURES WHEN THERE ARE STORAGE COSTS Let us specify this cost with the variable FV(SC,O,T), which denotes the value at time T (expiration) of the storage costs (excluding opportunity costs) associated with holding the asset over the period 0 to T. We would buy the asset at So, sell a futures contract at fo(T), store the asset and accumulate costs of FV(SC,O,T), and deliver the asset at expiration to receive the futures price. The total payoff is fo(T) - FV(SC,O,T). This amount is risk free. To avoid an arbitrage opportunity, its present value should equal the initial outlay, So, required to establish the position. Thus, [fo(T) - FV(SC,O,T)] / (1 + r) T = S0 Solving for the futures price gives fo(T) = S0 (1 + r)T + FV(SC,O,T) This result says that the futures price equals the spot price compounded over the life of the futures contract at the risk-free rate, plus the future value of the storage costs over the life of the contract.
Q. The price of Silver was $ 7.511 per ounce in the New York on April 15, 2005. At the end of the trading day the settlement price of the December Futures contract price was $8.456. The rate of lending is 11% p.a. on Eurodollars. The cost of storing silver is negligible. Find: 1. The cost-of-carry price relationship between the cash price of silver and the Silver futures price. 2. Is there any arbitrage opportunity based on your answer above.
Ans. The fair price of the Futures can be calculated as follows: fo(T) = S0 (1 + r)T + FV(SC,O,T) Therefore Fair price of Futures is = 7.511 *(1+0.11)^8/12 + 0 = $ 8.061 per ounce 2. Futures are now priced at $8.456 but the fair price is $ 8.061, thus the futures is overpriced.
So the strategy should be to sell the futures and buy the silver in spot market. April, 2005 Cash Silver : $7.511 per ounce December 2005 Futures price is $ 8.061 per ounce.
Actions 1. On April 2005 Sell Dec Futures Borrow $ 7.511 Buy Cash Silver
0 +7.511 -7.511 0 +8.456 -8.061 0.395 per ounce
On December 2005 1. Deliver cash silver against futures 2. Payback borrowed amount with principal 3. Net Arbitrage Profit
Example: An asset is selling for $225. A futures contract expires in 150 days (T = 150/365 = 0.41 1). The risk-free rate is 7.5 percent, and the net cost of carry is $5.75. The futures price will be?
Ans: fo(T) = fo(O.411) = $225(1.075)0.411+$5.75 = $237.54 Sometimes the opportunity cost of interest is converted to dollars and imbedded in the cost of carry. Then we say that fo(T) = So + FV(CB,0,T); the futures price is the spot price plus the cost of carry,
doc_526035102.pptx