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# Futures and Options

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1. The CBOT offers a mini Dow Jones future contract. The multiplier on the contract is 10. The initial margin is \$6,000; maintenance margin is \$2,500. As of the close of trading Monday, February 18 the June contract was priced at 12358. You can find quotes at the Wall Street Journal's Market Data Center. Assume that on Monday the 21st you take a short position in one contract (at the closing price). You deposit \$6,000 margin.

A. Record settlement prices for trading on Tuesday - Friday (February 19-22).
B. Construct a table showing charges and credits to the margin account.
C. At what price will (or did) a margin call occur?

2. The DJIA closed on February 18 at 12348.21. The September 2008 future contract (214 days) was priced at 12366. Continuously compounded interest rates are 4%.

A. Assuming the contract is correctly priced compute the dividend yield for the DJIA.
B. Now assume that the dividend yield is 3%. Compute the correct price for the contract.
C. Given your answer in B describe an arbitrage strategy you could profit from given that the future is priced at 12500. Describe all transactions. How much profit would you earn?

3. The spot price of 40,000 pounds of live-cattle is \$35,000. You are interested in an August 2008 (6 months) cattle forward contract. The cost of caring for cattle between now and August 2008 is \$6000. This amount would be paid in three equal installments in February 2008, May 2008 2007 and August 2008. Interest rates are 6%.

A. Compute the theoretical future price for the contract.
B. You take a long position in the contract at the price computed in part A. What is the value of the forward contract when you enter it? In April 2008 cattle forwards are selling for \$47,000.Compute the value of your contract.

4. Today the spot price of Brazilian coffee is \$1.07/ pound. The December 2008 future is priced at 117.50 cents per pound. Each contract is for 40,000 pounds. You are a coffee grower and expect to have 120,000 pounds of coffee ready for delivery in December 2008.
A. Describe the position you should take in the futures market to hedge your price risk.
B. You enter into the position described in (A). Three months from now (in May) you sell your coffee in the spot market and close your future position. At this time
(December) the spot price of coffee is \$1.15 per pound and the future is priced at \$1.19. Compute the effective price per pound you receive for your coffee.

5. A shirt manufacturer would like to hedge against an increase in the price of materials. She finds that cotton futures have an 85% correlation with her raw material costs. The price of cotton futures has a standard deviation of 15 cents; her raw material costs have a standard deviation of 20 cents. She anticipated purchasing 500,000 pounds of material in September 2008. Cotton futures contracts are for 50,000 pounds.
A. What position should the shirt manufacturer take in the futures market (Long/short and number of contracts)?
B. Has she eliminated price risk? Briefly explain.

6. You have \$2 million of retirement savings. Your funds are invested in a mutual fund with a beta of .7.
A. You are worried about a market correction so you would like to reduce your beta to 0 between now and June by using the future contract from Problem #1. Should you take a long or a short position? How many contracts should you use?
B. Assume you take the position described in A. In June the DJIA has increased to
12600. Your portfolio has increased in value to \$2.1 million. How close did you come to the desired result?
C. Now assume that you feel the market will do well so you would like to increase your beta to 1.4. What position should you take in the June DJIA future?

7. The Dow Jones is currently listed at 12348.21. You find that a Put on a June 2008 futures contract (X = 12500) is selling for \$697. Interest rates are 4%. Compute the theoretical value of a June 2008 call with exercise price = 12500.

8. Use the Black model to compute the value of the call option priced in number 7. Volatility is 15%

#### Solution Preview

Practice problems for exam 2. Attempt problems and we will discuss during the review session in Cramer Hall. Any necessary equations can be created using Microsoft's equation editor (Insert/Object/Microsoft Equation).

1. The CBOT offers a mini Dow Jones future contract. The multiplier on the contract is 10.
The initial margin is \$6,000; maintenance margin is \$2,500. As of the close of trading
Monday, February 18 the June contract was priced at 12358. You can find quotes at the Wall Street Journal's Market Data Center.
Assume that on Monday the 18th you take a short position in one contract (at the closing price). You deposit \$6,000 margin.

Monday, February 18, 2008 12,358

A. Record settlement prices for trading on Tuesday - Friday (February 19-22).

Tuesday, February 19, 2008 12,397
Wednesday, February 20, 2008 12,440
Thursday, February 21, 2008 12,329
Friday, February 22, 2008 12,405

B. Construct a table showing charges and credits to the margin account.

Since there is a short position in futures, a gain occurs when price falls and a loss occurs when price increases.

Multiplier on the Contract 10
Price at which the contract is entered into: 12,358

Initial Margin \$6,000

Date Closing price Change in price (Daily settlement) Gain/Loss Amount in margin account
Tuesday, February 19, 2008 12,397 39 =12397-12358 -\$390 =-10x39 \$5,610 =-390+6000
Wednesday, February 20, 2008 12,440 43 =12440-12397 -\$430 =-10x43 \$5,180 =-430+5610
Thursday, February 21, 2008 12,329 -111 =12329-12440 \$1,110 =-10x-111 \$6,290 =1110+5180
Friday, February 22, 2008 12,405 76 =12405-12329 -\$760 =-10x76 \$5,530 =-760+6290

C. At what price will (or did) a margin call occur?

Multiplier on the Contract 10
Price at which the contract is entered into: 12,358

Initial Margin \$6,000
Maintenance margin \$2,500

A margin call will occur when the amount in the margin account drops below \$2,500
Therefore the price will have to rise above 12,358 by 350 =(6000 - 2500)/10
i.e the future price will be 12,708 =12358+350

2. The DJIA closed on February 18 at 12348.21. The September 2008 future contract (214 days) was priced at 12366. Continuously compounded interest rates are 4%.

A. Assuming the contract is correctly priced compute the dividend yield for the DJIA.

F0 = S0 e(r-q )T

Spot price today = S0: = 12348.21
Futures price today = F0: = 12366
Time until delivery date = T: = 0.5863 years =214/365
Risk-free interest rate for maturity T = r: = 4%
dividend yield = q = to be determined

Therefore, q= 3.75% =0.04-(LN(12366/12348.21) / 0.5863)

B. Now assume that the dividend yield is 3%. Compute the correct price for the contract.

F0 = S0 e(r-q )T

Spot price today = S0: = 12348.21
Futures price today = F0: = to be determined
Time until delivery date = T: = 0.5863 years =214/365
Risk-free interest rate for maturity T = r: = 4%
dividend yield = q = 3%

Therefore, F0= 12420.82 ...

#### Solution Summary

Answers questions on Future contracts (margin account, theoretical future price for the contract, hedging price risk using futures, future contract to reduce beta of an investment) and Options (put, theoretical value, Black model to compute the value of the call option)

\$2.19