Exam 21: Forward and Futures Contracts

Financial futures have become an increasingly attractive investment alternative since the Chicago Board of Trade (CBOT) began trading them in 1977, and their hedging function partly accounts for the growth in trading. Which of the following statements concerning financial futures is true?

Exhibit 21.10 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The S&P 500 stock index is at 1300. The annualized interest rate is 4.0% and the annualized dividend is 2%. You are currently considering purchasing a 2-month futures contract for your portfolio. -Refer to Exhibit 21.10. Calculate the current price of the futures contract.

Exhibit 21.8 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Consider a portfolio manager with a $20,500,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1250 and has a multiplier of 250. The portfolio beta is 1.25. -Refer to Exhibit 21.8. Calculate the number of contract required to hedge the risk exposure and indicate whether the manager should be short or long.

Exhibit 21.9 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) As a portfolio manager, you are responsible for a $150 million portfolio, 90 percent of which is invested in equities, with a portfolio beta of 1.25. You are utilizing the S&P 500 as your passive benchmark. Currently the S&P 500 is valued at 1202. The value of the S&P 500 futures contract is equal to $250 times the value of the index. The beta of the futures contract is 1.0. -Refer to Exhibit 21.9. If you anticipate a cash inflow of $2 million next week, how many futures contracts should you buy or sell in order to mitigate the effect of this inflow on the portfolio's performance (rounded to the nearest integer)?

Exhibit 21.11 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Consider a portfolio manager with a $10,000,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1350 and has a multiplier of 250. The portfolio beta is 1.50. -Refer to Exhibit 21.11. Calculate the overall profit.

The basis (B_t,T) at time t between the spot price (S_t) and a futures contract expiring at time T (F_t,T) is: S_t -F_t,T.

Exhibit 21.8 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Consider a portfolio manager with a $20,500,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1250 and has a multiplier of 250. The portfolio beta is 1.25. -Refer to Exhibit 21.8. Calculate the overall profit.

The main tradeoff between forward and future contracts is

Exhibit 21.12 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Suppose you are a loan officer for a commercial bank and one of your clients has just approached you about a one-year loan for $4,000,000. Interest on the new loan will be paid at the end of each quarter based on the prevailing level of LIBOR at the beginning of each quarter. The LIBOR yield curve in the cash market is as follows: 90 -day LIBOR 2.70\% 180 -day LIBOR 2.85\% 270 -day LIBOR 3.10\% 360 -day LIBOR 3.40\% -Refer to Exhibit 21.12. What is the implied 90-day forward rate at the beginning of the second quarter?

Like future contracts, all forward contracts are processed by a clearing corporation.

Exhibit 21.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) In late January 2004, The Union Cosmos Company is considering the sale of $100 million in 10-year debentures that will probably be rated AAA like the firm's other bond issues. The firm is anxious to proceed at today's rate of 10.5 percent. As treasurer, you know that it will take until sometime in April to get the issue registered and sold. Therefore, you suggest that the firm hedge the pending issue using Treasury bond futures contracts each representing $100,000. Case 1 Case 2 Current Value - January 2004 Bond Rate 10.5\% 10.5\% June 2004 Treasury B onds 78.875 78.875 Estimated Values - April 2004 Bond Rate 11.0\% 10.0\% June 2004 Treasury B onds 75.93 81.84 -Refer to Exhibit 21.1. What is the dollar gain or loss assuming that future conditions described in Case 2 actually occur? (Ignore commissions and margin costs, and assume a naive hedge ratio.)

Which of the following is not considered a "cost of carry"?

The inclusion of dividends in the cost of carry model will increase the futures price.

Exhibit 21.5 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The S&P 500 stock index is at 1100. The annualized interest rate is 3.5% and the annualized dividend is 2%. -Refer to Exhibit 21.5. If the futures contract was currently available for 1250, indicate the appropriate strategy that would earn an arbitrage profit.

Exhibit 21.3 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) As a relationship officer for a money-center commercial bank, one of your corporate accounts has just approached you about a one-year loan for $3,000,000. The customer would pay a quarterly interest expense based on the prevailing level of LIBOR at the beginning of each quarter. As is the bank's convention on all such loans, the amount of the interest payment would then be paid at the end of the quarterly cycle when the new rate for the next cycle is determined. You observe the following LIBOR yield curve in the cash market: 90 -day LIBOR 4.70\% 180 -day LIBOR 4.85\% 270 -day LIBOR 5.10\% 360 -day LIBOR 5.40\% -Refer to Exhibit 21.3. Assuming the yields inferred from the Eurodollar futures contract prices for the next three settlement periods are equal to the implied forward rates, calculate the dollar value of the annuity that would leave the bank indifferent between making the floating-rate loan and hedging it in the futures market, and making a one-year fixed-rate loan.

Exhibit 21.3 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) As a relationship officer for a money-center commercial bank, one of your corporate accounts has just approached you about a one-year loan for $3,000,000. The customer would pay a quarterly interest expense based on the prevailing level of LIBOR at the beginning of each quarter. As is the bank's convention on all such loans, the amount of the interest payment would then be paid at the end of the quarterly cycle when the new rate for the next cycle is determined. You observe the following LIBOR yield curve in the cash market: 90 -day LIBOR 4.70\% 180 -day LIBOR 4.85\% 270 -day LIBOR 5.10\% 360 -day LIBOR 5.40\% -Refer to Exhibit 21.3. If 90-day LIBOR rises to the levels "predicted" by the implied forward rates, what will the dollar level of the bank's interest receipt be at the end of the fourth quarter?

As a contract approaches maturity, the spot price and forward price

Exhibit 21.11 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Consider a portfolio manager with a $10,000,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1350 and has a multiplier of 250. The portfolio beta is 1.50. -In late January 2011, Starlight Corporation is considering the sale of $50 million in 10-year debentures rated AAA. The issue will most likely be registered and sold some time in April. Therefore, Starlight Corporation desires to hedge the pending issue using Treasury bond futures contracts each representing $100,000. Explain how you would go about hedging the bond issue?

Exhibit 21.11 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Consider a portfolio manager with a $10,000,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1350 and has a multiplier of 250. The portfolio beta is 1.50. -Refer to Exhibit 21.11. Assume that a month later the equity portfolio has a market value of $9,500,000 and the stock index future is priced at 1300 with a multiplier of 250. Calculate the profit on the equity position.

According to the cost of carry model the relationship between the spot (S₀) and futures price (F_0,T) is