Exam 21: Forward and Futures Contracts

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: -Refer to Exhibit 21.12. What is the implied 90-day forward rate at the beginning of the third quarter?

In your portfolio you have $1 million of 20 year, 8 5/8 percent bonds which are selling at 83.15 (or 83 15/32) against this position. Because you feel interest rates will rise you sell 10 bond futures at 81.15 (or 81 15/32) against this position. Two months later you decide to close your position. The bonds have fallen to 78 and the futures contracts are at 75.16 (75 16/32). Disregarding margin and transaction costs, what is your gain or loss?

Exhibit 21.2 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Assume you are the Treasurer for the Johnson Pharmaceutical Company and in late July 2004, the company is considering the sale of $500 million in 20-year debentures that will most likely be rated the same as the firm's other debt issues. The firm would like to proceed at the current rate of 8.5%, but you know that it will probably take until November to bring the issue to market. Therefore, you suggest that the firm hedge the pending issue using Treasury bond futures contracts which each represent $100,000. -Refer to Exhibit 21.2. What is the dollar gain or loss assuming that future conditions described in Case 1 actually occur? (Ignore commissions and margin costs, and assume a naive hedge ratio.)

The major difference between valuing futures versus forward contracts stems from the fact that future contracts are

The main tradeoff between forward and future contracts is

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

The number of future contracts needed to hedge a unit of the spot assets is solely a function of the variance of the spot prices.

Exhibit 21.4 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) A 3-month T-bond futures contract (maturity 20 years, coupon 6%, face $100,000) currently trades at $98,781.25 (implied yield 6.11%). A 3-month T-note futures contract (maturity 10 years, coupon 6%, face $100,000) currently trades at $101,468.80 (implied yield 5.80%). Assume semiannual compounding. -Refer to Exhibit 21.4. If you expected the yield curve to steepen, the appropriate NOB futures spread strategy would be

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. -Refer to Exhibit 21.1. What is the dollar gain or loss assuming that future conditions described in Case 1 actually occur? (Ignore commissions and margin costs, and assume a naive hedge ratio.)

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: -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 third quarter?

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

Stock index futures are useful in providing a hedge against movements in an underlying financial asset.

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. Assume that a month later the equity portfolio has a market value of $20,000,000 and the stock index future is priced at 1150 with a multiplier of 250. Calculate the profit on the stock index futures position.

Exhibit 21.4 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) A 3-month T-bond futures contract (maturity 20 years, coupon 6%, face $100,000) currently trades at $98,781.25 (implied yield 6.11%). A 3-month T-note futures contract (maturity 10 years, coupon 6%, face $100,000) currently trades at $101,468.80 (implied yield 5.80%). Assume semiannual compounding. -Refer to Exhibit 21.4. Suppose the yield curve changed so the that the new yield on the T-bond contract rose to 6.5% and the new yield on the T-note contract fell to 5.5%. Calculate the profit on the NOB futures spread. (Assume coupons are paid semiannually)

The optimal hedge ratio is a function of all of the following except

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 1050, indicate the appropriate strategy that would earn an arbitrage profit.

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. -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.)

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: -Assume that you manage a $50 million equity portfolio. The portfolio beta is 0.85. You anticipate a cash inflow of $5 million into the portfolio. Calculate the number of contracts you would need to hedge your position and indicate whether you would go short or long. Assume that the price of the S&P 500 futures contract is 1062 and the multiplier is 250.

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: -Refer to Exhibit 21.12. What is the implied 90-day forward rate at the beginning of the second quarter?

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.