Exam 21: Forward and Futures Contracts

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 1 actually occur? (Ignore commissions and margin costs, and assume a naive hedge ratio.)

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. How many contracts should you buy or sell in order to increase the portfolio beta to 1.30 (rounded to the nearest integer)?

The Chicago Board of Trade (CBT) uses conversion factors to correct for differences in deliverable bonds.

A bond portfolio manager expects a cash inflow of $12,000,000. The manager plans to hedge potential risk with a Treasury futures contract with a value of $105,215. The conversion factor between the CTD and the bond specified in the Treasury futures contract is 0.85. The duration of bond portfolio is 8 years, and the duration of the CTD bond is 6.5 years. Indicate the number of contracts required and whether the position to be taken is 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. How many contracts should you buy or sell in order to reduce the portfolio beta to 0.80 (rounded to the nearest integer)?

If you were bearish on the near term outlook for the stock market but did not want to sell your portfolio, you could hedge against the decline by selling stock index futures.

Exhibit 21.7 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Assume that you observe the following prices in the T-Bill and Eurodollar futures markets T-Bill Eurodollar September 95.24 94.6 -Refer to Exhibit 21.7. Assume that a month later the price of the September T-Bill future is 96.25 and the price of the Eurodollar future is 95.9. Calculate the profit on the T-Bill futures position.

Financial futures include all of the following underlying securities except

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)

A bond portfolio manager expects a cash outflow of $35,000,000. The manager plans to hedge potential risk with a Treasury futures contract with a value of $105,215. The conversion factor between the CTD and the bond specified in the Treasury futures contract is 0.85. The duration of bond portfolio is 8 years, and the duration of the CTD bond is 6.5 years. Indicate the number of contracts required and whether the position to be taken is short or long.

Forward contracts are individually designed agreements, and can be tailored to the specific needs of the ultimate end-user.

The bond that maximizes the difference between the invoice price and the delivery price is referred to as the

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. Calculate the price of the futures contract now.

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 number of contract required to hedge the risk exposure and indicate whether the manager should be short or long.

Which of the following is true when F_0,T < E(S_T)?

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. What is the implied 90-day forward rate at the beginning of the third quarter?

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. What is the implied 90-day forward rate at the beginning of the second quarter?

According to the cost of carry model the futures price is the present value of the spot price discounted at the risk free rate.