Exam 15: Forward, Futures, and Swap Contracts

A riskless stock index arbitrage profit is possible if the following condition holds: F_0,T = S₀(1 + r_f - d)^T, where spot price now is S₀, value now of a futures contract expiring at time T is (F_0,T), r_f is the risk free rate, and d is the dividend.

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 15.10. 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 equity position.

In the strategy known as _____, the arbitrageur will always hold the security denominated in the currency that is the least expensive to deliver in the futures market.

The settlement price is set by the futures exchange after trading ends to reflect the midpoint of the closing price range.

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 15.13. 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.

Equity swaps are traded in the OTC markets.

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

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 bonds 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 15.1. What is the dollar gain or loss assuming that future conditions described in Case 1 actually occur? (Ignore commissions and margin costs.)

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 15.13. Assume that a month later the equity portfolio has a market value of $10,000,000 and the stock index future is priced at 1300 with a multiplier of 250. Calculate the profit (loss) on the stock index futures position.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Darden Industries has decided to borrow $25,000,000.00 for six months in two three-month issues. As the Treasurer, you are concerned that interest rates will rise over the next three months and the rate upon which the second payment will be based will be undesirable. (The amount of Darden's first payment will be known at origination.) To reduce the company's interest rate exposure, you decide to purchase a 3 * 6 FRA whereby you pay the dealer's quoted fixed rate of 4.5 percent in exchange for receiving three-month LIBOR at the settlement date. In order to hedge her exposure, the dealer buys LIBOR from McIntire Industries at its bid rate of 4 percent. (Assume a notional principal of $25,000,000.00 and that there are 60 days between month 3 and month 6.) -Refer to Exhibit 15.15. Assuming that three-month LIBOR is 5.00 percent on the rate determination day, and the contract specified settlement in advance, describe the transaction that occurs between the dealer and McIntire.

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

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Darden Industries has decided to borrow $25,000,000.00 for six months in two three-month issues. As the Treasurer, you are concerned that interest rates will rise over the next three months and the rate upon which the second payment will be based will be undesirable. (The amount of Darden's first payment will be known at origination.) To reduce the company's interest rate exposure, you decide to purchase a 3 * 6 FRA whereby you pay the dealer's quoted fixed rate of 4.5 percent in exchange for receiving three-month LIBOR at the settlement date. In order to hedge her exposure, the dealer buys LIBOR from McIntire Industries at its bid rate of 4 percent. (Assume a notional principal of $25,000,000.00 and that there are 60 days between month 3 and month 6.) -Refer to Exhibit 15.15. Assuming that three-month LIBOR is 5.00 percent on the rate determination day, and the contract specified settlement in arrears at month 6, describe the transaction that occurs between the dealer and Darden.

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 bonds 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 15.2. What is the dollar gain or loss assuming that future conditions described in Case 2 actually occur? (Ignore commissions and margin costs .)

The forward rate agreement is the most complicated of the OTC interest rate contracts.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Assume that you observe the following prices in the T-Bill and Eurodollar futures markets -Refer to Exhibit 15.5. Assume that a month later the price of the September T-Bill future is 93 and the price of the Eurodollar future is 90.25. Calculate the profit on the T-Bill futures position.

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 eight 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.

An investor in a hedge position is no longer exposed to the absolute price movement of the underlying asset, but the investor is still exposed to basis risk.

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 15.3. 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.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The WallMal Company has entered into a four-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8 percent per year and receive six-month LIBOR. The notional principal is $50,000,000. -Refer to Exhibit 15.19. Assuming that one year after the swap was initiated the fixed rate on a new three-year receive fixed pay floating LIBOR swap has fallen to 7 percent per year, calculate the market value of the 8 percent fixed rate bond based on a $100 face value. Settlement is on a semiannual basis.

A backwardated futures market occurs when