1. Suppose you can earn 6% riskfree forever. You will need $100,000 in 12 years. A hypothetical riskfree zero coupon bond will "bullet immunize" this cash requirement.
a. What should the market price of this bond be?
b. What should the duration of this bond be?
c. What should the yield to maturity of this bond be?
2. A bank has interest sensitive assets of $567 million; its interest sensitive liabilities are $233 million, with a duration of 5.56 years. What should the duration of the interest sensitive assets be in order to immunize the bank's portfolio?
3.Given the following data:
Portfolio par value = $75 million
Price of bond portfolio = 94% of par
Duration of bond portfolio = 11.50
Yield to maturity of bond portfolio = 7.75%
Price of selected futures contract = 97 % of par
Duration of cheapest to deliver bond = 9.00
Yield to maturity of cheapest to deliver bond = 7.95%
Price of cheapest to deliver bond = 100%
CBT correction factor for cheapest to deliver bond = 0.9200
What is the appropriate hedge ratio?
4.In Problem 3, suppose the task is to hedge 75% of a $100 million bond portfolio. How many of the indicated T bond futures contracts should be used?
5.What is the basis point value of the bond portfolio in Problem 3?
6.What is the basis point value of the cheapest to deliver bond in Problem 3?
7.7.Suppose you wanted to increase the duration of the bond portfolio in Problem 3 to 13.00. How many of the indicated futures contracts would be necessary?
8.Include a current Wall Street Journal listing. Listed below are summary statistics on a U.S. Treasury bond portfolio:
par value market value duration
$12,000,000 $10,100,000 10.55
If the cheapest to deliver bond sells for $980 and has a duration of 12.0, how many "next March" Treasury bond futures must be bought or sold in order to hedge the entire portfolio?
9.What role does the duration statistic play in hedging with interest rate futures?
10.While reviewing some reference material, your supervisor finds the following statement: “While both stock index futures and put options can be used to reduce the risk of a stock portfolio, futures contracts are cheaper to use. The trade-off is between the option premium and the symmetric/asymmetric return distributions.”
a. Explain why a futures contract might be a cheaper means of reducing portfolio risk than using put options.
b. Explain how the return distribution of a stock portfolio hedged with index futures differs from the return distribution of a stock portfolio hedged with put options.
11.You manage a portfolio that is currently 75% stock, 25% bonds. You determine that 300 S&P 500 stock index futures would completely hedge the stock portion of the portfolio, and that 100 T-bond futures would completely hedge the bond portion. At present, you have no open futures positions. You decide to change your asset allocation to 50% stock, 50% bonds. Calculate the number of contracts of each type of futures contract you would buy or sell (state which) in order to achieve the desired mix without changing the underlying portfolio.