You are provided the information outlined as follows to be used in solving this problem.

Situation A. A fixed-income manager holding a $20 million market value position of U.S. Treasury 11¾% bonds maturing November 15, 2024, expects the economic growth rate and the inflation rate to be above market expectations in the near future. Institutional rigidities prevent any existing bonds in the portfolio from being sold in the cash market.

Situation B. The treasurer of XYZ Corporation has recently become convinced that interest rates will decline in the near future. He believes it is an opportune time to purchase his company’s sinking fund bonds in advance of requirements because these bonds are trading at a discount from par value. He is preparing to purchase in the open market $20 million par value XYZ Corporation 12½% bonds maturing June 1, 2015. A $20 million par value position of these bonds is currently offered in the open market at 93. Unfortunately, the treasurer must obtain approval from the board of directors for such a purchase, and this approval process can take up to 2 months. The board of directors’ approval in this instance is only a formality.

For each of these two situations, demonstrate how interest rate risk can be hedged using the Treasury bond futures contract. Show all calculations, including the number of futures contracts used.

Modified Duration* Yield to Issue Price Maturity 7.6 years 11.75% U.S. Treasury bond 1134% maturing Nov. 15, 2024 100 U.S. Treasury long bond futures contract (contract expiration in 6 months) 8.0 years 63.33 11.85% XYZ Corporation bond 12%% maturing June 1, 2015 (sinking fund debenture, rated AAA) Volatility of AAA corporate bond yields relative to U.S. Treasury bond yields = 1.25 to 1.0 (1.25 times) Assume no commission and no margin requirements on U.S. Treasury long bond futures contracts. Assume no taxes. 7.2 years 93 13.50% One U.S. Treasury bond futures contract is a claim on $100,000 par value long-term U.S. Treasury bonds. *Modified duration - Duration/(1 + y).