Compute the cross-hedge ratio and the number of T-bond futures contract.

It is March 1. A corporation plans to issue $10 million in sukuks on June 1, with coupon rate 6.25 percent, maturity 20 years, and yield 7.5 percent. Fearing a rise in interest rates, the corporation decides to hedge against a decline in value of its sukuk issue. It hedges its position through selling T-bond futures contracts with delivery June 1. The underlying is a hypothetical T-bond, 6 percent coupon, 20-year maturity, $100 face value, with yield 6.15 percent selling at FT = 98.28722. The corporation determines that the cheapest-to-deliver bond (CTD) will be a Treasury bond with coupon rate 6.75 percent, yield of 5.95 percent, and 16 years remaining to maturity at the delivery date. Compute the conversion factor for the CTD bond. Compute the target yield of the CTD and of the sukuk. Compute the modified durations of the CTD and of the sukuk. Compute the cross-hedge ratio and the number of T-bond futures contract.

 

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