Assuming that Guyton wishes to hedge its net worth position with T-bond futures

Question

Assuming that Guyton wishes to hedge its net worth position with T-bond futures (20-year maturity, 8% coupon) and that the current price of the underlying T-bond is $82,841 on face of $100,00. The annualized market yield is therefore 10.00%, and the duration for these bonds is 9.3854. How many contracts are necessary to fully hedge Guyton assuming that yield changes in the spot and futures markets are equivalent? Explain.

Guyton’s balance sheet is given below (in millions): Assets $200 Liabilities $150 Asset Duration (DA): 7.0 Equity $ 50 Liabs Duration (DL): 4.5 Total $200 Total $200

Explanation / Answer

Number of contracts = (Da - (L/A)*Dl )*A / (Db*Pb)

Number of contracts = ( 7 - (150/200)*4.5)*200*106 / (9.3854*82841)

   = 932.4808

= 932 contracts

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