Yields on short-term bonds tend to be more volatile than yields on long-term bon

Question

Yields on short-term bonds tend to be more volatile than yields on long-term bonds. Suppose that you have estimated that the yield on 20-year bonds changes by 7.5 basis points for every 39.15 basis point move in the yield on 5 year bonds. You hold a $1 million portfolio of 5-year maturity bonds with modified duration 4 years and desire to hedge your interest rate exposure with T-bond futures, which currently have modified duration 9 years and sell at F $80. How many futures contracts should you sell? (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Number of future contracts

Explanation / Answer

?P/P = -(Modified Duration)*?y

?P = -(Modified Duration)*?y*P

You need to adjust in such a way that duration of portfolio is zero.

1,000,000*4 + 80*9*N = 0

N = -4,000,000 / 720 = -5,555.56

You need to short 5,556 contract.

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