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 25.65-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 F0 = $80. How many futures contracts should you sell?

You should sell 142 contracts

Explanation:

According to the give data we have the following:

Portfolio Value=$1,000,000

Modified Duration=4 years

Bond portfolio yield=25.65 basis

Loss on the porftolio=Portfolio Value*Modified Duration*Bond portfolio yield

Loss on the porftolio=$1,000,000*0.2565%*4

Loss on the porftolio=$10,260

Therefore, change in future price=80*0.0001*9

change in future price=$0.072

Therefore, amount of contracts you should sell=$10,260/$72

amount of contracts you should sell=142 contracts

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