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 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? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)

Answer 1

Solution

The number of futures contracts that he should sell can be calculated as shown below:

As per the presumption the portfolio loss considering the given information would be:

P = Portfolio value

=$1,000,000

D ^* = Modified duration

=4 years

Δy =Bond portfolio yield

=25.65 basis

= 1000000*0.000002565*4

=10.26

The change in the futures price (per $100 par value) will be as calculated below:

=80*10.26*0.0000075

= 0.006156

Par value contract = 61.56

Contracts to sell = 10.26/61.56*100

= 16.667 ~ 17 contracts