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 10 basis points for every 21-basis-point move in the yield on 5-year bonds. You hold a $1.5 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 = $70. How many futures contracts should you sell? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)

Answer 1

The yield on momentary securities tends to be more eccentric than yields on long haul securities. In the event that it is assessed that the yield on 20-year securities changes by 10 premise focuses for each 15-premise point move in the yield on 5-year securities. One is holding a $1 million arrangement of 5-year development securities with changed length 4 years and ready to support his loan cost introduction with T-bond prospects. T-bond fates as of now have adjusted term 9 years and sell at $95 (F0).

The quantity of prospects gets that he should sell can be determined as demonstrated as follows: according to the assumption the portfolio misfortune considering the given data would be:

P = Portfolio esteem =$1,000.000

D = Modified length =4 years

Ay =Bond portfolio yield =15 premise

Misfortune on the Portfolio = P x Ay =$1,000,000 x 0.15%x 4 = $6,000

The adjustment in the fates cost (per $100 standard worth) will be as determined underneath:

$95 x 0.0001x 9 = $0.0855

This is a difference in $85.50 on a $100,000 standard worth agreements. Along these lines you should sell: $6,000/$85.50= 70

Hence, he ought to go short is 70 contracts.