Chapter 23, Problem 17PS

Summary Introduction

To calculate: The number of bonds to be sold for hedging the risk surrounding the position in which both the bond and the contract are at par value.

Introduction: When there is market down, to overcome this situation selling of bonds is better solution. The hedging strategy is used to maintain the position in the market and minimize the risk value.

Answer to Problem 17PS

The number of bonds is 133 to be sold to hedge the position.

Explanation of Solution

  $\begin{array}{l}Changeinbonds’value=bondvalue\times change\times modifiedduration\hfill \\ =\$10,000,000\times 0.0001\times 8\hfill \\ =\$8,000\hfill \end{array}$

Now calculate the value change in treasury future,

  $\begin{array}{l}Valuechangeintreasuryfutures=T-futuresvalue\times change\times duration\hfill \\ =\$10,000,000\times 0.0001\times 6\hfill \\ =\$60\hfill \end{array}$

Hence the change in 1-basis point on treasury bonds is $60.

Now, $\begin{array}{l}numberofcontractstobesold=\left(changeinbondvalue\right)/\left(changeintreasuryfuture\right)\hfill \\ =\$8000/\$60\hfill \\ =133\hfill \end{array}$

Hence the 133 bonds should be sold to hedge the position in market.