Chapter 16, Problem 12CP

Summary Introduction

To calculate: The change in price of the both strategy.

Introduction: The change in price is calculated by the modified duration and change in yield. Price change is product of the modified duration to the interest rates of the strategy. It simply shows the change of the prices compared to the initial value.

Answer to Problem 12CP

The change in price of strategy $1$ is $-4.14\%$ and $-3.59\%$ of strategy $2$ .

Explanation of Solution

Here, the formula of modified duration is given,

$Modifiedduration=\left(Pricechange/Initialprice\right)/Yieldchange$ , the price change is calculated by this formula. Calculation of price change is given below,

For strategy $1$ , there are three types of maturity periods, a) $5$ years with modified duration is $4.83$ and interest rates is $0.75$ with $\$5$ million investment in it, b) $15$ years with modified duration is $14.35$ and interest rates is $0.25$ but investment in it is $0million, c) $25$ years with modified duration of $23.81$ with $0.50$ interest rates and $\$5$ million investment in it.

Now price change for $5$ year’s maturity is given below,

  $Pricechange=modifiedduration\times interestrates$

  $\begin{array}{l}=-4.83\times -0.75\%\hfill \\ =3.6225\%\hfill \end{array}$

Price change for $25$ year’s maturity is given below,

  $\begin{array}{l}Pricechange=-23.81\times -0.50\%\hfill \\ \text{ =}-11.905\%\hfill \end{array}$

Hence the total price change is given below,

  $\begin{array}{l}Netpercentagechange=\left(0.50\times 3.6225\%\right)+\left(0.50\times -11.905\%\right)\hfill \\ \text{ =}-4.14\%\hfill \end{array}$

Hence percentage change in strategy $1$ is $-4.14\%.$

Calculate for strategy $2$ , it consists only $15$ year’s maturity period with $14.35$ modified duration and $\$10$ million investments in it.

  $\begin{array}{l}Pricechange=-14.35\times 0.25\%\hfill \\ \text{ =}-3.5875\%\hfill \end{array}$

Hence change in price of strategy $2$ is $-3.59\%.$