Question

Frank Meyers, CFA, is a fixed-income portfolio manager for a large pension fund. A member of the Investiment Committee, Fred Spice, is very interested in learning about the management of fixed-income portfolios. Spice has approached Meyers with several questions. Specifically, Spice would like to know how fixed-income managers position portfolios to capitalize on their expectations of future interest rates. 

Meyers decides to illustrate fixed-income trading strategies to Spice using a fixed-rate bond and note. Both bonds have samiannual coupon periods. Unless otherwise stated, all interest rate (yield curve) changes are parallel. The characteristic of these securities are shown in the following table. He also considers a nine-year floating-rate bond (floater) that pays a floating rate semiannually and is currently yielding 5%.

Fixed-rate bond: price 107.18, YTM 5%, TMT (years) 18, modified duration (years) 6.9848.

Fixed-rate note: price 100, YTM 5%, TMT (years) 8, modified duration (years) 3.5851.

Spice asks Meyers to quantify price changes from changes in interest rates. To illustrate, Meyers computes the value change for the fixed-rate note in the table. Specifically, he assumes an increase in the level of interest rate of 100 basis points. What is the predicted change in the price of the fixed-rate note?

Answer 1

Solution

a)

The characteristics of fixed income bond and fixed income notes are given below:

a.

The increase in interest rate will decrease the worth of the portfolio. If the duration of the portfolio will be shorter, then the change in the worth of the portfolio will be lesser. Thus, the bond manager will chose to shorten the duration of the portfolio.

Hence, the most appropriate strategy is to shorten the duration.

b.

The duration of bonds is more than the duration of notes. Thus, the bonds are more sensitive to change in interest rate compared to notes. Therefore, the addition of fixed-rate bond is not a good strategy.

Thus, the option b is not a good strategy.

c.

The duration of the bond is the measure of change in price of the bond due to change in the market rate of interest. The duration and market rate of interest has inverse relationship. The lengthening of duration will increase the sensitivity of the portfolio. If the interest rate will increase then the value of the portfolio will decrease more.

Thus, the option c is not a good strategy.

b)

Modified Duration is a measure of the approximate sensitivity of a bonds’ value to interest rate changes.

Here, the modified duration of fixed rate note is 3.5851. So, if there will be 100 basis point (1%) of increase in the level of interest rate, the price of the bond will be reduced by 3.5851%.

Hence, the predicted change in price will be:

Plug the values in the formula,

Hence, the predicted change in price of fixed rate note is $3.5851.