Question

If a bond portfolio has a market value of $35 million and a Macaulay duration of 5.4 years, what is the expected change in market value for a 1% decrease of interest rates using the modified duration approximation? The portfolio has a yield-to-maturity of 7%.

a. -$1.89 million

b. -$1.77 million

c. +$1.77 million

d. +$1.89 million

Answer 1

Before we arrive at the solution, let's see how change in interest rate will change the market value of the bond portfolio.

Let's substitute the value of YTM and Duration

=5.0467%

The above figure means that if rate changes by 1% the price will change by 5.0467%

In the said question, a decrease in rate by 1% will increase the price by 5.0467% due to the inverse relationship.

Market Value = $35 million

Change in market value = 5.0467% of 35 million = $1.766 million or $1.77 million(rounded off)

The correct answer is Option C (+$1.77 million)