An open-end bond mutual fund is holding a three-year,$1 million face value 5 percent annual coupon bond selling at par.What is the impact on the total asset value of the fund of a 1 percent decrease in interest rates?
A)A decrease of $10,000.
B)An increase of $10,000.
C)A decrease of $26,730.
D)An increase of $27,751.

Question

Quizplus · Accepted Answer

First, we need to calculate the current market value of the bond. Since it is selling at par, the market value is equal to its face value:

Current market value = $1 million

Next, we need to calculate the bond's price sensitivity to changes in interest rates, which is measured by its duration. We are not given the duration of the bond, so we need to calculate it:

Duration = (1 x 3) + [(1 - 1/1.05^3)/0.05] 
= 3.78

Now we can use the duration to estimate the bond's price change in response to a 1 percent decrease in interest rates:

Price change = -duration x (change in interest rates) x (current market value) 
= -3.78 x (-0.01) x $1 million 
= $37,800

Since the fund holds the entire bond, the price change also represents the change in the total asset value of the fund. Therefore, a 1 percent decrease in interest rates would result in an increase in total asset value of $37,800 or approximately $27,751 rounded up to the nearest dollar.

Therefore, the correct answer is D.

An Open-End Bond Mutual Fund Is Holding a Three-Year,$1 Million