Question

The modified duration of a bond portfolio worth $175 million is 4.625 years. By approximately how much does the value of the portfolio change, if all yields increase by 25 basis points?

a. Decrease $2,023,500
b. Decrease $437,500
c. Increase $2,500,500
d. Decrease $250,500

Answer 1

The value of the portfolio is expected to increase by approximately $2,031,250 if all yields increase by 25 basis points.

Step-by-step explanation:

The modified duration of a bond portfolio measures the sensitivity of the portfolio's value to changes in interest rates. In this case, the modified duration of the bond portfolio is given as 4.625 years. A basis point is equivalent to 0.01%, so a 25 basis point increase is equivalent to a 0.25% increase in interest rates. To calculate the approximate change in the value of the portfolio, you can use the formula:

Change in portfolio value = (Modified duration) x (Change in interest rates) x (Current value of the portfolio)

Plugging in the given values, we get:

Change in portfolio value = 4.625 x 0.0025 x $175 million

Change in portfolio value = $2,031,250

Therefore, the value of the portfolio is expected to increase by approximately $2,031,250 if all yields increase by 25 basis points.