What does the change in present value of a bond portfolio equal?

The correct answer is that the change in present value of a bond portfolio equals the negative of dollar duration multiplied by change in yield. This relationship stems from the principles of bond pricing and interest rate sensitivity.

Dollar duration is a measure of the sensitivity of a bond's price to interest rate changes. It quantifies how much the dollar value of the bond will change for a given change in interest rates. Specifically, dollar duration indicates the change in the price of a bond for a 1% change in yield.

When yields increase, the present value (or price) of a bond decreases, thus the change in present value is negative. Conversely, when yields decrease, the present value of a bond increases. This inverse relationship between bond prices and interest rates is crucial to understand when assessing the value of a bond portfolio.

Therefore, the correct formula to calculate the change in present value is the negative of dollar duration multiplied by the change in yield. This captures the expected change in the bond portfolio’s value in response to shifts in yield, reflecting the fundamental concept that bond prices will decrease (resulting in a negative change) as interest rates rise, and vice versa.