What does the duration formula represent?

The duration formula represents the sensitivity of the price of a bond or fixed income instrument to changes in interest rates. Specifically, the formula captures how much the price of the bond will change in response to a change in yield, which is a critical concept in risk management for interest rate risk.

In the chosen formula, the negative sign indicates that there is an inverse relationship between bond prices and yield; as interest rates increase (a rise in yield), the price of the bond decreases, and vice versa. By defining duration as the negative change in price divided by the product of the initial price and the change in yield, it effectively provides a measure of the percentage change in price per 1% change in yield. This analysis of interest rates helps in understanding how sensitive a bond’s price is to fluctuations in yield, which is essential information for investors managing interest rate risk.

The other options do not accurately express the fundamental relationship between price changes and yield changes nor do they factor in the necessary negative sign to reflect the inverse price-yield relationship. This highlights why the selected formula is appropriate in the context of duration analysis in financial risk management.