What formula represents effective duration?

Effective duration is a measure of a bond's sensitivity to interest rate changes, taking into account the potential changes in cash flow due to embedded options, such as call or put features. The formula for effective duration captures how the price of a bond changes in response to interest rate movements, reflecting the convexity in cash flows.

The correct formula for effective duration is represented as follows: (Price up - Price down) / (2 x change in "i" x original price). This formula effectively calculates the average price change of the bond for a small change in yield, normalized by the bond's original price. The "Price up" and "Price down" represent the bond's price when interest rates decrease and increase, respectively, while "change in i" signifies the small change in interest rates.

By dividing the price change by the product of 2, the change in interest, and the original price, this formula captures a more comprehensive measure of duration that accounts for both sides of the price movement linked to interest rate fluctuations. It emphasizes the average sensitivity of the bond's price to changes in interest rates, making it particularly effective when the bond has embedded options that can alter cash flows.

The other formulas provided do not adequately reflect the characteristics of effective duration