Chartered Financial Analyst (CFA) Practice Exam Level 2

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What formula is used to calculate Effective Duration (ED) of a bond?

ED = (P- + P+)/[2(P0)(Change Y)]
ED = (Change in Price)/(Change in Yield)
ED = Macaulay Duration / (1 + YTM)
ED = (Present Value of Cash Flows)/(Price of Bond)

The correct answer is: ED = (P- + P+)/[2(P0)(Change Y)]

Effective Duration (ED) is a measure that assesses the sensitivity of a bond's price to changes in yield, taking into account the possibility of cash flow changes due to embedded options. The correct formula emphasizes how bond pricing reacts to shifts in interest rates, making it suitable for bonds that may not have fixed cash flows. The formula for Effective Duration is as follows: ED = (P- + P+)/[2(P0)(Change Y)]. Here, P- denotes the price of the bond when yield decreases, P+ is the price when yield increases, P0 is the initial price of the bond, and Change Y reflects the change in yield. This formula effectively captures the asymmetrical relationship between price changes and yield changes in a bond that may have option-like features. This approach considers both directions of yield change, providing a more accurate measure of the bond's risk exposure relative to interest rate fluctuations. Taking the average of the price changes (P- and P+) while normalizing it against the initial price and the change in yield yields a comprehensive perspective that is particularly beneficial for managing fixed income portfolios.