Differentiate between Macaulay duration and modified duration.

• A. Macaulay duration is weighted average time to cash flows; Modified duration adjusts Macaulay for yield and estimates percentage price change for small yield shifts.
• B. Macaulay duration measures percentage price change; Modified duration measures time to cash flows.
• C. Macaulay duration equals maturity.
• D. Macaulay duration is the yield; Modified duration is the risk.

Answer: (A)

The main idea tested here is how duration types relate to bond price sensitivity and timing of cash flows. Macaulay duration is the weighted average time to receive the bond’s cash flows, with weights based on the present value of each cash flow relative to the bond’s price. It’s measured in years and tells you when, on average, you get your money back, reflecting the timing of payments rather than how much price might move.

Modified duration takes that timing measure and adjusts it for yield to convert it into a price-change indicator. Specifically, modified duration equals Macaulay duration divided by (1 plus the yield per period). It then estimates the percentage change in the bond’s price for a small change in yield. So the correct statement captures both parts: Macaulay duration as the time-weighted average to cash flows, and modified duration as the yield-adjusted measure that approximates price sensitivity to yield changes.

Other descriptions mix these roles—for example, treating Macaulay duration as a price-change metric or equating duration with maturity—so they don’t fit as accurately.