What is the difference between 'duration' and 'modified duration'?

• A. Duration is the sensitivity to parallel yield shifts, and modified duration is the exact percentage change.
• B. Duration is the weighted average time of cash flows; Modified duration approximates percentage price change for small yield changes: MD ≈ D/(1+y).
• C. Duration and modified duration are the same.
• D. Modified duration measures convexity.

Answer: (B)

The main idea is that duration and modified duration measure two related but different things: duration is a time-based measure of when cash flows are received, while modified duration translates that timing into how sensitive the price is to changes in yield. Macaulay duration is the weighted average time to receive all cash flows, expressed in years. Modified duration takes that timing information and converts it into a price sensitivity: MD ≈ D / (1 + y), where y is the yield per period. This means that for a small change in yield Δy, the approximate percentage change in price is -MD × Δy. The minus sign reflects that prices fall when yields rise. Convexity is a separate effect and becomes important for larger yield moves, where the simple MD approximation is less accurate. The other statements aren’t correct because modified duration is not the exact price change (it’s an approximation), duration and modified duration are not the same, and MD does not measure convexity.