Answer: Macaulay duration.

## Explanation **Macaulay duration** is the correct answer because it measures the weighted average time to receive the bond's cash flows, and it represents the point in time where the interest rate risk from price changes is offset by the reinvestment risk from coupon payments. ### Key Concepts: 1. **Macaulay Duration**: - Measures the weighted average time until cash flows are received - Calculated as: \(\text{Macaulay Duration} = \frac{\sum_{t=1}^{n} \frac{t \times C_t}{(1+y)^t}}{P}\) - Where: - \(C_t\) = cash flow at time t - \(y\) = yield to maturity - \(P\) = bond price 2. **Why Macaulay Duration is Correct**: - When interest rates change, two opposing effects occur: - **Price effect**: Bond price changes inversely with interest rates - **Reinvestment effect**: Coupon payments can be reinvested at the new rate - Macaulay duration identifies the time horizon where these two effects exactly offset each other - At the Macaulay duration point, the gain from reinvesting coupons equals the loss from price decline (or vice versa) 3. **Comparison with Other Duration Measures**: - **Modified Duration**: Measures price sensitivity to interest rate changes (percentage change in price for a 1% change in yield) - **Effective Duration**: Similar to modified duration but accounts for embedded options - Neither modified nor effective duration identify the time point where reinvestment and price effects offset ### Example**: For a bond with Macaulay duration of 5 years: - If interest rates rise, the bond price will decline - However, coupon payments can be reinvested at higher rates - After 5 years, the gain from higher reinvestment rates will exactly offset the initial price decline This makes Macaulay duration particularly useful for immunization strategies where investors want to lock in a specific rate of return regardless of interest rate movements.

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