Answer: zero-coupon bond.

## Explanation When the Macaulay duration of a bond equals its time-to-maturity, this is a characteristic property of **zero-coupon bonds**. Here's why: ### Key Concepts: 1. **Macaulay Duration**: Measures the weighted average time until a bond's cash flows are received, weighted by the present value of each cash flow. 2. **Zero-Coupon Bonds**: These bonds make no periodic coupon payments. The only cash flow is the principal repayment at maturity. ### Mathematical Reasoning: For a zero-coupon bond: - There is only one cash flow at maturity (the face value) - The present value weight of this single cash flow is 100% - Therefore, the weighted average time to receive cash flows equals the time-to-maturity ### For Other Bond Types: - **Coupon bonds trading at par**: Macaulay duration is less than time-to-maturity because coupon payments are received before maturity, reducing the weighted average time. - **Coupon bonds trading at premium/discount**: Macaulay duration is also less than time-to-maturity, though the relationship varies with yield-to-maturity. ### Formula Insight: For a zero-coupon bond with maturity T: \[ D_{\text{Macaulay}} = \frac{\sum_{t=1}^{T} t \times PV(CF_t)}{P} = \frac{T \times PV(Face\ Value)}{P} = T \] Since PV(Face Value) = P for a zero-coupon bond. Therefore, the correct answer is **A. zero-coupon bond**.

Author: LeetQuiz .