Question at position 3 For bonds, price sensitivity to a given change in interest rates is generally greater the longer before the bond matures.TrueFalse单项选择题
A
True
B
False

Question

Question at position 3 For bonds, price sensitivity to a given change in interest rates is generally greater the longer before the bond matures.TrueFalse

BlackTom AI · Accepted Answer

Bond price sensitivity to interest-rate changes is captured by duration (and convexity). Macaulay duration measures the weighted-average time to receive cash flows; modified duration = Macaulay / (1 + yield) approximates the percentage price change for a small change in yield: ΔP/P ≈ −(modified duration) × Δy. Longer maturity generally means cash flows are weighted farther in the future, raising Macaulay duration and thus modified duration; therefore price sensitivity to a given Δy rises with maturity.

Step-by-step reasoning:
1. Relevant formulae: Macaulay duration D_M = Σ[t × PV(CF_t)] / Price. Modified duration D_mod = D_M / (1 + y). Approximate percentage price change: ΔP/P ≈ −D_mod × Δy.
2. For a zero-coupon bond, all cash flow is at maturity t = n, so D_M = n. Thus D_mod = n / (1 + y). A longer n gives a larger D_mod, so a larger |ΔP/P| for the same Δy.
3. Numerical illustration: assume yield y = 5% and Δy = +1% (0.01). For a 10-year zero-coupon, D_M = 10, so D_mod = 10 / 1.05 = 9.5238. Approximate percent price change = −9.5238 × 0.01 = −9.52%. For a 2-year zero-coupon, D_mod = 2 / 1.05 = 1.9048 → −1.90% change. The 10-year bond is much more sensitive.
4. Why this is true: later cash flows are discounted more heavily when rates rise, and a larger fraction of value being far in the future amplifies the impact of rate changes.

Why the other option is wrong:
- “False” contradicts the duration concept. While coupon size and current yield also affect sensitivity (higher coupons and higher yields reduce duration), the general rule holds: longer maturity → greater sensitivity, all else equal.

Final confirmation: The correct answer is True, matching the provided answer.

Question at position 3 For bonds, price sensitivity to a given change in interest rates is generally greater the longer before the bond matures.TrueFalse单项选择题

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