Madhu Chandarasekaran, CFAThe Maturity Effect in Bond Duration: Understanding the Exception for Low-Coupon Discount Bonds
Defining the
The Maturity Effect in Bond Duration: Understanding the Exception for Low-Coupon Discount Bonds
Defining the Maturity Effect (Interest Rate Risk and Maturity)
In bond investing, maturity effect refers to the general rule that longer-term bonds are more sensitive to interest rate changes than shorter-term bonds This concept is rooted in duration – the time-weighted present value of cash flows – which serves as a measure of a bond’s interest rate risk (price sensitivity to yield changes). Under normal circumstances, increasing a bond’s maturity will increase its Macaulay duration (and thus modified duration), indicating higher yield sensitivity (greater price volatility when rates move).
However, the CFA Level I curriculum also notes that there are rare exceptions to the maturity effect. Specifically, the maturity effect “always holds” for certain types of bonds (like zero-coupon bonds or bonds priced at par/premium) but can break down in one particular scenario: a low-coupon, long-term bond trading at a discount. Let’s compare the given scenarios – a zero-coupon bond (Option A), a low-coupon long-term discount bond (Option B), and a low-coupon long-term premium bond (Option C) – and then examine why Option B is the exception where the maturity effect is least likely to hold.
Comparing the Three Bond Scenarios (A, B, C)
To clarify the setup, consider how coupon level and pricing (discount or premium) interact with maturity and duration:
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Option A – Zero-Coupon Bond (All Cash at Maturity): A zero-coupon bond pays no periodic interest; its only cash flow is the face value at maturity. This means 100% of its present value is received at the final maturity date. As a result, zero-coupon bonds have the maximum possible duration for a given maturity (equal to the maturity itself in years). The maturity effect always holds for zero-coupon bonds In short, Option A follows the maturity effect – longer maturity always means greater yield sensitivity in this case.
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Option B – Low-Coupon, Long-Term Bond Trading at a Discount: This bond pays interest, but the coupon rate is low relative to prevailing yields, so the bond’s price is below par (a discount). “Long-term” suggests a considerable maturity (e.g. 20+ years). The low coupon means that a large portion of the bond’s total cash flow comes from the final principal repayment, and trading at a discount means the required YTM is high (higher than the coupon). Under usual conditions, a long maturity and heavy weight on the final payment would imply high duration. However, in this scenario the maturity effect is least likely to hold – in fact this combination (low coupon, long maturity, high YTM) is exactly where the typical rule can reverse
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Option C – Low-Coupon, Long-Term Bond Trading at a Premium: This bond also has a low coupon rate but is priced above par, meaning the market YTM is lower than the coupon rate. The bond still has a long maturity, but because it’s at a premium, the yield is relatively low. A lower yield-to-maturity implies less discounting of future cash flows. Even though the coupon is “low” in absolute terms, if the bond is at a premium it actually means the coupon > YTM (not extremely low relative to yield). More of the bond’s value comes from coupon payments and the final payment isn’t as heavily discounted. In this case, the maturity effect holds as usua
Why a Low-Coupon Discount Bond Can Defy the Maturity Effect (Option B)
The counterintuitive behavior of Option B boils down to how duration is calculated and how cash flow weighting shifts when yields are high. Recall that Macaulay duration is the weighted average time to receive the bond’s cash flows, where each cash flow’s time is weighted by its present value relative to the bond’s price. Modified duration (which directly measures yield sensitivity) is Macaulay duration adjusted for yield (Modified ≈ Macaulay / (1+YTM) for annual compounding). The key factors at play for a low-coupon, high-YTM (discount) bond are:
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Heavy Discounting Reduces the Weight of Distant Cash Flows: A low-coupon bond already concentrates most of its value in the final principal repayment (since the coupons are small). But if the bond’s yield is very high (deep discount), the present value of that distant principal is severely eroded by discounting. For a long maturity, the final $100 (par) received decades from now is divided by
(1+YTM)^T, which becomes a huge denominator when YTM is large and T is long. This means the final payment’s PV share of the bond’s price becomes much smaller than it would be at lower yields or shorter horizons. In Option B, the final payment, which normally “drags” the duration out to the maturity, no longer has the same pulling power because its weight in the PV calculation has shrunk dramatically. Essentially, the farthest cash flow loses influence on the average due to extreme discounting.
– Why Option B Is Correct
In summary, Option B is least likely to obey the maturity effect because the combination of low coupon and high yield (discount) means increasing maturity beyond a certain point doesn’t increase interest rate risk as it normally would. The final cash flow’s influence is diluted by heavy discounting, and the bond’s duration is dominated by nearer-term cash flows. Therefore, compared to a zero-coupon bond or a premium bond (where longer maturity does consistently increase duration), the low-coupon discount bond is the odd one out. For exam preparation, remember this key point: except for the rare case of a long-term, low-coupon bond at a deep discount, longer maturity always implies higher duration. Option B exemplifies that rare case, which is why it is the correct answer in the context of the maturity effect question