The duration rule always ________ the value of a bond following a change in its yield

Question

BlackTom AI · Accepted Answer

To approach this question, consider what the duration rule actually does and what it ignores.
Option A: 'Underestimates.' The duration rule is a linear, first-order approximation of how price changes with yield. It tends to miss the curvature of the price–yield relationship (convexity). In many cases, ignoring convexity leads not to underestimation but to mis-estimation of the magnitude, and the sign can still align with the actual move. So calling it simply an underestimation is not precise and generally not correct given the convex nature of prices.
Option B: 'Provides an unbiased estimate.' The bond price as a function of yield is convex, which means the first-order (linear) approximation using duration does not capture the curvature. This introduces a bias in the estimate, so it is not unbiased. Therefore this statement is false.
Option C: 'Overestimates.' Because the true price change incorporates convexity, the linear duration approximation often overstates the magnitude of the price change for a given yield move, especially as Δy grows beyond very small levels. In other words, ignoring convexity makes the estimate too large in magnitude compared to the actual change when convexity works against the straight-line projection. This aligns with common textbook results about the limitations of using duration alone.
Option D: 'The estimated price may be biased either upward or downward, depending on whether the bond is trading at a discount or a premium.' While convexity can cause the magnitude of the error to vary with the bond’s level (discount/premium), the standard teaching emphasizes the typical overestimation due to ignoring convexity, not an entirely unpredictable bias that flips direction based on discount/premium. This makes the statement less accurate as a general rule.
In summary, the core idea is that duration provides a linear (first-order) estimate and does not account for convexity. The convexity effect tends to reduce the actual price change in magnitude relative to the duration-based linear projection for many yield moves, leading to an overestimation by the duration rule. This explains why Option C is the most appropriate characterization among the choices.

BU.232.750.51.FA25 Final Exam Fall 2025- Requires Respondus LockDown Browser

The duration rule always ________ the value of a bond following a change in its yield

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