Answer: The decomposition result states that the return due to the passage of time is the instantaneous spot rate.

## Explanation Let's analyze the Ito's Lemma decomposition for the bond price: $$ dP = \frac{\partial P}{\partial t}dt + \frac{\partial P}{\partial r}dr + \frac{1}{2}\frac{\partial^2 P}{\partial r^2}\sigma^2 dt $$ This can be rewritten in terms of bond return: $$ \frac{dP}{P} = \frac{1}{P}\frac{\partial P}{\partial t}dt + \frac{1}{P}\frac{\partial P}{\partial r}dr + \frac{1}{2}\frac{1}{P}\frac{\partial^2 P}{\partial r^2}\sigma^2 dt $$ For a zero-coupon bond: - **Duration** = $-\frac{1}{P}\frac{\partial P}{\partial r}$ - **Convexity** = $\frac{1}{P}\frac{\partial^2 P}{\partial r^2}$ Now let's evaluate each option: **A. Incorrect** - The decomposition doesn't mention "spread" changes. It decomposes return into time passage, rate changes, and volatility effects. **B. Incorrect** - Decreases in rates actually **increase** bond returns (bond prices rise when rates fall), and the effect is proportional to duration. **C. Correct** - The term $\frac{1}{P}\frac{\partial P}{\partial t}dt$ represents the return due to the passage of time. For a zero-coupon bond, this equals the instantaneous spot rate $r_t$ (this is the drift term in the bond pricing equation). **D. Incorrect** - Lowering rate volatility **increases** bond return in proportion to convexity, not reduces it. The convexity term $\frac{1}{2}\frac{1}{P}\frac{\partial^2 P}{\partial r^2}\sigma^2 dt$ is positive for bonds, so lower volatility reduces this positive component. Therefore, option C is the correct statement about the bond return decomposition.

Author: LeetQuiz .