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.