Consider two option-free 5% annual pay bonds from the same issuer and the same seniority. One of the bonds has a mod dur of 3.5 and approx. convexity of 25. The other has a mod dur of 4.0 and approx. convex of 40. Can the lower duration bond have more px volatility than the higher duration bond?

- No because it also exhibits lower convexity.
- Yes, because shifts in yield curve may be non-parallel.
- No, because its price will respond relatively less in response to changes in yield.

I answered #3. Looking at the formula -mod dur (delta bp) + convexity(delta bp)^2/2 would tell you the answer is 3.

The answer is actually #2. The rationale is duration based estimated of bond value changes assume the yield curve shifts in a parallel manner. If instead short-term interest rates are more volatile than long-term interest rates, it is possible for a bond with lower duration to have more price volatility than a bond with higher duration.

Can anyone explain this because the explanation directly conflicts with the answer as you assume the yield curves shift in a parallel manner.