# Fixed Income - Convexity

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?

1. No because it also exhibits lower convexity.
2. Yes, because shifts in yield curve may be non-parallel.
3. 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.

The formula is based on the assumption that there IS a parallel shift in the yield curve, which isn’t always the case and one of the drawbacks of it. Therefor, two would be correct.

It’s a poorly written question.

What they’re saying is that the maturity of the bonds may be different, so the changes in yield may be different.