I have a confusion regarding bond convexity and whether or not it is considered to be a ‘good’ thing:

  1. On the one hand, the curriculum mentions that bond convexity is a desirable property as if yields fall, then convex bonds will experience larger price rises that non-convex bonds. And if yields rise, the price drop for convex bonds will be less than non-convex bonds. I think the curriculum also mentions that therefore, convex bonds command a price premium vs. non-convex bonds.

  2. On the other hand, when talking about portfolio convexity, the curriculum mentions that convexity is a proxy for structural risk. Therefore higher convexity could be considered a ‘bad’ thing as it means the portfolio has a higher structural risk. To justify this, it provides the formula: Portfolio convexity = (MacDur + MacDur^2 + Dispersion) / (1 + cashflow yield)^2. Holding everything else in the formula equal, we can see that a higher convexity results from higher dispersion (which can be interpreted as higher risk.)

Can anyone help me reconcile these 2 seemingly conflicting statements? Is there a difference between individual bond convexity (point 1) and portfolio convexity (point 2)? Or am I missing something else here?

Thanks in advance.

Here is how I understood it from studying the first 2 readings in the fixed income section:

For a parallel shift in the yield curve, the positive convexity will be desirable in the immunized portfolio as it will increase the value of the asset compared with the future liability. This is because the starting point of the PVA will be higher than the starting point of PVL, BUT the rate of the increase in the portfolio IRR will be the same as the rate of increase in the discount rate of PVL.

However, if there was a nonparallel shift in the yield curve, the rate of increase in the portfolio IRR and the discount rate of PVL will differ, and high convexity will be a problem as it is linked to dispersion ==> high structural risk, and therefore we should minimize the asset convexity (as long as it exceed those of the liabilities for immunized portfolio) to minimize dispersion.

As an example of why high dispersion is a negative thing, there will be a problem if the coupon asset and liability due date differ. If we receive the coupon before the liability due date we are exposed to reinvestment risk (compound interest rate), or if we receive the coupon after the liability due date we will have to make the payment by borrowing money at a different rate.

That’s great - thanks for your help