Economic Surplus and Convexity

From 2013 AM section, question 8.D, the answer states that because the convexity of the liabilities is less than the convexity of the assets, the value of the liabilities will decline more from an interest rate increase than the value of the assets, increasing economic surplus.

Is the general rule that a higher convexity results in a lower price decline from an interest rate increase? I thought it was the opposite but didn’t see much explanation in the reading. Can anybody help explain this?

Yes, higher convexity implies less sensitivity to interest rate movements increases

Not quite.

Less sensitivity to interest rate _ increases _, but _ more _ sensitivity to interest rate decreases. (Both assuming that duration is the same, so the only difference is convexity.)

isn’t this out? I could be wrong, but I don’t recall anything at all about economic surplus and I read the full 2015 curriculum cover to cover a few times

there is defintely talk of economic surplus…recall contingent immunization?

the surplus efficient frontier?

For OP:

REfer to the following diagram to follow along:

If you look at a diagram where the x axis is interest rate and the y axis is the bond price, this graph will be convex to the origin.

So if you draw a tangent line to the curve, that will be the bond duration at that point.

The distance between the duration line and the bond price curve is the convexity adjustment.

If rates move down, the duration has underestimated the bond price increase (as seen by the distance between the tangent and the curve), and there will be an positive convexity adjustment to the bond price (resulting in a higher price_

If rates move up, the duration has overestimated the price decline (as seen by the distance between…), and there will be a positive convexity adjustment (resulting in a higher price than what was estimated by the duration).

^ that doesn’t sound the same as economic surplus though. I agree with all the stuff you wrote, definitely I remember that stuff, but not economic surplus. I think economic surplus was in the WACC reading from back in the day (saw it in an outdated shwesser thing i downloaded)

^ pretty sure economic surplus equals market value of assets minus PV liabilities.

See page 159 of reading 21 - section 4.1.2.1

the above things i noted are just strategies for managing the economic surplus

o ya, that thing, i was wrong. good catch