FI Portf. Convexity and Dispersion regarding Single liab. immunization

CFA Level III Fixed Income
#1

in Schweser note(p.248~p.249),

assume portf. convexity exceeds convexity of the single CF liab and

it makes benefits from the structural risk.

But, rules for immunizing a single liab.in p.248 describe in

minimize portf. convexity. (to minimize dispersion of asset CF)

If C(A) > C(L) is benefit situation,

Why immunizing a single liab. rule says minimize Portf. convexity?

It looks like conflict concept, isn’t it?

#2

there are two concepts here (Read the official curriculum):

  1. So, Cov (A) > Cov (L). The reason here is that Asset portfolio goes down less than Liabilities (L) when the interest rate goes up and goes up more when the interest rate goes down. this ensures A>L

  2. However, if you have to chose from multiple asset (A) portfolios, go with the (A) asset portfolio which has the minimum Convexity. The reason here is that you want minimum dispersion of cash flows around the single liability (i.e. minimize structural risk).

Do BB #2 and #4 from CFA curriculum and the above become more clear

Cheers

#3

Thank you for your kind reply.

You mean the condition 1) must be satisfied prior to condition 2),

than we must consider 2) because minimize structural risk

right?

#4

You are right

#5

I thought for multiple liability matching --> pick portfolio with higher convexity and

for a single liability matching --> pick portfolio with lower convexity?

#6

You must pick portfolio with higher convexity than liabilities, but not too high, in order to minimize structural risk.

The objective is to minimize convexity (lower structural risk) but make it greater than that of the liabilities.