# BPV - Immunization

As I understand, the first requirement for immunization is to MATCH BPV of assets and liabilities and convexity of assets must be slightly higher than that of liabilities.

In one of Schweser’s mocks, the liability BPV is 7,496 and convexity is 47.75. We must choose one of the 4 portfolios below to immunize.

Portfolio P: Convexity = 46.03 | BPV = 7,476

Portfolio Q: Convexity = 47.60 | BPV = 7,215

Portfolio R: Convexity = 47.89 | BPV = 7,474

Portfolio S: Convexity = 68.34 | BPV = 7,471

I chose R mainly because of convexity, which is the answer.

According to the answer, “the first requirement for immunization is to match the BPV of assets and liabilities.”

It seems convexity is being given more emphasis here as all of the BPVs are lower.

My question is what’s the definition of MATCH here. Is slightly lower also acceptable?

Schweser Practice Exam Book 2 - Exam 2 Afternoon, Q44.

I would go with portfolio R if it was a multiple liability. Closely match between Duration, but slightly higher convexity. What’s the answer?

I think the matching the duration should be prioritized, so the first portfolio be considered is Portfolio P, right?

Btw, Just to confirm my thinking: for both multiple and single liability, to avoid structural risk, we should have convexity greater (but not too much) the liability’s convexity, right?

The difference between Portfolio P and Portfolio R is minor (7.476 vs 7.474) but the convexities paint different pictures (lower vs higher). Structure risk arise from twist and shifts and should be reduced by managing convexity. So go far matching, but slightly higher. That is at least the notes that i have written down, but i may be incorrect.

My summary:

Multiple liabilities:

1. Match PV asset and PV liabilities

2. Match duration

3. Duration of assets wider than liabilities / higher convexity

Single liability:

1. PV assets equal or larger than Pv liabilities

2. Match duration

3. Lower convexity

Answer is Portfolio R, which makes sense due to convexity, but BPV is lower which makes selecting R uncertain. The answer clearly says MATCH…

Depends on the interest rate expectations— structural and parallel up shifts would rather have liabilities bpv > assets bpv and therefore you might underhedge.

1. convexity always values better than what duration would determine ie in either direction

i guess the point is, choose the best among alternatives. +2 in bpv vs -2 in convexity. You want to error in favor of convexity rather, as long as the mismatch is NOT material.