# Impact of convexity mismatch and yield curve shifts

HI all,

What are the impacts of the following situations if convexity is mismatched between the assets and liabilities:

1. Asset convexity > Liability convexity and the yield curve shifts upwards

2. Asset convexity > Liability convexity and the yield curve shifts downwards

3)Asset convexity < Liability convexity and the yield curve shifts upwards

1. Asset convexity < Liability convexity and the yield curve shifts downwards

Im struggling to wrap my head around convextity impacts. See CFAI 2013 AM, Question 8 part D.

Also, In the 2013 AM, in parts C and D of question 7, the answer key references the WACC calculations. Something I thought we left back in L2. Am I the only one who thought this question came out of left field, and are we likely to see cost of capital questions in the actual exam>

1. AC>LC = Good

2. AC

3. Remember 1 and 2

assuming asset duration = Liability duration

Case 1: Asset Convexity = 5, Liability Convexity = 4 (AC > LC)

All the below are impact on Price due to Convexity Change

Rate falls 1% or rises 1%

– Asset rise in Price due to convexity = 0.0005, Liability Rise in Price = 0.0004

So if the two were 100M -> Asset Rise = 0.05 M, Liability Rise = 0.04M -. Surplus Rises 0.01 M

=============

Case 2: AC = 5, LC = 6 (AC < LC)

Rate falls or rises 1%

Surplus Falls 0.01 M (on a 100M Base)