convexity adjustment and the like

[cfa_mixer]

Quick Q from one of the past exams.
So here is the situation.
its the classical immunization. Asset Durations = Liability Duration, fine.
But convexity of assets is GREATER than convexity of liabilities, fine.
So, the yield curve shifts UPWARD by 100bps.
Does the surplus decrease or increase????
Well„ my thought proess is the following: Higher convexity of assets will cause a greater decrease in the asset position relative to liabilities who have less convexity. So suprlus shrinks.
So, the problem is that the answer is opposite. Saying liabilities decrease will be greater. Anyone able to spit some knowledge at the mixah?

 

[MrSmart]

Convexity of A > COL = Bigger surplus

 

[realLIFE]

Convexity of Assets > Convexity of Liabilities
=> If yield up then Assets’ value are less reduced than that of liabilities
=> If yield down then Asset’s value are more increased than that of liabilities
maybe price change approximation ~ - Duration * (change in yield) + (1/2) * Convexity * (change in yield)^2
in general Convexity > 0 when bonds don’t include callable options. so the higher positively convexity the better the price

 

[S2000magician]

cfa_mixer wrote:Well„ my thought proess is the following: Higher convexity of assets will cause a greater smaller decrease in the asset position relative to liabilities who have less convexity. So suprlus shrinks grows.

Fixed that for you.
higher convexity gives greater price appreciation when rates fall, smaller price depreciation when rates rise (assuming duration is the same).

 

[cfa_mixer]

Thanks S2k, as usual you make everything very clear. Now I think it makes better sense why callable bonds have negative convexity.