Classical Immunization

[beingthatguy]

Hi All,

Quick question in regards to the behavior of assets/liabilities in a classical immunization strategy. Consider the following scenario:

1. PV of assets = PV of liabilities
2. Duration of assets = duration of liabilities.
3. Convexity is higher for the assets.
If there is a parallel upward shift in rates…will the assets of liabilities decline more? My thought was that the assets would decline more in value as convexity is higher which would essentially reduce the economic surplus. 2013 CFA mock states liabilities will fall faster increasing the value of economic surplus?

Anyone have thoughts on this?

 

[cpk123]

surplus = PV(Assets) - PV(Liabilities)
Assets = 100, Duration = 5, Convexity = 4
Liabs = 100, Duration = 5, Convexity = 3
Surplus = 0
Rate changes +1% -> Change in Assets = -5*1% + 4 * 1%^2 = -0.0496
Assets become = 95.04
Change in Liabs: -5*1% + 3* 1%^2 = -0.049-0.0497
liabs = 95.03
Surplus = 0.01

 

[S2000magician]

Higher convexity leads to higher price increases when rates decrease and lower price decreases when rates increase.

 

[beingthatguy]

Got it! Thanks guys

 

[S2000magician]

You’re welcome.