# Immunization logic for contingent immunization vs Classical immunizatoin

I understand that the portfolio value is insulated from parallel shifts of interest rate at the horizon date and this is accomplished by offesetting price and reinvestment risk. We need to match the duration of assets with the duration of liabilities to accomplish immunziation.

But then contingent immunization generally the immunization rate increases instantaneously to some rate and we can pursue active management. But why? If our interest rate is increasing and the duration of assets = duration of liabilities, isn’t the point of classical immunization to fund the liabilities regardless of changes in interest rate? I thought we get an assured rate regardless of these changes in interest rate to fund the predetermined liabilities. Even if interest rates increase, using the logic of offsetting price and reinvestment risk, the terminal value will decline while its reinvestments rate increases keeping the portfolio value constant at the horizon date…

Or is it just that the change in rate is not a parallel shift and is instantaneous that this works?

I understand how to do the numerical questions but I’m missing something logic wise because these concepts are not connecting.

Much appreciated.

I just revised this chapter…so take it with a grain of salt.

First, if rates rise, we have to immunize in theory. The value of Port (Which was greater than our required and PVL), will decline, reducing the cushion spread. When rates DECLINE, we can pursue even more active because of the cushion spread widening.

Contingent immunization lets you pursue a mix of passive and active management, right? One reason it is cited being used, is because classic just looks at risk, which may not be as effective as looking at return and risk.

They way I understood it, it allows us to pursue some active management as long as the cushion spread exist. Remember it hinges on immunized rate > required rate. You can pursue either part or total active management, as long as that spread exist, once the spread drops to 0 (rates up), you must immunize it.

The book takes the example where the port is funded with 500M (greater than the PVL), invest in 500M of bonds, and then rates go down. Their port goes up, and thus cushion spread goes up. So they could in theory sell a portion and pursue AM.

On the flip side, if rates go up, the value of the portfolio (an cushion goes down), we are forced to immunize the entire portfolio (if not done so already).

Reading section 4.1.2 really helped I think. You should do it again. Also, hopefully S2000 doesn’t eat me alive haha.

I think I understand now anyways.