Immunization - quick tutorial

Can someone go over the main points of immunization? I have gone over it so many times and still don’t get it… AHH!

I think it’s just to lock in the liability. Like you have a liability to pay $100 in a year, you can invest the money you have now in order to pay for that liability in a year. But the growth of that money is open to market fluctuations. When you immunize, you lock in a return, the immunization rate. That’s why the zero coupon is the best instrument to use, because it will pay you that $100 at it’s maturity, which should coincide with the maturity of the liability. You buy the bond now, you know it’ll meet the $100 liability in one year.

This is the simplist case, using zero coupon to immunize one liability. But when you have multiple liabilities or you have to use other instruments, it gets more complicated and you are open to immunization risks.

You have a liability (or set of liabilities) at some date in the future. You want to buy fixed income securities that will provide the needed cash at said dates.

The safest way to do this would be to buy a risk-free zero-coupon government security with the same maturity as the liability. However, that is probably not realistic because such a security might not exist, and in addition even if it did the low return from it would mean you need to have more cash up front, which is suboptimal. So you will buy different types of securities with higher returns and monitor the risk over time instead. This is classical immunization.

A related concept is contingent immunization, where you attempt to earn an active return with your fixed income portfolio, so long as you have a safety cushion to do so. Relevant calculations are:

PVA * (1 + s/2) ^ 2*T = FVL

PVL = FVL / [(1 + i/2) ^ 2*T]


FVL = future value of liability (think of this as the required terminal value)

PVL = present value of liabilities (think of this as the required initial value)

PVA = present value of assets, in other words what your portfolio is worth right now

s = safety rate of return, the lowest value that will grow your current holdings to exactly the required terminal value

i = immunized rate of return. The rate available for securities that you want to use to reach your objectives.

Semi-annual coupons are the norm and should be assumed unless instructed otherwise.

They might ask you about the cushion spread ( i - s ) or the current cushion or amount above the safety threshold ( PVA - PVL ).