21-Bond Portfolio Man Page 667 Wednesday, February 4, 2004 1:12 PM
Bond Portfolio Management 667chapter we discuss dedication in a multistage stochastic formulation, as
well as other bond portfolio optimization problems. Let’s now discuss
portfolio immunization, which is the numerical/analytical solution of a
special dedication problem under a stochastic framework.Portfolio Immunization
The actuary generally credited with pioneering the immunization strat-
egy is Reddington, who defined immunization in 1952 as “the invest-
ment of the assets in such a way that the existing business is immune to
a general change in the rate of interest.”^13 The mathematical formula-
tion of the immunization problem was proposed by Fisher and Weil in1971.^14 The framework is the following in the single liability case
(which we refer to as single period immunization): Given a predeter-
mined liability at a fixed time horizon, create a portfolio able to satisfy
the given liability even if interest rates change.
The problem would be simple to solve if investors were happy to
invest in U.S. Treasury zero-coupon bonds (i.e., U.S. Treasury strips)
maturing at exactly the given date of the liability. However, investors seek
to earn a return greater than the risk-free rate. For example, the typical
product where a portfolio immunization strategy is used is a GIC offered
by an insurance company. This product is typically offered to a pension
plan. The insurer receives a single premium from the pension sponsor and
in turn guarantees an interest rate that will be earned such that the pay-
ment to the policyholder at a specified date is equal to the premium plus
the guaranteed interest. The interest rate offered on the policy is greater
than that on existing risk-free securities, otherwise a potential policy
buyer can do the immunization without the need for the insurance com-
pany’s service. The objective of the insurance company is to earn a higher
rate than that offered on the policy (i.e., the guaranteed interest rate).^15
The solution of the problem is based on the fact that a rise in interest
rates produces a drop in bond prices but an increase in the reinvestment
income on newly invested sums while a fall of interest rates increases bond
prices but decreases the reinvestment income on newly invested sums. One
(^13) F.M. Reddington, “Review of the Principle of Life-Office Valuations,” Journal of
the Institute of Actuaries 78 (1952), pp. 286–340.
(^14) L. Fisher and R.L. Weil, “Coping with the Risk of Interest-Rate Fluctuations: Re-
turns to Bondholders from Naive and Optimal Strategies,” Journal of Business (Oc-
tober 1971), pp. 408–431.
(^15) For a discussion of the implementation issues associated with immunization, see
Frank J. Fabozzi and Peter F. Christensen, “Bond Immunization: An Asset/Liability
Optimization Strategy,” Chapter 44 in The Handbook of Fixed Income Securities:
Sixth Edition.