A Risk Minimizing Strategy for Portfolio Immunization

Abstract

Consider a fixed‐income portfolio whose duration is equal to the length of a given investment horizon. It is shown that there is a lower limit on the change in the end‐of‐horizon value of the portfolio resulting from any given change in the structure of interest rates. This lower limit is the product of two terms, of which one is a function of the interest rate change only, and the other depends only on the structure of the portfolio. Consequently, this second term provides a measure of immunization risk. If this measure is minimized, the exposure of the portfolio to any interest rate change is the lowest.

Default Risk and the Duration of Zero Coupon Bonds

“…D uration is a subject of much concern to researchers and bond portfolio managers. In the last five decades, the literature on duration has grown from a simple explication of its property as a measure of average maturity (Macaulay (1938)) to sophisticated strategies such as funding multiple liabilities (Fong and Vasicek (1984)). Duration, however, is not without its critics.…”

The effect of yield curve shape and level on bond immunisation effectiveness

“…Bierwag, Kaufman, and Toevs (1983) further suggested that a hybrid of immunisation and active strategies could produce a strategy that guarantees a minimum return, but allow for the possibility of higher returns, known as contingent immunisation (Bierwag, et al, 1983). Fong and Vasicek (1984) expressed concern that the portfolio would not be immunised unless interest rate changes actually conformed to the predicted stochastic process. To overcome this, a bond portfolio was established and the exposure of interest rate changes to each portfolio characteristic determined.…”

“…By minimising these risk measures, a portfolio could be structured in such a way as to have as little exposure to interest rate fluctuations as possible. At the time, Fong and Vasicek said, "[T]his is indeed the perfectly immunised portfolio, since no interest rate change affects its end-ofhorizon value" (Fong & Vasicek, 1984, p. 1543. Shiu (1987) repeated Fisher and Weil's (1971) immunisation tests and found that the durationbased immunisation did not work nearly as well as originally reported.…”

“…Matching the duration of the asset portfolio with the duration of the liability, in theory, allows for both the asset and liability to move by the same amount when the interest rate changes, such that the expected value of the asset portfolio is at least as much as the expected value of the liability, regardless of interest rate fluctuations. In the case where a liability is not involved, immunisation would mean matching the duration of the portfolio with a target horizon so that the future value of the portfolio at the target horizon date is at least as much as the expected target value for that date (Fong & Vasicek, 1984).…”

Shape Factors and Cross-Sectional Risk

“…An early strand of literature, referred to as functional immunization, assigned speci c functional forms to any admissible term structure updating (e.g., parallel shifts in Fisher and Weil (1972), arbitrary variations in Fong and Vasi cek (1984), and selected analytical forms in Chambers and Carleton (1988), Prisman and Shores (1988), Barrett et al (1995), Phoa andShearer (1997), andRodrigues De Almeida et al (1998)) and provided selection criteria for bond portfolios to make them nancially insensitive to these deformations. The approach exhibits the remarkable feature of accounting for full information about the crosssection.…”