ABSTRACT
In a previous article in this Journal, Fisher and Weil demonstrate that, in the absence of default and taxes, an investor can immunize a portfolio of coupon bonds by selecting a portfolio whose duration is equal to the holding period. 1 Immunization is defined as obtaining a realized yield for a given holding period that is, at minimum, equal to the promised yield to maturity. Duration is defined as a weighted average of the payment periods where the weights are related to the present values of the payments in each period. 2 Fisher and Weil show that “as long as there exist two bonds whose durations t 1 and t 2 satisfy t 1 ≤ T ≤ t 2, an immunized investment for a holding period of length T can be achieved.” 3 Thus, immunization permits risky assets to be effectively converted into a riskless asset with a known yield for any 211given holding period. This comment shows (1) why a duration strategy provides the most complete immunization for a portfolio of coupon bonds, and (2) that the definition of duration that achieves immunization is dependent upon the nature of the random shocks that are assumed to affect Interest rates after the purchase of the portfolio.
