A Dynamic Global Portfolio Immunization Strategy in the World of Multiple Interest Rate Changes: A Dynamic Immunization and Minimax Theorem

Abstract

man [5], and Khang [9] demonstrate that it is possible to immunize a portfolio of default-free assets against unexpected interest rate changes so that at the end of the planning period the investor will realize at least the returns expected at pur? chase. However, this immunization strategy is applicable for the case in which the change in unexpected interest rate occurs only once at the instant after the purchase of the asset. Obviously, the case depicted above is not likely to resemble the real world situation in at least two respects. First, the interest rate change is likely to occur at any time and, second, the interest rate change is likely to occur many times during the investor's planning period. Bierwag [4] deals with the case in which the interest rate change may occur many times during the planning period, each occurring at the instant after the beginning of each time period, and shows that, provided the interest rate changes are small, the investor can, at the end of the planning period, realize the returns expected at purchase by constructing the portfolio whose duration at the begin? ning of each period is equal to the length of the remaining planning period. Thus, Bierwag's [4] immunization theorem is a local theorem. Bierwag makes a conjecture that the theorem is not likely to hold true globally. This paper shows that the strategy of keeping the portfolio duration, calcu? lated on the basis of the term structure observed at each moment of time, equal to the length of the remaining planning period during the entire planning period, guarantees at least the returns expected (or promised) at purchase, regardless of when and how many times interest rate changes occur during the planning period and regardless of sizes of change in the interest rate structure. Thus, the theorem proven in the paper is a global theorem in a very general setting as opposed to Bierwag's [4] local theorem. A corollary is that Bierwag's unconditional im? munization policy does not immunize unless all changes in the term structure are * University of Oregon. The author expresses thanks to an anonymous referee whose careful reading of the paper resulted in an improvement.