CONSTRUCTION OF A K - IMMUNIZATION STRATEGY WITH THE HIGHEST CONVEXITY

Assuming that interest rate shocks are proportional to their values pl us one, we prove in Theorem 1 the existence of and construct a portfol io Z with the highest convexity in the class of portfolios that solve the immunization problem to meet the liability to pay C dollars K yea rs from now. Z appears to be a barbell strategy with two zero-coupon bonds with the shortest and the longest maturities. This intuitively c lear result has been obtained here in a rigorous way by means of the K -T conditions. In addition, we show that our result is strictly relate d to the problem of maximization of the unanticipated rate of return o n a portfolio solving the above immunization problem (Theorem 2). Two more results concerning the unanticipated return after K years are pro vided with proofs. An example illustrating the role of convexity in ma ximization of the unanticipated return is included. Despite the fact t hat there exists a pretty vast literature on bond portfolio strategies , the present paper offers a new methodological approach to this area (see Ingersoll, Skelton, Well, 1978).