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Abstrakty
Assuming that interest rate shocks are proportional to their values plus one, we prove in Theorem 1 the existence of and construct a portfolio Z[sup *] with the highest convexity in the class of portfolios that solve the immunization problem to meet the liability to pay C dollars K years from now. Z[sup *] appears to be a barbell strategy with two zero-coupon bonds with the shorest and the longest maturities. This intuitively clear result has been obtained here in a rigorous way by means of the K-T conditions. In addition, we show that our result is stricly related to the problem of maximization of the unanticipated rate of return on a portfolio solving the above immunization problem (Theorem 2). Two more results concerning the unanticipated return after K years are provided with proofs. An example illustrating the role of convexity in maximization of the unanticipated return is included. Despite the fact that there exists a pretty vast literature on bond portfolio strategies, the present paper offers a new methodological approach to this area (see Ingersoll, Skelton, Weil, 1978).
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
135--144
Opis fizyczny
Bibliogr. 8 poz.,
Twórcy
autor
- Systems Research Institute, Polish Academy Sciences, Warszawa, Poland, Izaremba@ibspan.wa.pl
Bibliografia
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT2-0001-0280