Shadow risk-free returns when hedging the interest rate risk

This paper addresses the hedging of bond portfolios interest rate risk by drawing on the classical one period no-arbitrage approach of Financial Economics (Ingersoll (1987)). Under quite weak assumptions on the interest rate behavior several shadow riskless assets are introduced by means of semi-infinite mathematical programming problems. Then, these assets are interpreted as hedging strategies or, under adequate hypotheses, as immunized portfolios. The technique applies in a quite broad range of cases since, for instance, short-selling or convexity restrictions are not necessarily required and the uniqueness of the horizon planning period does not have to be imposed. The set of admissible shocks on the interest rate contains a vast number of possibilities, the solutions are robust and do not significantly depend on the random field framework affecting the interest rate, and under some conditions, derivative securities may be also included in the analysis. Furthermore, appropriate algorithms are developed in a very general mathematical setting. Finally, a few examples illustrate the way they work in practice along with the general form of the hedging portfolio.