PARTIAL IMMUNIZATION BOUNDS AND NON-PARALLEL TERM STRUCTURE SHIFTS

A variety of approaches have been proposed to extend classical fixed income portfolio immunization theory to cases where shifts in the term structure are not parallel. Following Reitano (1991a, 1991b, 1992, 1996) and Poitras (2007), this paper uses partial durations and convexities to specify benchmark partial immunization bounds for non-parallel term structure shifts. Theoretical results are obtained by exploiting properties of the multivariate Taylor series expansion of the spot interest rate pricing function. It is demonstrated that the partial immunization bounds can be effectively manipulated by adequate selection of the securities being used to immunize the portfolio. The inclusion of time values permits the results obtained to be related to previous studies by Christensen and Sorensen (1994), Chance and Jordan (1996), Barber and Copper (1997) and Poitras (2005, Ch. 5) on the time value-convexity tradeoff.