Dispersion measures as risk immunization measures

The quadratic and linear cash flow dispersion measures M2 and N~ are two immunization risk measures designed to build immunized bond portfolios. This paper generalizes these two measures by showing that any dispersion measure is an immunization risk measure and therefore, it sets up a tool to be used in empirical testing. Each new measure is derived from a different set of shocks (changes on the term structure of interest rates) and depends on the corresponding subset of worst shocks. Consequently, a criterion for choosing appropriate immunization risk measures is to take those developed from the most reasonable sets of shocks and the associated subset of worst shocks and then select those that work best empirically. Adopting this approach, this paper then explores both numerical examples and a short empirical study on the Spanish Bond Market in the mid-1990s to show that measures between linear and quadratic are the most appropriate, and amongst them, the linear measure has the best properties. This confirms previous studies on US and Canadian markets that maturityconstrained-duration-matched portfolios also have good empirical behavior.