Designing an immunized portfolio: Is M-squared the key?

Dispersion measures as immunization risk measures

“…These tests also show that the linear measure usually includes a maturity matching bond. Furthermore, tests on maturity-constrained duration-matched portfolios, as suggested in Bierwag et al (1993) and others, perform well empirically. This confirms previous empirical results on US and Canadian markets.…”

“…Both portfolios minimize theÑ N linear measure. This result is not robust since, for instance, it depends on the convexity property noted in Bierwag et al (1993), but it is illustrative of the linear measure.…”

“…The portfolios are arranged according to their M 1 measure. As Bierwag et al (1993) showed, a bullet portfolio does not always minimize the M 2 measure. However, this simple example satisfies the conditions for a bullet portfolio to minimize the M 2 measure.…”

“…The purpose of the latter group is twofold, first to see if there is an improvement over the first group after including a m-m bond, and second, to see which of the first group strategies usually includes a m-m bond. Note that there are no theoretical arguments to include a m-m bond, only strong empirical evidence (see Bierwag et al, 1993).…”

“…For example, Lacey and Nawhalka (1993) empirically demonstrated the effectiveness of matching duration and minimizing the M 2 measure. Bierwag et al (1993) showed that among matching duration portfolios, the inclusion of a maturity matching bond works best empirically. Balb a as and Ib a añ nez (1998) illustrated with examples that the matching duration portfolio that minimizes theÑ N measure usually requires a matu-2 For instance, parallel shifts or other non-parallel shifts (Bierwag, 1977;Chambers et al, 1988;Prisman and Shores, 1988), shifts in an equilibrium models context (Cox et al, 1979;Brennan and Schwartz, 1983), or empirically estimated shifts (Litterman and Scheinkman, 1991;Chance and Jordan, 1996;and others).…”