Dispersion measures as immunization risk measures

Abstract

The quadratic and linear cash flow dispersion measures M 2 andÑ 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. Ó

Dynamic immunisation does not imply cash flow matching: a hard application to Spain

“…Furthermore, and linked with the above, although M 2 has been proved not to perform badly, it is clearly some distance from financial sense. There have been many proposals, knowing that any dispersion measure is an immunisation risk measure (Balbás & Ibáñez, 1995), and among them an interesting step forward could be M A (Nawalkha & Chambers, 1996): this is rather similar to M 2 , but it measures risk in financial units and not in its squares and is thus more closely tied in with financial reality. However, even this measure is bound to statistics and has no real financial sense, which is why it also has problems measuring immunisation risk.…”

Financial Innovation and Arbitrage in the Spanish Bond Market

“…In fact, assume that X is a strong sequential arbitrage portfolio whose short position X ¡ has a price equal to one dollar. 3 It may be proved that the price of X + veri…es pX ¡T ¡ pX + T · $ ¤¤ and, moreover, there exists a strong sequential arbitrage portfolio X ¤¤ such that pX ¡T ¤¤ = 1 and pX…”

“…For instance it maximizes the ratio between sequential 3 As usual, ® + = Sup{®; 0g, ® ¡ = Sup{0; ¡®g and ® = ® + ¡ ® ¡ for every ® 2 IR. Similar notations are also used for vectors and matrices.…”

“…Although bond markets and the T SIR deserved and will go on deserving a major attention, see for instance Elton et al (1990), Bowden (1997), Jaschke (1998), Aniz and Prisman (2000) or Balbás et al (2001) for recent results, there is a clear lack of empirical analyses related to the existence and computation of sequential arbitrage strategies in practice. This fact is probably provoked because there are no well-known arbitrage strategies and formulas when dealing with …xed income securities, unless their derivatives are also involved.…”

Immunization using a stochastic-process independent multi-factor model: The Portuguese experience

“…Non-parallel shifts were proposed byBierwag (1977),Khang (1979) andBabbel (1983) or, in an equilibrium setting, byCox et al (1979),Ingersoll et al (1978),Brennan and Schwartz (1983),Nelson and Schaefer (1983) andWu (2000), among others. SeeBravo (2001) for a detailed analysis of interest rate risk models.2 SeeNawalkha and Chambers (1996),Balbás and Ibáñ ez (1998) andBalbás et al (2002) for alternative definitions of interest rate risk dispersion measures.3 In these models, the direction of interest rate shifts can be set on an a priori basis, or can be based on real data. In the latter case, the historical movements in the term structure of interest rates are used to identify a limited number of state variables, observable or not, which govern the yield curve.…”