PORTFOLIO OPTIMIZATION UNDER A PARTITIONED-BETA MODEL

Portfolio optimization has been a highly researched area in finance. Since the seminal work of Markowitz (1959) there had been many advances in portfolio analysis, attempting to combine the conceptual world of scholars with the pragmatic view of practitioners and to couple with increased electronic computing power. Among the proposals, the Capital Asset Pricing Model (CAPM) is one of the potential solutions to simplify the calculation of optimal portfolios and to directly relate each stock return to the return referred to a market index. CAPM assumes that stock riskiness, which are captured by their market beta, are constant over the do-main. However, there exists substantial empirical evidence that this assumption may be inaccurate and haz-ardous in asset allocation decisions, mainly when the relationship between risk and excess returns in “Bear” and “Bull” markets would be modelled separately. In this paper we propose the use of a mixture of truncated normal distributions in returns modelling. An opti-mization algorithm has been developed to obtain the best fit both in the univariate and in the bivariate case. Moreover, the procedure permits to decompose the global beta coefficient into local betas referred to specific regions of the market returns domain. Partitioning the domain provides a set of disjoint conditional regions where the local relationship between portfolio components and the benchmark can be slightly different with respect to the one on the domain as a whole. To appreciate how much closed to reality our proposal is, we provide an empirical analysis referred both to Country and Sector data.