Why D-CAPM is a Big Mistake? The Incorrectness of the Cosemivariance Statistics

Abstract

The concept of downside risk is logically approved and plausible for investment evaluation, especially in the absence of normality of underlying distribution of returns. Markowitz (1959) suggested the semivariance and semideviation as proper measures for portfolio selection. The DCAPM is a modification of CAPM model considered superior when the underlying distribution of returns is asymmetric. However the DCAPM framework suggested by Hogan and Warren (1974), Bawa and Lindenberg (1977), Harlow and Rao (1989) and later “improved” and popularized by Javier Estrada is inconsistent with the diversification purposes and with the portfolio theory. Though the semivariance measures are quite useful and correct, the formula for calculating the cosemivariance (downside correlation) is a wrong statistic that cannot represent real dependencies between the two assets. This measure ignores the ability of upside returns of one asset to hedge the downside returns of another asset in a portfolio. The simulation shows that if the assets are perfectly positively correlated the DCAPM’s estimation percentage error is zero, and if the assets are perfectly negatively correlated the DCAPM’s estimation percentage error is infinity. If the assets have zero correlation, the percentage error is quite significant (under data used in simulation the % error may reach 15% in the simulation under appropriate weights). The magnitude of the estimation error varies both with correlation between data, weights of the assets and the data themselve. So the algorithm cannot provide reliable estimates. As a consequence the downside beta is a misleading measure, useless for portfolio diversification purposes and for determining the semivariance of the portfolio.

Keywords: CAPM, downside risk, downside beta, cost of capital, MLPM model, asymmetric returns, asset pricing

JEL Classification: G12