An Investigation of Beta and Downside Beta Based CAPM-Case Study of Karachi Stock Exchange

Abstract

Sharpe’s (1964) Capital Asset Pricing Model (CAPM) assumes that the relationship between risk and return is positive, linear and significant. However, it is not free from controversies and one of them advocates replacing CAPM’s beta by downside beta based on investors’ preference of downside risk. Roy (1952) debates that investor care for downside risk and Hogan and Warren (1974) replace variance with semivariance in CAPM as the first official version of downside risk based CAPM. Bawa (1975), Fishburn (1977) and Bawa and Lindenberg (1977) develop and extend proxy for downside risk/beta as Lower Partial Moment. This study empirically tests beta and downside beta based CAPM (DCAPM). Conceptual and empirical problems related in testing alternative models are discussed with adoption of Fama-MacBeth (1973) procedure by making it robust. This study inspects intercept, risk-return relationship, nonlinearities and effect of residuals for both CAPM and DCAPM. Intercept results are almost similar and they follow introduction of zero-beta models as outlined by Black et al. (1972). Both models show rejection of nonlinearities and effect of residuals. However, DCAPM comes out to be strong contender compared to CAPM for risk-return relationship. These results are consistent with Estrada (2002), Ang et al.(2004) and Post and Vliet (2004).