On Empirical Risk Measurement With Asymmetric Returns Data

By formulating a nested test of the asymmetric response model of Bawa, Brown, and Klein (1981), the mean-lower partial moment CAPM (LPMCAPM) of Bawa and Lindenberg (1977) and the mean-variance CAPM of Sharpe (1963, 1964), Lintner (1965) and Mossin (1969), this paper investigates the relative merits of symmetric and asymmetric risk measures using UK equity data for di®erently sized companies and at di®erent frequencies. Our analysis shows that, when equity returns are not normal which is the case for most daily and weekly returns, and for a large portion of smaller ̄rms the CAPM is rejected in 30%-50% of cases, and the optimal choice of alternative model is LPM-CAPM in over two thirds of these. These, and our further results, have strong consequences for the accurate measurement of equity risk, performance and prices, as downside and/or asymmetric risk measures often outperform the traditional CAPM framework, thus rendering it's related and widely-used current approaches sub-optimal for some company sizes/data frequency combinations. JEL Classi ̄cations: C10, G12