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 differently sized companies and at different 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 firms - 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.

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