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Non-normality of asset returns in the assessment of risk -adjusted performance: Three empirical tests of the Leland alternative asset pricing model

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  • Economics
  • Finance
  • Computer Science
  • Economics


This dissertation research examines the theoretical model offered by Leland (1999) as an alternative to the Capital Asset Pricing Model (CAPM). Leland's alternative risk-adjusting parameter, B, should improve over the CAPM β where the model is misspecified by the impact of a non-normal return distribution. This is especially true in highly skewed portfolios. ^ In the first essay, we provide the first empirical examination of Leland's model using actual security returns. We seek to identify characteristics of securities where β and B differ significantly. We find the most significant differences between β and B occur where the security returns are most non-normal (high skewness and kurtosis). The primary conclusion drawn from this empirical analysis is that, while we often find significant differences between the two parameters, we cannot conclusively state that these are a result of a non-normal return distribution. ^ In the second essay, we use the alternative Leland model to re-examine “Momentum” and “Contrarian” portfolio formation strategies. Analysis of the characteristics of the securities that make up the “winner” and “loser” portfolios shows that these securities have distinctly non-normal return distributions; consequently, there is strong theoretical support for higher order moments to be significant. We find, however, that the differences between the CAPM β and the Leland B for these securities are extremely small. ^ Finally, in the third essay, we form portfolios on the basis of estimation period skewness and compare Leland's measure, B, with the traditional CAPM measure, β. We then use the alternative risk-adjustment factors to evaluate risk-adjusted performance of high skewness and low skewness portfolios. We find, again, that the differences between the CAPM β and the Leland B are extremely small. ^ The ultimate conclusion of this dissertation research is that the small differences between risk-adjustment factors produce inconsequentially different abnormal performance measurements. Even where the differences are statistically significant, they are so small in absolute terms, they would likely not be economically significant. Even in the environment where Leland's alternative model “should” offer the most significant “improvement” over CAPM, we find virtually no added utility from the employment of the more computationally cumbersome model. ^

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