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|Title||CAPM Extensions – Comparing Higher Moments to Fama and French|
|Institution||University of Zurich|
|Faculty||Faculty of Business, Economics and Informatics|
|Number of Pages||49|
|Zusammenfassung||Insights of the cumulative prospect theory have indicated that agents tend to be loss averse and overestimate the probability of extreme outcomes. Furthermore, it is a stylised fact that assets’ return distributions tend to deviate from normality. Considering the shortcomings of the capital asset pricing model (CAPM) in the form of pricing anomalies such as the size or the value premium, the notion of mean-variance optimisation seems inappropriate to sufficiently model investor behaviour. To better depict agent preferences, this thesis pursues the approach to add higher than second moments as risk factors in the framework of the CAPM. In the theoretical part, the validity of mean-variance optimisation is discussed, and the necessary implications to expand preferences to a higher order are presented. In conclusion, investor preferences for higher moments can be expanded at will, even when the core assumptions of non-satiation and risk aversion remain. More particularly, the validity of the assumption of standard risk aversion is discussed in which preferences for skewness and kurtosis can be assigned to model investors’ asset allocation. The empirical part of this thesis examines the influence of higher moments on both a single stock and a portfolio basis. To quantify the risk exposures of the individual assets, conditional risk factors are calculated on a monthly rolling basis. The estimated risk coefficients are based on monthly returns over a two-year period and take covariance, coskewness, or cokurtosis risks into account. On an individual level, the results show that neither the conditional CAPM nor the conditional four-moment CAPM is capable of sufficiently explaining the cross-sectional variation of asset returns. Specifically, the additional moment factors appear to offer no significant added value compared to the mean-variance model. However, when coskewness and cokurtosis risks are added on a portfolio basis, it improves the statistical fit. The contradicting results can be explained insofar as the empirical methods for both approaches differ. Whilst on a single-stock basis, the conditional risk coefficients are directly chosen as pricing variables, they are used as moment factors in the sense of small minus big (SMB) or high minus low (HML) for the portfolios. The results for single stocks suggest that taking the conditional factors based on monthly returns over a two-year window as pricing variables is presumably not suitable to assess the influence of higher moments as the risk factors can be prone to large fluctuations and may be too imprecise. Conversely, the associated premia for the created moment factors correspond to the theoretically postulated preferences for higher moments. Therefore, besides improving the statistical fit on a portfolio basis, the expansion of preferences to higher moments becomes justified from a utility perspective as well. Additional examinations of the thesis focus on the interrelations of the higher moment risks with the size and value premia. The results reveal that the observed overperformances of high-value portfolios cannot be justified by an increased exposure towards higher moments. However, portfolios with a notable exposure towards the SMB factor are found to exhibit high sensitivities towards moment factors. Nevertheless, the additions for higher moments do not suffice to fully legitimise SMB from a utility-based perspective. More particularly, the results indicate that SMB alone accounts for variations in which the moment factors fall short. Ultimately, because of the methodical restrictions to estimate risk exposures based on past return variations, it remains open whether either SMB or HML can contain information about ex ante moment risks. Conclusively, SMB and HML remain necessary additions to better explain the cross-sectional variation of asset returns even in the presence of higher moments.|