Multi-moment Asset Allocation & Pricing Models
B. Maillet

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“When I developed the first multi-moment CAPM as the lead paper in my dissertation in 1970, I had high hopes that this would lead to significant improvements in asset pricing. I felt intuitively that at least the skewness and kurtosis of portfolio returns would matter to investors. Skewness preference captures asymmetric concern over downside outcomes and kurtosis captures the implications of extreme rare events, that are more numerous than indicated by normal distributions. Unfortunately, very little interest was shown in the multi-moment model for the next 30 years. Indeed, in prominent reviews of the CAPM, the generalization to many moments was rarely even mentioned. Then, the apparent empirical failure of the two-moment CAPM and the publication of several recent articles that take higher-order moments seriously, and now even a full book just devoted to the subject, have given new life to these ideas.” —Mark Rubinstein, Paul Stephens Professor of Applied Investment Analysis, UC Berkeley, USA “In a less well-known part of his path-breaking 1952 article on ‘Portfolio Selection’, Harry Markowitz details the conditions whereby mean-variance efficient portfolios will not be optimal. Markowitz argues that if investors have utility which depends on not only mean and variance but also skewness, then this could lead to a different set of optimal portfolios. This insight lay fallow for more than 20 years. It was revived in the important work of Mark Rubinstein in 1973. Since the late 1990s, we have seen an explosion of research on higher moments. People are beginning to think of the efficient frontier – as the efficient surface (incorporating skewness and other higher moments). This interest is sparked by five factors. First, it is obvious that people have a preference for positively skewed outcomes rather than negatively skewed returns (holding mean and variance constant). Second, most asset returns are non-normal. Third, it is widely acknowledged that two-moment CAPM has trouble fitting the data. Fourth, there is a large growth in a style of investing, sometimes referred to as alternatives, whose expected returns have option-like, non-normal features. Finally, computing power has advanced to such a degree that we can feasibly tackle the difficult problem of solving for optimal portfolios in the presence of higher moments. The time is right for a book on higher moments in asset pricing - and this is the right book.” —Campbell R. Harvey, J. Paul Sticht Professor of International Business, Duke University, USA “Plenty of evidence has emerged in the financial literature that the distributional assumptions underlying mean-variance analysis do not hold. Returns on many individual assets as well as returns on actively managed mutual funds have been found to be skewed and fat-tailed and are affected by occasional outliers. Unless investors have quadratic preferences, in equilibrium an asset's skew and kurtosis should generally be priced. The focus of the traditional CAPM on the first two moments was made out of analytical convenience, but we now have better tools to go beyond this analysis. The time is right for a book on the multi-moment CAPM and its related topics.” —Allan Timmermann, Professor of Economics, University of California at San Diego, USA