A Generalized Higher-Moment Capital Asset Pricing Model, with Theoretical Implications and Legal Applications
87 Pages Posted: 30 Mar 2017
Date Written: March 29, 2017
The conventional capital asset pricing model (CAPM) has come under severe attack for its failure to reflect investor behavior. This paper describes financial decision-making under uncertainty in formal mathematical terms as a generalized higher-moment capital asset pricing model. It develops that model through the Taylor series expansion of the logarithm of expected financial returns. This mathematical expedient treats the conventional two-moment CAPM and a four-moment variant (expressed in terms of mean, variance, skewness, and kurtosis) as convenient, mentally tractable special cases of a generalized higher-moment model.
This paper then explores the theoretical implications and legal applications of higher-moment asset pricing. In prospect theory, perhaps the best known expression of behavioral economics, a “fourfold pattern” of decisionmaking under uncertainty predicts risk-seeking behavior in particular circumstances. Skewness preference arises in a wide variety of economic settings. Diverse bodies of financial regulation address transactions that strongly resemble legalized gambling, ranging from prize-linked savings to initial public offerings. Over time, cycles of misperception of risk and return consistent with the “disposition effect” of behavioral finance generate systematic gaps between hypothetical investment returns and actual returns realized by investors.
Keywords: asset pricing, CAPM, capital asset pricing model, Taylor series, risk aversion, risk seeking, prospect theory, securities law, IPO, initial public offering, behavioral economics, behavioral finance
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