Skewness Preference and the Valuation of Risk Assets

Abstract

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Realized Skewness

“…When r is not lognormally distributed, the premium depends also on higher moments (as noted for example by Kraus and Litzenberger, 1976), and the premium rate required is…”

“…The literature going back to Kraus and Litzenberger (1976), and including more recently Harvey and Siddique (2000), Ang, Hodrick, Xing and Zhang (2006), Ang, Cheng and Xing (2006) and Xing, Zhang and Zhao (2010), suggests that the asymmetry of the returns distribution both for individual stocks and for the market as a whole is important for asset pricing and investment management. Skewness is central to the debate on the role of large rare disasters in explaining the equity risk premium (Rietz (1988), Longstaff and Piazzesi (2004), Barro (2009), andBackus, Chernov andMartin (2011)).…”

Option pricing with Lévy-Stable processes generated by Lévy-Stable integrated variance

“…Financial data suggests that returns are skewed rather than symmetric, see for example [KL76], [CLM97], [CW03]. For instance, since the stock market crash of 1987, the US stock index options market has shown a pronounced skewed implied volatility (volatility smirk) which indicates that, under the risk-neutral measure, log-returns have a negatively skewed distribution.…”

Modern portfolio theory, 1950 to date

“…Early work developed necessary conditions on either the utility function of investors or the return distribution of assets that would result in mean variance theory being optimal (see, for example, Tobin, 1958). In addition, researchers (see Lee, 1977;Kraus and Litzenberger, 1976) o ered alternative portfolio theories that included more moments such as skewness or were accurate for more realistic descriptions of the distribution of return (Fama, 1965;Elton and Gruber, 1974). Nevertheless, mean variance theory has remained the cornerstone of modern portfolio theory despite these alternatives.…”