Increases in skewness and three-moment preferences

We call an agent skewness affine if and only if his marginal willingness to accept a risk increases when the distribution of the risk becomes more skewed to the right. Skewness affinity is shown to be equivalent to the marginal rate of substitution between mean and variance of wealth being decreasing in the skewness. This property allows us to characterize the comparative static effect of increases in the skewness in quasi-linear decision problems. Over domains of skewness-comparable lotteries skewness affinity is equivalent to the von Neumann-Morgenstern utility index of relative temperance being smaller than three.

[1]  John D. Tressler,et al.  Increasing Downside Risk , 1980 .

[2]  Luisa Tibiletti,et al.  Beneficial changes in random variables via copulas: An application to insurance , 1995 .

[3]  A. Sandmo.  On the theory of the competitive firm under price uncertainty , 1971 .

[4]  Hiroshi Konno,et al.  A mean-absolute deviation-skewness portfolio optimization model , 1993, Ann. Oper. Res..

[5]  Fatma Lajeri-Chaherli,et al.  Partial derivatives, comparative risk behavior and concavity of utility functions , 2003, Math. Soc. Sci..

[6]  Campbell R. Harvey,et al.  Conditional Skewness in Asset Pricing Tests , 1999 .

[7]  Andrew J. Patton.  On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation , 2002 .

[8]  Joseph H. Golec,et al.  Bettors Love Skewness, Not Risk, at the Horse Track , 1998, Journal of Political Economy.

[9]  Arun J. Prakash,et al.  Portfolio selection and skewness: Evidence from international stock markets , 1997 .

[10]  Andreas Wagener,et al.  The Demand for a Risky Asset: Signing, Jointly and Separately, the Effects of Three Distributional Shifts , 2005 .

[11]  H. Levy.  Two-Moment Decision Models and Expected Utility Maximization: Comment , 1989 .

[12]  S. Ekern.  Increasing Nth degree risk , 1980 .

[13]  I. Ehrlich,et al.  Market Insurance, Self-Insurance, and Self-Protection , 1972, Journal of Political Economy.

[14]  H. Konno,et al.  A MEAN-VARIANCE-SKEWNESS PORTFOLIO OPTIMIZATION MODEL , 1995 .

[15]  Yuzo Honda,et al.  DOWNSIDE RISK AND THE COMPETITIVE FIRM( , 1985 .

[16]  Jingyuan Li,et al.  Multiplicative risk apportionment , 2010, Math. Soc. Sci..

[17]  M. Lane,et al.  Pricing Risk Transfer Transactions1 , 2000, ASTIN Bulletin.

[18]  Louis Eeckhoudt,et al.  Changes in Risk and the Demand for Saving , 2008, SSRN Electronic Journal.

[19]  Thomas A. Garrett,et al.  Why People Choose Negative Expected Return Assets - an Empirical Examination of a Utility Theoretic Explanation , 2006 .

[20]  W. Henry Chiu,et al.  Skewness Preference, Risk Taking and Expected Utility Maximisation , 2010 .

[21]  Peter C. Fishburn,et al.  Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk , 1976 .

[22]  Haim Levy,et al.  A UTILITY FUNCTION DEPENDING ON THE FIRST THREE MOMENTS , 1969 .

[23]  Chun-Hao Chang,et al.  Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets , 2003 .

[24]  R. Litzenberger,et al.  SKEWNESS PREFERENCE AND THE VALUATION OF RISK ASSETS , 1976 .

[25]  T. Garrett,et al.  Gamblers favor skewness, not risk: Further evidence from United States’ lottery games , 1999 .

[26]  C. Menezes,et al.  Outside Risk Aversion and the Comparative Statics of Increasing Risk in Quasi-Linear Decision Models , 1995 .

[27]  Larry G. Epstein.  Decreasing Risk Aversion and Mean-Variance Analysis , 1985 .

[28]  Edward E. Schlee,et al.  Mean‐Variance Preferences and Investor Behaviour , 2001 .

[29]  Fred Schroyen,et al.  The values of relative risk aversion and prudence: A context-free interpretation , 2009, Math. Soc. Sci..

[30]  Philip A. Horvath,et al.  On The Direction of Preference for Moments of Higher Order Than The Variance , 1980 .

[31]  Josef Hadar,et al.  A Note on Beneficial Changes in Random Variables , 1992 .