On the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors

This paper studies some properties of stochastic dominance (SD) for risk-averse and risk-seeking investors, especially for the third order SD (TSD). We call the former ascending stochastic dominance (ASD) and the latter descending stochastic dominance(DSD). We first discuss the basic property of ASD and DSD linking the ASD and DSD of the first three orders to expected-utility maximization for risk-averse and risk-seeking investors. Thereafter, we prove that a hierarchy exists in both ASD and DSD relationships and that the higher orders of ASD and DSD cannot be replaced by the lower orders of ASD and DSD. Furthermore, we study conditions in which third order ASD preferences will be 'the opposite of' or 'the same as' their counterpart third order DSD preferences. In addition, we construct examples to illustrate all the properties developed in this paper. The theory developed in this paper provides investors with tools to identify first, second, and third order ASD and DSD prospects and thus they could make wiser choices on their investment decision.

[1]  Fariborz Moshirian,et al.  Evolution of International Stock and Bond Market Integration: Influence of the European Monetary Union , 2006 .

[2]  Peter C. Fishburn,et al.  Decision And Value Theory , 1965 .

[3]  C. Bonferroni.  Il calcolo delle assicurazioni su gruppi di teste , 1935 .

[4]  Jack A. Meyer,et al.  Second Degree Stochastic Dominance with Respect to a Function , 1977 .

[5]  H. Levy,et al.  Efficiency analysis of choices involving risk , 1969 .

[6]  H. Lean,et al.  Stochastic dominance and behavior towards risk: The market for Internet stocks , 2008 .

[7]  Alain Trannoy,et al.  Even (Mixed) Risk Lovers Are Prudent , 2013 .

[8]  H. Levy,et al.  Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs , 2005 .

[9]  Wing-Keung Wong,et al.  International momentum strategies: a stochastic dominance approach , 2005 .

[10]  Louis Eeckhoudt,et al.  Background Risk, Prudence, and the Demand for Insurance , 1992 .

[11]  Thorsten Dickhaus,et al.  Simultaneous Statistical Inference , 2014, Springer Berlin Heidelberg.

[12]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[13]  M. Rothschild,et al.  Increasing risk II: Its economic consequences , 1971 .

[14]  Lars Thorlund-Petersen,et al.  Third-degree stochastic dominance and axioms for a convex marginal utility function , 2001, Math. Soc. Sci..

[15]  P. Fishburn,et al.  TWO‐PIECE VON NEUMANN‐MORGENSTERN UTILITY FUNCTIONS* , 1979 .

[16]  L. J. Savage,et al.  The Utility Analysis of Choices Involving Risk , 1948, Journal of Political Economy.

[17]  G. Frankfurter,et al.  Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances , 1971, Journal of Financial and Quantitative Analysis.

[18]  Michael Hoy,et al.  The Normative Significance of Using Third-Degree Stochastic Dominance in Comparing Income Distributions , 1994 .

[19]  Vijay S. Bawa,et al.  An Efficient Algorithm to Determine Stochastic Dominance Admissible Sets , 1979 .

[20]  Man-Chung Ng,et al.  A Remark on Third Degree Stochastic Dominance , 2000 .

[21]  Peter C. Fishburn,et al.  Decision And Value Theory , 1965 .

[22]  Michael McAleer,et al.  Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China , 2012 .

[23]  J. Quirk,et al.  Admissibility and Measurable Utility Functions , 1962 .

[24]  Wing-Keung Wong,et al.  A note on convex stochastic dominance , 1999 .

[25]  William E. Stein,et al.  Risk Averse Decisions in Business Planning , 1992 .

[26]  Rudi Zagst,et al.  Stochastic dominance of portfolio insurance strategies , 2011, Ann. Oper. Res..

[27]  Lisa Farrell,et al.  Can Expected Utility Theory Explain Gambling , 2002 .

[28]  Leigh Tesfatsion,et al.  Stochastic Dominance and the Maximization of Expected Utility , 1976 .

[29]  Friedrich Schmid,et al.  A note on third degree stochastic dominance , 2005, OR Spectr..

[30]  Hua Li,et al.  Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications , 2007 .

[31]  M. Richardson,et al.  Dotcom Mania: A Survey of Market Efficiency in the Internet Sector , 2001 .

[32]  J. Tobin.  Liquidity Preference as Behavior towards Risk , 1958 .

[33]  Wei Xiong,et al.  Overconfidence and Speculative Bubbles , 2003, Journal of Political Economy.

[34]  C. Williams.  Attitudes toward Speculative Risks as an Indicator of Attitudes toward Pure Risks , 1966 .

[35]  Fred D. Arditti.  RISK AND THE REQUIRED RETURN ON EQUITY , 1967 .

[36]  G. Whitmore,et al.  Third-Degree Stochastic Dominance , 1970 .

[37]  H. Levy.  Stochastic Dominance: Investment Decision Making under Uncertainty , 2010 .

[38]  Gordon Anderson,et al.  Toward an empirical analysis of polarization , 2004 .

[39]  Hiroshi Konno,et al.  Third Degree Stochastic Dominance and Mean-Risk Analysis , 2000 .

[40]  Wing-Keung Wong,et al.  Preferences over location-scale family , 2008 .

[41]  Wing-Keung Wong,et al.  Preferences Over Meyer's Location-Scale Family , 2005 .

[42]  Ephraim Clark,et al.  Investors’ Preference Towards Risk: Evidence from the Taiwan Stock and Stock Index Futures Markets , 2014 .

[43]  V. Bawa.  OPTIMAL, RULES FOR ORDERING UNCERTAIN PROSPECTS+ , 1975 .

[44]  J. Hammond.  Simplifying the Choice between Uncertain Prospects Where Preference is Nonlinear , 1974 .

[45]  Ronny Aboudi,et al.  Efficient Algorithms for Stochastic Dominance Tests Based on Financial Market Data , 1994 .

[46]  James K. Weeks.  Stochastic Dominance: A Methodological Approach to Enhancing the Conceptual Foundations of Operations Management Theory , 1985 .

[47]  Peter C. Fishburn,et al.  Convex stochastic dominance with continuous distribution functions , 1974 .

[48]  Wing-Keung Wong,et al.  Stochastic dominance relationships between stock and stock index futures markets: International evidence , 2013 .

[49]  R. Thaler,et al.  Gambling with the house money and trying to break even: the effects of prior outcomes on risky choice , 1990 .

[50]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[51]  H. Markowitz.  The Utility of Wealth , 1952, Journal of Political Economy.

[52]  Josef Hadar,et al.  Stochastic dominance and diversification , 1971 .

[53]  Ward Whitt,et al.  Comparison methods for queues and other stochastic models , 1986 .

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

[55]  R. Jagannathan,et al.  Price Momentum in Stocks: Insights from Victorian Age Data , 2008 .

[56]  James R. Wart,et al.  Efficient Algorithms for Conducting Stochastic Dominance Tests on Large Numbers of Portfolios: Reply , 1975, Journal of Financial and Quantitative Analysis.

[57]  Chi-Kwong Li,et al.  Extension of stochastic dominance theory to random variables , 1999, RAIRO Oper. Res..

[58]  Moshe Levy,et al.  Prospect Theory: Much Ado About Nothing? , 2002, Manag. Sci..

[59]  H. Levy,et al.  Risk aversion and skewness preference , 2008 .

[60]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[61]  M. Le Breton,et al.  Third-degree stochastic dominance and inequality measurement , 2009 .

[62]  Wing-Keung Wong,et al.  Stochastic dominance and mean-variance measures of profit and loss for business planning and investment , 2007, Eur. J. Oper. Res..

[63]  Thierry Post,et al.  Multivariate Tests for Stochastic Dominance Efficiency of a Given Portfolio , 2004, Journal of Financial and Quantitative Analysis.

[64]  Clifford S. Asness,et al.  Value and Momentum Everywhere , 2009 .