Testing for the Stochastic Dominance Efficiency of a Given Portfolio

We propose a new statistical test of the stochastic dominance efficiency of a given portfolio over a class of portfolios. We establish its null and alternative asymptotic properties, and define a method for consistently estimating critical values. We present some numerical evidence that our tests work well in moderate‐sized samples.

[1]  James N. Bodurtha,et al.  On Determination of Stochastic Dominance Optimal Sets , 1985 .

[2]  D. McFadden.  Testing for Stochastic Dominance , 1989 .

[3]  Empirical Tests of the Mean-Semivariance CAPM , 2005 .

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

[5]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[6]  Harshinder Singh,et al.  Testing for Second-Order Stochastic Dominance of Two Distributions , 1994, Econometric Theory.

[7]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[8]  V. Chernozhukov,et al.  Estimation and Confidence Regions for Parameter Sets in Econometric Models , 2007 .

[9]  Joseph P. Romano,et al.  Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions , 1994 .

[10]  W. R. Russell,et al.  Representative Sets for Stochastic Dominance Rules , 1989 .

[11]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[12]  D. Pollard,et al.  An introduction to functional central limit theorems for dependent stochastic processes , 1994 .

[13]  F. Black,et al.  The Capital Asset Pricing Model: Some Empirical Tests , 2006 .

[14]  T. Post.  Wanted: A Test for Fsd Optimality of a Given Portfolio , 2005 .

[15]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[16]  M. Sion.  On general minimax theorems , 1958 .

[17]  Vijay S. Bawa,et al.  Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework , 1977, Journal of Financial and Quantitative Analysis.

[18]  R. Davidson,et al.  Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality , 1998 .

[19]  Thierry Post,et al.  Empirical Tests for Stochastic Dominance Efficiency , 2003 .

[20]  Stephen A. Ross,et al.  A Test of the Efficiency of a Given Portfolio , 1989 .

[21]  Haim Levy,et al.  Sampling Errors and Portfolio Efficient Analysis , 1980, Journal of Financial and Quantitative Analysis.

[22]  Vijay S. Bawa,et al.  Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework , 1977 .

[23]  William W. Hogan,et al.  Toward the Development of an Equilibrium Capital-Market Model Based on Semivariance , 1974, Journal of Financial and Quantitative Analysis.

[24]  J. Horowitz.  The bootstrap in econometrics , 2003 .

[25]  E. Fama,et al.  Risk, Return, and Equilibrium: Empirical Tests , 1973, Journal of Political Economy.

[26]  Thierry Post,et al.  A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion , 2008, Journal of Financial and Quantitative Analysis.

[27]  Arnold J Stromberg,et al.  Subsampling , 2001, Technometrics.

[28]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[29]  O. Linton,et al.  Consistent Testing for Stochastic Dominance Under General Sampling Schemes , 2003 .

[30]  Stephen E. Fienberg,et al.  Testing Statistical Hypotheses , 2005 .

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

[32]  Timo Kuosmanen,et al.  Efficient Diversification According to Stochastic Dominance Criteria , 2004, Manag. Sci..

[33]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

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

[35]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[36]  Timothy J. Nantell,et al.  Variance and Lower Partial Moment Measures of Systematic Risk: Some Analytical and Empirical Results , 1982 .

[37]  R. Jagannathan,et al.  The Conditional CAPM and the Cross-Section of Expected Returns , 1996 .

[38]  John Odenckantz,et al.  Nonparametric Statistics for Stochastic Processes: Estimation and Prediction , 2000, Technometrics.