Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-03T02:52:19.321Z Has data issue: false hasContentIssue false
  • English
  • Français

Multivariate Tests for Stochastic Dominance Efficiency of a Given Portfolio

Published online by Cambridge University Press:  06 April 2009

Thierry Post  and
Philippe Versijp
Thierry Post
Affiliation:
[email protected], Erasmus University Rotterdam, P.O. Box 1738, Rotterdam, DR 3000, The Netherlands.
Philippe Versijp
Affiliation:
[email protected], Erasmus University Rotterdam, P.O. Box 1738, Rotterdam, DR 3000, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

We develop empirical tests for stochastic dominance efficiency of a given investment portfolio relative to all possible portfolios formed from a given set of assets. Our tests use multivariate statistics, which result in superior statistical power properties compared to existing stochastic dominance efficiency tests and increase the comparability with existing mean-variance efficiency tests. Using our tests, we demonstrate that the mean-variance inefficiency of the CRSP all-share index relative to beta-sorted portfolios can be explained by tail risk not captured by variance.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 42 , Issue 2 , June 2007 , pp. 489 - 515
Copyright
Copyright © School of Business Administration, University of Washington 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arditti, F. D. “Risk and the Required Return on Equity.” Journal of Finance, 22 (1967), 19–36.CrossRefGoogle Scholar
Barrett, G. F., and Donald, S. G.. “Consistent Tests for Stochastic Dominance.” Econometrica, 71 (2003), 71–104.CrossRefGoogle Scholar
Bawa, V. “Optimal Rules for Ordering Uncertain Prospects.” Journal of Financial Economics, 2 (1975), 95–121.CrossRefGoogle Scholar
Bawa, V., and Lindenberg, E. B.. “Capital Market Equilibrium in a Mean-Lower Partial Moment Framework.” Journal of Financial Economics, 5 (1977), 189–200.CrossRefGoogle Scholar
Black, F.; Jensen, M. C.; and Scholes, M.. “The Capital Asset Pricing Model: Some Empirical Tests.” In Studies in the Theory of Capital Markets, Jensen, M. C., ed. New York, NY: Praeger (1972), 79–121.Google Scholar
Bowden, R. J. “Ordered Mean Difference Benchmarking, Utility Generators, and Capital Market Equilibrium.” Journal of Business, 78 (2005), 441–467.CrossRefGoogle Scholar
Cooley, P. L. “A Multidimensional Analysis of Institutional Investor Perception of Risk.” Journal of Finance, 32 (1977), 67–78.Google Scholar
Dardanoni, V., and Forcina, A.. “Inference for the Lorenz Curve Orderings.” Econometrics Journal, 2 (1999), 49–75.CrossRefGoogle Scholar
Davidson, R., and Duclos, J.-Y.. “Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality.” Econometrica, 68 (2000), 1435–1464.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “The Cross-Section of Expected Stock Returns.” Journal of Finance, 47 (1992), 427–465.Google Scholar
Fama, E. F., and Macbeth, J.. “Risk, Return and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607–636.CrossRefGoogle Scholar
Ferson, W. E., and Foerster, S. R.. “Finite Sample Properties of the Generalized Method of Moments in Tests of Conditional Asset Pricing Models.” Journal of Financial Economics, 36 (1994), 29–55.CrossRefGoogle Scholar
Friend, I., and Blume, M.. “A New Look at the Capital Asset Pricing Model.” Journal of Finance, 28 (1973), 19–33.Google Scholar
Friend, I., and Westerfield, R.. “Co-Skewness and Capital Asset Pricing.” Journal of Finance, 35 (1980), 897–913.Google Scholar
Gibbons, M. R.; Ross, S. A.; and Shanken, J.. “A Test of the Efficiency of a Given Portfolio.” Econometrica, 57 (1989), 1121–1152.CrossRefGoogle Scholar
Hansen, L. P. “Large Sample Properties of Generalized Method of Moments Estimators.” Econometrica, 50 (1982), 1029–1054.CrossRefGoogle Scholar
Hansen, L. P.; Heaton, J.; and Yaron, A.. “Finite-Sample Properties of Some Alternative GMM Estimators.” Journal of Business and Economic Statistics, 14 (1996), 262–280.CrossRefGoogle Scholar
Hansen, L. P., and Jagannathan, R.. “Assessing Specification Errors in Stochastic Discount Factor Models.” Journal of Finance, 52 (1997), 557–590.CrossRefGoogle Scholar
Harlow, W. V., and Rao, R. K. S.. “Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence.” Journal of Financial and Quantitative Analysis, 24 (1989), 285–311.CrossRefGoogle Scholar
Harvey, C. R., and Siddique, A.. “Conditional Skewness in Asset Pricing Tests.” Journal of Finance, 55 (2000), 1263–1295.CrossRefGoogle Scholar
Jagannathan, R., and Wang, Z.. “The Conditional CAPM and the Cross-Section of Expected Returns.” Journal of Finance, 51 (1996), 3–53.Google Scholar
Kimball, M. S. “Precautionary Saving in the Small and Large.” Econometrica, 58 (1990), 53–73.CrossRefGoogle Scholar
Kraus, A., and Litzenberger, R. H.. “Skewness Preference and the Valuation of Risk Assets.” Journal of Finance, 31 (1976), 1085–1100.Google Scholar
Kuosmanen, T. “Efficient Diversification According to Stochastic Dominance Criteria.” Management Science, 50 (2004), 1390–1406.CrossRefGoogle Scholar
Lettau, M., and Ludvigson, S.. “Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying.” Journal of Political Economy, 109 (2001), 1238–1287.CrossRefGoogle Scholar
Levy, H.Stochastic Dominance. Norwell, MA: Kluwer Academic Publishers (1998).CrossRefGoogle Scholar
Linton, O.; Maasoumi, E.; and Whang, Y.-J.. “Consistent Testing for Stochastic Dominance under General Sampling Schemes.” Review of Economic Studies, 72 (2005), 735–765.CrossRefGoogle Scholar
Lo, A. W., and MacKinlay, A. C.. “Data-Snooping Biases in Tests of Financial Asset Pricing Models.” Review of Financial Studies, 3 (1990), 431–467.CrossRefGoogle Scholar
Loughran, T. “Book-to-Market across Firm Size, Exchange, and Seasonality.” Journal of Financial and Quantitative Analysis, 32 (1997), 249–268.CrossRefGoogle Scholar
MacKinlay, A. C., and Richardson, M. P.. “Using Generalized Method of Moments to Test Mean-Variance Efficiency.” Journal of Finance, 46 (1991), 511–527.Google Scholar
Post, T. “Empirical Tests for Stochastic Dominance Efficiency.” Journal of Finance, 58 (2003), 1905–1932.CrossRefGoogle Scholar
Post, T., and Levy, H.. “Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs.” Review of Financial Studies, 18 (2005), 925–953.CrossRefGoogle Scholar
Price, K.; Price, B.; and Nantell, T. J.. “Variance and Lower Partial Moment Measures of Systematic Risk: Some Analytical and Empirical Results.” Journal of Finance, 37 (1982), 843–855.CrossRefGoogle Scholar
Reinganum, M. R. “A New Empirical Perspective on the CAPM.” Journal of Financial and Quantitative Analysis, 16 (1981), 439–462.CrossRefGoogle Scholar
Russell, W. R., and Seo, T. K.. “Representative Sets for Stochastic Dominance Rules.” In Studies in the Economics of Uncertainty: In Honor of Josef Hadar, Fomby, T. B. and Seo, T. K., eds. New York, NY: Springer Verlag (1989), 59–76.CrossRefGoogle Scholar
Varian, H. R. “Nonparametric Analysis of Optimising Behaviour with Measurement Error.” Journal of Econometrics, 30 (1985), 445–458.CrossRefGoogle Scholar
Whitmore, G. A. “Third-Degree Stochastic Dominance.” American Economic Review, 60 (1970), 457–459.Google Scholar