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A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean-Variance Efficiency

Published online by Cambridge University Press:  06 April 2009

J. D. Jobson  and
Bob Korkie
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Abstract

The purpose of this paper is to provide a link between the various multivariate tests of asset pricing and a performance measure for asset sets. The paper includes a unified summary of various F tests for mean-variance efficiency, intersection, and spanning for sets and subsets of financial assets. Both the risk-free asset and no risk-free asset environments are discussed. These tests are then related to the concept of potential performance for asset sets. The potential performance measure can be viewed as an extension of the Sharpe performance measure for single portfolios. The economic intuition behind the tests is that the multivariate tests of portfolio efficiency, intersection, and spanning are tests of zero potential performance at particular margins between the asset or portfolio subset and the full asset set.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 24 , Issue 2 , June 1989 , pp. 185 - 204
Copyright
Copyright © School of Business Administration, University of Washington 1989

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References

Admati, A. R., and Ross, S. A.. “Measuring Investment Performance in a Rational Expectations Equilibrium Model.” Journal of Business, 58 (01 1985), 1–26.CrossRefGoogle Scholar
Amsler, C. E., and Schmidt, P.. “A Monte Carlo Investigation of the Accuracy of Multivariate CAPM Tests.” Journal of Financial Economics, 14 (09 1985), 359–375.CrossRefGoogle Scholar
Anderson, T. W.An Introduction to Multivariate Analysis. New York: John Wiley & Sons (1984).Google Scholar
Gibbons, M. “Multivariate Tests of Financial Models: A New Approach.” Journal of Financial Economics, 10 (03 1982), 3–27.Google Scholar
Gibbons, M. R.; Ross, S. A.; and Shanken, J.. “A Test of the Efficiency of a Given Portfolio.” Research Paper #853, Stanford Univ. (1986).Google Scholar
Huberman, G., and Kandel, S.. “Likelihood Ratio Tests of Asset Pricing and Mutual Fund Separation.” CRSP Working Paper, Graduate School of Business, Univ. of Chicago (1986).Google Scholar
Huberman, G. “Mean-Variance Spanning.” Journal of Finance, 42 (09. 1987), 873–888.Google Scholar
Jobson, J. D., and Korkie, R.. “Potential Performance and Tests of Portfolio Efficiency.” Journal of Financial Economics, 10 (12 1982), 433–456.Google Scholar
Jobson, J. D., and Korkie, R. “Some Tests of Linear Asset Pricing with Multivariate Normality.” Canadian Journal of Administrative Sciences, 2 (06 1985), 114–138.CrossRefGoogle Scholar
Kandel, S. “Likelihood Ratio Statistics of Mean-Variance Efficiency without a Riskless Asset.” Journal of Financial Economics, 13 (12 1984), 575–592.Google Scholar
Kandel, S. “The Geometry of the Maximum Likelihood Estimator of the Zero-Beta Return.” Journal of Finance, 41 (06 1986), 339–346.Google Scholar
Kandel, S., and Stambaugh, R. F.. “On Correlations and Inferences about Mean-Variance Efficiency.” Journal of Financial Economics, 18 (03 1987), 61–90.Google Scholar
Lehmann, B. N. “Orthogonal Frontiers and Alternative Mean-Variance Efficiency Tests.” Journal of Finance, 42 (07 1987), 601–619.Google Scholar
MacKinlay, A. C. “On Multivariate Tests of the CAPM.” Journal of Financial Economics, 18 (06 1987), 341–372.Google Scholar
Merton, R. C. “An Analytic Derivation of the Efficient Portfolio Frontier.” Journal of Financial and Quantitative Analysis, 7 (09 1972), 1851–1872.CrossRefGoogle Scholar
Roll, R. “A Critique of the Asset Pricing Theory's Tests; Part I: On Past and Potential Testability of the Theory.” Journal of Financial Economics, 4 (03 1977), 129–176.CrossRefGoogle Scholar
Roll, R. “A Note on the Geometry of Shanken's CSR T2 Test for Mean/Variance Efficiency.” Journal of Financial Economics, 14 (09 1985), 349–357.Google Scholar
Ross, S. A. “A Test of the Efficiency of a Given Portfolio.” A paper presented at the World Econometric meetings, Aix-en-Provence (1980).Google Scholar
Seber, G. A. F.Multivariate Observations. New York: John Wiley & Sons (1984).CrossRefGoogle Scholar
Shanken, J. “Multivariate Tests of the Zero-Beta CAPM.” Journal of Financial Economics, 14 (09 1985), 327–348.Google Scholar
Shanken, J. “Testing Portfolio Efficiency when the Zero Beta Rate is Unknown: A Note.” Journal of Finance, 41 (03 1986), 269–276.Google Scholar
Stambaugh, R. F. “On The Exclusion of Assets from Tests of the Two Parameter Model: A Sensitivity Analysis.” Journal of Financial Economics, 10 (11 1982), 237–268.Google Scholar
Van Zijl, T. “Risk Decomposition: Variance and Standard Deviation—A Reexamination and Extension.” Journal of Financial and Quantitative Analysis, 22 (09 1987), 237–248.CrossRefGoogle Scholar