Abstracts
Abstract
We propose double bootstrap methods to test the mean-variance efficiency hypothesis when multiple portfolio groupings of the test assets are considered jointly rather than individually. A direct test of the joint null hypothesis may not be possible with standard methods when the total number of test assets grows large relative to the number of available time-series observations, since the estimate of the disturbance covariance matrix eventually becomes singular. The suggested residual bootstrap procedures based on combining the individual group p-values avoid this problem while controlling the overall significance level. Simulation and empirical results illustrate the usefulness of the joint mean-variance efficiency tests.
Download the article in PDF to read it.
Download
Appendices
Acknowledgements
We would like to thank Ian Christensen, Antonio Diez de los Rios, Jonathan Witmer, Bo Young Chang, and seminar participants at the Bank of Canada for helpful comments and useful conversations. All remaining errors and omissions are our own.
Bibliography
- Affleck-Graves, J., and B. McDonald (1989). “Nonnormalities and Tests of Asset Pricing Theories.’’ Journal of Finance, 44: 889-908.
- Affleck-Graves, J., and B. McDonald (1990). “Multivariate Tests of asset pricing: the comparative power of alternative statistics.’’ Journal of Financial and Quantitative Analysis, 25: 163-185.
- Beaulieu, M.-C., J.-M. Dufour, and L. Khalaf (2007). “Multivariate Tests of Mean-variance Efficiency with Possibly Non-Gaussian Errors.’’ Journal of Business and Economic Statistics, 25: 398-410.
- Beran, R. (1987). “Prepivoting to reduce level error of confidence sets.’’ Biometrika, 74: 457-468.
- Beran, R. (1988). “Prepivoting test statistics: abootstrap view of asymptotic refinements.’’ Journal of the American Statistical Association, 83: 687-697.
- Campbell, J., A. Lo, and A. MacKinlay (1997). The Econometrics of Financial Markets. Princeton University Press.
- Chou, P.-H., and G. Zhou (2006). “Using Bootstrap to Test Portfolio Efficiency.’’ Annals of Economics and Finance, 1: 217-249.
- Dufour, J.-M., L. Khalaf, and M. Voia (2014). “Finite-sample Resampling-based Combined Hypothesis Tests, with Applications to Serial Correlation and Predictability.’’ Communications in Statistics–Simulation and Computation, forthcoming.
- Folks, J.L. (1984). “Combination of Independent Tests.’’ in Krishnaiah, P.R., and P.K. Sen, (Eds), Handbook of Statistics 4: Nonparametric Methods. North- Holland, Amsterdam, pp. 113-121.
- Gibbons, M., S. Ross, and J. Shanken (1989). “A test of the efficiency of a given portfolio.’’ Econometrica, 57: 1121-1152.
- Godfrey, L. (2005). “Controlling the overall significance level of a battery of least squares diagnostic tests.’’ Oxford Bulletin of Economics and Statistics, 67: 263-279.
- Gungor, S., and R. Luger (2013), “Testing linear factor pricing models with large cross-sections: adistribution-free approach.’’ Journal of Business and Economic Statistics, 31: 66-77.
- Hein, S., and P. Westfall (2004). “Improving tests of abnormal returns by bootstrapping the multivariate regression model with event parameters.’’ Journal of Financial Econometrics, 2: 451-471.
- Jobson, J., and B. Korkie (1982). “Potential performance and tests of portfolio Efficiency.’’ Journal of Financial Economics, 10: 433-466.
- Kothari, S., J. Shanken, and R. Sloan (1995), “Another Look at the Cross-section of Expected stock Returns.’’ Journal of Finance, 50: 185-224.
- Lewellen, J., S. Nagel, and J. Shanken (2010). “A skeptical appraisal of asset pricing tests.’’ Journal of Financial Economics, 96: 175-194.
- Lintner, J. (1965). “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.’’ Review of Economics and Statistics, 47: 13-37.
- MacKinnon, J. (2009). “Bootstrap Hypothesis Testing.’’ in Belsley D., and J. Kontoghiorghes (Eds.), Handbook of Computational Econometrics, pp. 183-213. Wiley.
- Nankervis, J.C. (2003). “Stopping Rules for Double Bootstrap Tests.’’ Working Paper No. 03/14, Department of Accounting, Finance and Management, University of Essex.
- Nankervis, J.C. (2005). “Computational Algorithms for Double Bootstrap Confidence Intervals.’’ Computational Statistics and Data Analysis, 49: 461-475.
- Ross, S. (1976). “The Arbitrage Theory of Capital Asset Pricing.’’ Journal of Economic Theory, 13: 341-360.
- Savin, N. (1984). “Multiple Hypothesis Testing.’’ in Griliches, Z., and M. Intriligator (Eds.), Handbook of Econometrics, pp. 827-879. North-Holland, Amsterdam.
- Sentana, E. (2009). “The econometrics of mean-variance effiency: a survey.’’ Econometrics Journal, 12: 65-101.
- Shanken, J. (1996). “Statistical methods in tests of portfolio effiency: asynthesis.’’ in Maddala, G., and C. Rao (Eds.), Handbook of Statistics, Vol. 14: Statistical Methods in Finance, pp. 693-711. Elsevier Science B.V.
- Sharpe, W.F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk.’’ Journal of Finance, 19: 425-442.
- Theil, H., and K. Laitinen (1980). “Singular Moment Matrices in Applied econometric.’’ in P. Krishnaiah (Ed.), Multivariate Analysis. North-Holland, Amsterdam, pp. 629-649.
- Westfall, P.H., and S.S. Young (1993), Resampling-Based Multiple Testing: Examples and Methods for p-value Adjustment. Wiley, New York.