Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal modelFootnote

^†A brief version of this paper was presented at the third meeting of the Econometric Society of Thailand.

References

• Abramowitz, M., and I.A. Stegun. 1984. Pocketbook of mathematical functions. Frankfurt am Main: Verlag Harri Deutsch.
   Google Scholar
• Adcock, C.J. 2005. Exploiting skewness to build an optimal hedge fund with a currency overlay. European Journal of Finance 11, no. 5: 445–62.
   Google Scholar
• Adcock, C.J. 2010. Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution. Annals of Operation Research 176, no. 1: 221–34.
   Web of Science ®Google Scholar
• Amenguala, D., and E. Sentana. 2010. A comparison of mean–variance efficiency tests. Journal of Econometrics 154, no. 1: 16–34.
   Web of Science ®Google Scholar
• Arellano-Valle, R.B., and A. Azzalini. 2006. On the unification of families of skew-normal distributions. Scandinavian Journal of Statistics 33, no. 3: 561–74.
   Web of Science ®Google Scholar
• Athayde, G.M., and R.G. Flôres. 2004. Finding a maximum skewness portfolio – a general solution to three-moments portfolio choice. Journal of Economic Dynamics and Control 28, no. 7: 1335–52.
   Web of Science ®Google Scholar
• Basak, G., R. Jagannathan, and T. Ma. 2009. A jackknife estimator for tracking error variance of optimal portfolio. Management Science 55, no. 6: 990–1002.
   Web of Science ®Google Scholar
• Best, M.J., and R.R. Grauer. 1991. On the sensitivity of mean–variance-efficient portfolios to changes in asset means: Some analytical and computational results. Review of Financial Studies 4, no. 2: 315–42.
   Web of Science ®Google Scholar
• Bodnar, O. 2009. Sequential surveillance of the tangency portfolio weights. International Journal of Theoretical and Applied Finance 12, no. 6: 797–810.
   Google Scholar
• Bodnar, T., and A.K. Gupta. 2009. Construction and inferences of the efficient frontier in elliptical models. Journal of the Japan Statistical Society 39, no. 2: 193–207.
   Google Scholar
• Bodnar, T., and W. Schmid. 2008a. A test for the weights of the global minimum variance portfolio in an elliptical model. Metrika 67, no. 2: 127–43.
   Web of Science ®Google Scholar
• Bodnar, T., and W. Schmid. 2008b. Estimation of optimal portfolio compositions for Gaussian returns. Statistics & Decisions 26, no. 3: 179–201.
   Google Scholar
• Bodnar, T., and W. Schmid. 2009. Econometrical analysis of the sample efficient frontier. European Journal of Finance 15, no. 3: 317–35.
   Web of Science ®Google Scholar
• Britten-Jones, M. 1999. The sampling error in estimates of mean–variance efficient portfolio weights. Journal of Finance 54, no. 2: 655–71.
   Web of Science ®Google Scholar
• Cabras, S., and M.E. Castellanos. 2009. Default Bayesian goodness-of-fit tests for the skew-normal model. Journal of Applied Statistics 36, no. 2: 223–32.
   Web of Science ®Google Scholar
• Chen, J.T., A.K. Gupta, and C.G. Troskie. 2003. The distribution of stock returns when the market is up. Communications in Statistics: Theory and Methods 32, no. 8: 1541–58.
   Web of Science ®Google Scholar
• Conte, S.D., and C. de Boor. 1981. Elementary numerical analysis. London: McGraw-Hill.
   Google Scholar
• Domínguez-Molina, J.A., G. González-Farías, and A.K. Gupta. 2007. A matrix variate closed skew-normal distribution with applications to stochastic frontier analysis. Communications in Statistics: Theory and Methods 36, no. 9: 1691–703.
   Web of Science ®Google Scholar
• Flecher, C., P. Naveaua, and D. Allard. 2009. Estimating the closed skew-normal distribution parameters using weighted moments. Statistics and Probability Letters 79, no. 19: 1977–84.
   Web of Science ®Google Scholar
• Framstad, N.C. 2011. Portfolio separation properties of the skew-elliptical distributions, with generalizations. Statistics and Probability Letters 81, no. 12: 1862–66.
   Web of Science ®Google Scholar
• Gibbons, M.R., S.A. Ross, and J. Shanken. 1989. A test of the efficiency of a given portfolio. Econometrica 57, no. 5: 1121–52.
   Web of Science ®Google Scholar
• González-Farías, G., J.A. Domínguez-Molina, and A.K. Gupta. 2004. The closed skew normal distribution. In Skew-elliptical distributions and their applications: A journey beyond normality, ed. M.G. Genton, 25–42. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Greene, W.H. 2003. Econometric analysis. New Jersey: Prentice Hall.
   Google Scholar
• Gupta, A.K. 2004. Multivariate skew t-distribution. Statistics 37, no. 4: 359–63.
   Web of Science ®Google Scholar
• Gupta, A.K., and J.T. Chen. 2001. Goodness-of-fit tests for the skew normal distribution. Communications in Statistics –Simulation and Computation 30, no. 4: 907–30.
   Web of Science ®Google Scholar
• Harvey, C.R., J.C. Leichty, M.W. Leichty, and P. Muller. 2010. Portfolio selection with higher moments. Quantitative Finance 10, no. 5: 469–85.
   Web of Science ®Google Scholar
• Harville, D.A. 1997. Matrix algebra from a statistician's perspective. New York: Springer-Verlag.
   Google Scholar
• Jagannathan, R., and T. Ma. 2003. Risk reduction in large portfolio: Why imposing wrong constraints helps. Journal of Finance 58, no. 4: 1651–83.
   Web of Science ®Google Scholar
• Jobson, J.D. 1991. Confidence regions for the mean–variance efficient set: An alternative approach to estimation risk. Review of Quantitative Finance and Accounting 1, no. 3: 235–57.
   Google Scholar
• Jobson, J.D., and B. Korkie. 1980. Estimation of Markowitz efficient portfolios. Journal of the American Statistical Association 75, no. 371: 544–54.
   Web of Science ®Google Scholar
• Jobson, J.D., and B. Korkie. 1989. A performance interpretation of multivariate tests of asset set intersection, spanning, and mean–variance efficiency. Journal of Financial and Quantitative Analysis 24, no. 2: 185–204.
   Web of Science ®Google Scholar
• Jondeau, E., and M. Rockinger. 2006. Optimal portfolio allocation under higher moments. European Financial Management 12, no. 1: 29–55.
   Web of Science ®Google Scholar
• Jorion, P. 1986. Bayes–Stein estimation for portfolio analysis. Journal of Financial and Quantitative Analysis 21, no. 4: 293–305.
   Google Scholar
• Kan, R., and D.R. Smith. 2008. The distribution of the sample minimum-variance frontier. Management Science 54, no. 7: 1364–80.
   Web of Science ®Google Scholar
• Kroll Y., H. Levy, and H.M. Markowitz. 1984. Mean–variance versus direct utility maximization. Journal of Finance 39, no. 1: 47–61.
   Web of Science ®Google Scholar
• Ledoit, O., and M. Wolf. 2008. Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance 15, no. 5: 850–59.
   Web of Science ®Google Scholar
• Levy, H., and H.M. Markowitz. 1979. Approximating expected utility by a function of mean and variance. American Economic Review 69, no. 3: 308–17.
   Web of Science ®Google Scholar
• Markowitz, H.M. 1952. Portfolio selection. Journal of Finance 7, no. 1: 77–91.
   Web of Science ®Google Scholar
• Mateu-Figueras, G., P. Puig, and A. Pewsey, 2007. Goodness-of-fit tests for the skew-normal distribution when the parameters are estimated from the data. Communications in Statistics – Theory and Methods 36, no. 9: 1735–55.
   Web of Science ®Google Scholar
• Meintanis, S.G. 2007. A Kolmogorov–Smirnov type test for skew normal distributions based on the empirical moment generating function. Journal of Statistical Planning and Inference 137, no. 8: 2681–8.
   Web of Science ®Google Scholar
• Meintanis, S.G. 2010. Testing skew normality via the moment generating function. Mathematical Methods of Statistics 19, no. 1: 64–72.
   Google Scholar
• Meintanis, S.G., and Z. Hlávka. 2010. Goodness-of-fit tests for bivariate and multivariate skew-normal distributions. Scandinavian Journal of Statistics 37, no. 4: 701–14.
   Web of Science ®Google Scholar
• Mencía, J., and E. Sentana. 2009. Multivariate location–scale mixtures of normals and mean–variance skewness portfolio allocation. Journal of Econometrics 153, no. 2: 105–21.
   Web of Science ®Google Scholar
• Merton, R.C. 1972. An analytical derivation of the efficient frontier. Journal of Financial and Quantitative Analysis 7, no. 4: 1851–72.
   Web of Science ®Google Scholar
• Merton, R.C. 1980. On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics 8, no. 4: 323–61.
   Web of Science ®Google Scholar
• Okhrin, Y., and W. Schmid. 2006. Distributional properties of portfolio weights. Journal of Econometrics 134, no. 1: 235–56.
   Web of Science ®Google Scholar
• Patton, A.J. 2004. On the out-of-sample importance of skewness and asymmetric dependence for asset allocation. Journal of Financial Econometrics 2, no. 1: 130–68.
   Google Scholar
• Pérez Rodríguez, P., and J.A. Villaseñor Alva. 2010. On testing the skew normal hypothesis. Journal of Statistical Planning and Inference 140, no. 11: 3148–59.
   Web of Science ®Google Scholar
• Simaan, Y. 1993. What is the opportunity cost of mean–variance investment strategies? Management Science 39, no. 5: 578–87.
   Web of Science ®Google Scholar
• Wang, Z. 2005. A shrinkage approach to model uncertainty and asset allocation. Review of Financial Studies 18, no. 2: 673–705.
   Web of Science ®Google Scholar