Abstract
In the context of modern portfolio theory, we compare the out-of-sample performance of eight investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. In contrast to similar studies in the literature, we also consider short-selling constraints and a risk-free asset. We provide a way to extend the concept of minimum-variance strategies in the context of short-selling constraints. A main drawback of most empirical studies on that topic is the use of simple testing procedures which do not account for the effects of multiple testing. For that reason we conduct several hypothesis tests which are proposed in the multiple-testing literature. We test whether it is possible to beat a trivial strategy by at least one of the non-trivial strategies, whether the trivial strategy is better than every non-trivial strategy, and which of the non-trivial strategies is significantly outperformed by naive diversification. The empirical part of our study is conducted using US stock returns from the last four decades, obtained via the CRSP database.
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Andrews, D.W.K.: Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858 (1991)
Andrews, D.W.K., Monahan, J.C.: An improved heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 60, 953–966 (1992)
Bade, A., Frahm, G., Jaekel, U.: A general approach to Bayesian portfolio optimization. Math. Methods Oper. Res. 70, 337–356 (2008)
Behr, P., Güttler, A., Miebs, F.: On portfolio optimization: Imposing the right constraints matters. Discussion Paper, University of Frankfurt (2010)
Brown, S.J.: Optimal portfolio choice under uncertainty: a Bayesian approach. PhD thesis, University of Chicago (1976)
Ceria, S., Stubbs, R.A.: Incorporating estimation errors into portfolio selection: robust portfolio construction. J. Asset Manag. 7, 109–127 (2006)
Chopra, V.K., Ziemba, W.T.: The effect of errors in means, variances, and covariances on optimal portfolio choice. J. Portf. Manag. 19, 6–11 (1993)
DeMiguel, V., Garlappi, L., Nogales, F.J., Uppal, R.: A generalized approach to portfolio optimization: improving performance by constraining portfolio norms. Manag. Sci. 55, 798–812 (2009a)
DeMiguel, V., Garlappi, L., Uppal, R.: Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Rev. Financ. Stud. 22, 1915–1953 (2009b)
Frahm, G.: Testing for the best alternative with an application to performance measurement. Discussion Paper, University of Cologne (2007)
Frahm, G.: The likelihood-ratio test for ∧-hypotheses. Working Paper, University of Cologne (2009a)
Frahm, G.: Maximum-likelihood estimator for equicorrelated random vectors. Working Paper, University of Cologne (2009b)
Frahm, G., Memmel, C.: Dominating estimators for the global minimum variance portfolio. J. Econom. 159, 289–302 (2010)
Garlappi, L., Uppal, R., Wang, T.: Portfolio selection with parameter and model uncertainty: a multi-prior approach. Rev. Financ. Stud. 20, 41–81 (2007)
Goldfarb, D., Iyengar, G.: Robust portfolio selection problems. Math. Oper. Res. 28, 1–38 (2003)
Halldórsson, B.V., Tütüncü, R.H.: An interior-point method for a class of saddle-point problems. J. Optim. Theory Appl. 116, 559–590 (2003)
Hansen, P.R.: A test for superior predictive ability. J. Bus. Econ. Stat. 23, 365–380 (2005)
Jagannathan, R., Ma, T.: Risk reduction in large portfolios: Why imposing the wrong constraints helps. J. Finance 58, 1651–1684 (2003)
Jobson, J.D., Korkie, B.M.: Performance hypothesis testing with the Sharpe and Treynor measures. J. Finance 26, 889–908 (1981)
Jorion, P.: Bayes–Stein estimation for portfolio analysis. J. Financ. Quant. Anal. 21, 279–292 (1986)
Kalymon, B.A.: Estimation risk in the portfolio selection model. J. Financ. Quant. Anal. 6, 559–582 (1971)
Kan, R., Zhou, G.: Optimal portfolio choice with parameter uncertainty. J. Financ. Quant. Anal. 42, 621–656 (2007)
Kempf, A., Memmel, C.: Estimating the global minimum variance portfolio. Schmalenbach Bus. Rev. 58, 332–348 (2006)
Klein, R.W., Bawa, V.S.: The effect of estimation risk on optimal portfolio choice. J. Financ. Econ. 3, 215–231 (1976)
Kritzman, M., Page, S., Turkington, D.: In defense of optimization: the fallacy of 1/N. Financ. Anal. J. 66, 31–39 (2010)
Lahiri, S.N.: Resampling Methods for Dependent Data. Springer, New York (2003)
Ledoit, O., Wolf, M.: Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J. Empir. Finance 10, 603–621 (2003)
Ledoit, O., Wolf, M.: Honey, I shrunk the sample covariance matrix. J. Portf. Manag. 30, 110–119 (2004)
Ledoit, O., Wolf, M.: Robust performance hypothesis testing with the Sharpe ratio. J. Empir. Finance 15, 850–859 (2008)
Lo, A.W.: The statistics of Sharpe ratios. Financ. Anal. J. 58, 36–52 (2002)
Mao, J.C.T., Särndal, C.E.: A decision theory approach to portfolio selection. Manag. Sci. 12, B-323–334 (1966)
Markowitz, H.: Portfolio selection. J. Finance 7, 77–91 (1952)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management. Princeton University Press, Princeton (2005)
Politis, D.N., Romano, J.P.: A circular block-resampling procedure for stationary data. In: LePage, R., Billard, L. (eds.) Exploring the Limits of Bootstrap, pp. 263–270. Wiley, New York (1992)
Politis, D.N., Romano, J.P.: The stationary bootstrap. J. Am. Stat. Assoc. 89, 1303–1313 (1994)
Press, J.S.: Applied Multivariate Analysis. Holt, Rinehart and Winston, New York (1972)
Romano, J.P., Shaikh, A.M., Wolf, M.: Formalized data snooping based on generalized error rates. Econom. Theory 24, 404–447 (2008)
Romano, J.P., Wolf, M.: Stepwise multiple testing as formalized data snooping. Econometrica 73, 1237–1282 (2005)
Sharpe, W.F.: Mutual fund performance. J. Bus. 39, 119–138 (1966)
Stein, C.: Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In: Proceedings of the 3rd Berkeley Symposium on Probability and Statistics, vol. 1, pp. 197–206. University of California Press, Berkeley (1956)
The Federal Reserve System: 3-month treasury bill secondary market rate on a discount basis. http://www.federalreserve.gov/releases/H15/data/Monthly/H15_TB_M3.txt (2009). Accessed 14 October 2009
Tobin, J.: Liquidity preference as behavior towards risk. Rev. Econ. Stud. 25, 65–86 (1958)
White, H.: A reality check for data snooping. Econometrica 68, 1097–1126 (2000)
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Frahm, G., Wickern, T. & Wiechers, C. Multiple tests for the performance of different investment strategies. AStA Adv Stat Anal 96, 343–383 (2012). https://doi.org/10.1007/s10182-011-0166-1
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DOI: https://doi.org/10.1007/s10182-011-0166-1