Optimal portfolio choice: a minimum expected loss approach

The mainstream in finance tackles portfolio selection based on a plug-in approach without consideration of the main objective of the inferential situation. We propose minimum expected loss (MELO) estimators for portfolio selection that explicitly consider the trading rule of interest. The asymptotic properties of our MELO proposal are similar to the plug-in approach. Nevertheless, simulation exercises show that our proposal exhibits better finite sample properties when compared to the competing alternatives, especially when the tangency portfolio is taken as the asset allocation strategy. We have also developed a graphical user interface to help practitioners to use our MELO proposal.

[1]  Olivier Ledoit,et al.  Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks , 2017 .

[2]  Guofu Zhou,et al.  Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies ☆ , 2011 .

[3]  J. Neyman,et al.  INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION , 2005 .

[4]  Soo-Bin Park,et al.  Some sampling properties of minimum expected loss (MELO) estimators of structural coefficients , 1982 .

[5]  Sébastien Page,et al.  In Defense of Optimization: The Fallacy of 1/N , 2010 .

[6]  Arnold Zellner,et al.  Estimation of functions of population means and regression coefficients including structural coefficients : A minimum expected loss (MELO) approach , 1978 .

[7]  Philippe Jorion.  Bayes-Stein Estimation for Portfolio Analysis , 1986, Journal of Financial and Quantitative Analysis.

[8]  Alba V. Olivares-Nadal,et al.  Technical Note - A Robust Perspective on Transaction Costs in Portfolio Optimization , 2018, Oper. Res..

[9]  Arnold Zellner,et al.  The finite sample properties of simultaneous equations' estimates and estimators Bayesian and non-Bayesian approaches , 1998 .

[10]  Ľuboš Pástor.  Portfolio Selection and Asset Pricing Models , 1999 .

[11]  P. Bickel,et al.  Some contributions to the asymptotic theory of Bayes solutions , 1969 .

[12]  J. Vu.  Portfolio Selection and Asset Pricing Models , 2000 .

[13]  William R. Reichenstein,et al.  Long-Horizon Stock Predictability: Evidence and Applications , 2009, The Journal of Investing.

[14]  Andres Ramirez-Hassan,et al.  Focused econometric estimation for noisy and small datasets: A Bayesian Minimum Expected Loss estimator approach , 2018, 1809.06996.

[15]  Yarema Okhrin,et al.  Distributional properties of portfolio weights , 2006 .

[16]  Stephen J. Brown.  The Effect of Estimation Risk on Capital Market Equilibrium , 1979, Journal of Financial and Quantitative Analysis.

[17]  James Wolter,et al.  Multiple Regression Model Averaging and the Focused Information Criterion with an Application to Portfolio Choice , 2017 .

[18]  C. B. Barry.  PORTFOLIO ANALYSIS UNDER UNCERTAIN MEANS, VARIANCES, AND COVARIANCES , 1974 .

[19]  P. A. V. B. Swamy,et al.  Further Results on Zellner's Minimum Expected Loss and Full Information Maximum Likelihood Estimators for Undersized Samples , 1983 .

[20]  A. Zellner.  A Note on the Relationship of Minimum Expected Loss (MELO) and Other Structural Coefficient Estimates , 1980 .

[21]  Arnold Zellner,et al.  Minimum Expected Loss (MELO) Estimators for Functions of Parameters and Structural Coefficients of Econometric Models , 1979 .

[22]  A. F. M. Smith,et al.  Sampling-resampling techniques for the computation of posterior densities in normal means problems , 1992 .

[23]  Raymond Kan,et al.  Optimal Portfolio Choice with Parameter Uncertainty , 2007, Journal of Financial and Quantitative Analysis.

[24]  Fischer Black,et al.  How to Use Security Analysis to Improve Portfolio Selection , 1973 .

[25]  N. Hjort,et al.  The Focused Information Criterion , 2003 .

[26]  Victor DeMiguel,et al.  Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? , 2009 .

[27]  Peter A. Frost,et al.  An Empirical Bayes Approach to Efficient Portfolio Selection , 1986, Journal of Financial and Quantitative Analysis.

[28]  Olivier Ledoit,et al.  Improved estimation of the covariance matrix of stock returns with an application to portfolio selection , 2003 .

[29]  M. Pinar,et al.  On robust mean-variance portfolios , 2016 .

[30]  Richard O. Michaud.  The Markowitz Optimization Enigma: Is 'Optimized' Optimal? , 1989 .

[31]  R. C. Merton,et al.  On Estimating the Expected Return on the Market: An Exploratory Investigation , 1980 .

[32]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[33]  Vijay S. Bawa,et al.  The effect of estimation risk on optimal portfolio choice , 1976 .

[34]  W. Ziemba,et al.  The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice , 1993 .

[35]  Gabriel Frahm,et al.  Dominating estimators for minimum-variance portfolios , 2010 .

[36]  Jiahan Li.  Sparse and Stable Portfolio Selection With Parameter Uncertainty , 2014 .