A Probabilistic-Based Portfolio Resampling Under the Mean-Variance Criterion

  • Anmar Al Wakil University of Paris-Est, France
Keywords: Efficient Frontier, Mean-Variance Criterion, Portfolio Resampling, Bagging, Probabilistic Approach

Abstract

An abundant amount of literature has documented the limitations of traditional unconstrained mean-variance optimization and Efficient Frontier (EF) considered as an estimation-error maximization that magnifies errors in parameter estimates. Originally introduced by Michaud (1998), empirical superiority of portfolio resampling supposedly lies in the addressing of parameter uncertainty by averaging forecasts that are based on a large number of bootstrap replications. Nevertheless, averaging over resampled portfolio weights in order to obtain the unique Resampled Efficient Frontier (REF, U.S. patent number 6,003,018) has been documented as a debated statistical procedure. Alternatively, we propose a probabilistic extension of the Michaud resampling that we introduce as the Probabilistic Resampled Efficient Frontier (PREF). The originality of this work lies in addressing the information loss in the REF by proposing a geometrical three-dimensional representation of the PREF in the mean-variance-probability space. Interestingly, this geometrical representation illustrates a confidence region around the naive EF associated to higher probabilities; in particular for simulated Global-Mean-Variance portfolios. Furthermore, the confidence region becomes wider with portfolio return, as is illustrated by the dispersion of simulated Maximum-Mean portfolios.

References

Breiman, L. (1996). Bagging Predictors. Machine Learning, 24:123–140.

Da Silva, A. S., Lee, W., and Pornrojnangkool, B. (2009). The Black–Litterman Model for Active Portfolio Management. Journal of Portfolio Management, 35(2):61–70.

Efron, B. (2005). Bayesians, Frequentists, and Scientists. Journal of the American Statistical Association, 100(469):1–5.

Frahm, G. (2015). A Theoretical Foundation of Portfolio Resampling. Theory and Decision, 79(1):107–232.

Hill, P. (1985). Kernel Estimation of a Distribution Function. Communications in Statistics - Theory and Methods, 14(3):605–620.

Jobson, D. and Korkie, B. (1981). Putting Markowitz Theory to Work. Journal of Portfolio Management, 7(4):70–74.

Knight, F. H. (1921). Uncertainty and Profit. Hart, Schaffner and Marx.

Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7(1):77–91.

Markowitz, H. and Usman, N. (2003). Resampled Frontiers versus Diffuse Bayes. Journal of Investment Management, 1:1–17.

Michaud, R. O. (1989). The Markowitz Optimization Enigma: Is 'Optimized' Optimal? Financial Analysts Journal, 45(1):31–42.

Michaud, R. O. (1998). Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation. McGraw-Hill.

Michaud, R. O. and Michaud, R. (2003). An Examination of Resampled Portfolio Efficiency: A Comment and Response. Financial Analysts Journal, 59:15–16.

Michaud, R. O. and Michaud, R. (2008). Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset-Allocation. Oxford University Press, New York, 2nd edition.

Mossin, J. (1968). Optimal Multiperiod Portfolio Policies. The Journal of Business, 41:215–229.

Politis, D. and White, H. (2004). Automatic Block-Length Selection for the Dependent Bootstrap. Econometric Reviews, 23(1):53–70.

Scherer, B. (2002). Portfolio Resampling: Review and Critique. Financial Analysts Journal, 58(6):98–109.

Wolf, M. (2007). Resampling vs. Shrinkage for Benchmarked Managers. Wilmott Magazine, 24:76–81.

Published
2021-04-17
How to Cite
Al Wakil, A. (2021). A Probabilistic-Based Portfolio Resampling Under the Mean-Variance Criterion. Econometric Research in Finance, 6(1), 45 - 56. https://doi.org/10.2478/erfin-2021-0003
Section
Articles
Bookmark and Share