Abstract
Most portfolio selection rules based on the sample mean and covariance matrix perform poorly out-of-sample. Moreover, there is a growing body of evidence that such optimization rules are not able to beat simple rules of thumb, such as 1/N. Parameter uncertainty has been identified as one major reason for these findings. A strand of literature addresses this problem by improving the parameter estimation and/or by relying on more robust portfolio selection methods. Independent of the chosen portfolio selection rule, we propose using feature selection first in order to reduce the asset menu. While most of the diversification benefits are preserved, the parameter estimation problem is alleviated. We conduct out-of-sample back-tests to show that in most cases different well-established portfolio selection rules applied on the reduced asset universe are able to improve alpha relative to different prominent factor models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
See Kritzman (1993) who compares factor analysis and cross-sectional regression for that purpose.
In the following we use the term “feature selection” as synonym for “hierarchical clustering”.
Given the focus of this paper, we want to point out that the proposed investigation is not intended as a horse race between the different portfolio selection rules.
For example, finding the optimal universe of the least correlated 15 out of 50 assets would require approximately \(2.25 \times 10^{12}\) permutations.
The extreme reduction of dimensionality in this exhibition is used for the illustration purpose only.
The structured estimator is based on the constant correlation matrix (set equal to the average sample correlation), which corresponds to the default value in the package.
Given that the clusters are quite stable over time and the assets within a cluster are highly correlated, in order to reduce excessive trading we propose to apply feature selection on an annual basis.
The most time consuming operation is shrinkage. For the 49 industry portfolios the computational time for all results is less than 10 min.
When considering only out-of-sample returns of the same time-interval, we found that intermediate estimations windows of 10–20 years perform best. Results are available upon request.
References
Best, M. J., & Grauer, R. R. (1991). On the Sensitivity of mean–variance-efficient portfolios to changes in asset means: Some analytical and computational results. Review of Financial Studies, 4(2), 315–342.
Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48(5), 28–43.
Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57–82.
Chopra, V. K., & Ziemba, W. T. (1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. The Journal of Portfolio Management, 19(2), 6–11.
Clarke, R. G., de Silva, H., & Thorley, S. (2006). Minimum-variance portfolios in the US equity market. The Journal of Portfolio Management, 33(1), 10–24.
DeMiguel, V., Garlappi, L., Nogales, F. J., & Uppal, R. (2009a). A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms. Management Science, 55(5), 798–812.
DeMiguel, V., Garlappi, L., & Uppal, R. (2009b). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22(5), 1915–1953.
DeMiguel, V., & Nogales, F. J. (2009). Portfolio selection with robust estimation. Operations Research, 57(3), 560–577.
Duchin, R., & Levy, H. (2009). Markowitz versus the talmudic portfolio diversification strategies. The Journal of Portfolio Management, 35(2), 71–74.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56.
Frazzini, A., & Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1), 1–25.
Hartigan, J. A. (1981). Consistency of single linkage for high-density clusters. Journal of the American Statistical Association, 76(374), 388–394.
Haugen, R. A., & Baker, N. L. (1991). The efficient market inefficiency of capitalization-weighted stock portfolios. The Journal of Portfolio Management, 17(3), 35–40.
Jagannathan, R., & Ma, T. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. The Journal of Finance, 58(4), 1651–1684.
Jorion, P. (1986). Bayes-Stein estimation for portfolio analysis. The Journal of Financial and Quantitative Analysis, 21(3), 279–292.
Kan, R., & Zhou, G. (2007). Optimal portfolio choice with parameter uncertainty. Journal of Financial and Quantitative Analysis, 42(03), 621–656.
Kritzman, M. (1993). What practitioners need to know\(\ldots \) about factor methods. Financial Analysts Journal, 49(1), 12–15.
Kritzman, M., Page, S., & Turkington, D. (2010). In defense of optimization: The fallacy of 1/ N. Financial Analysts Journal, 66(2), 31–39.
Ledoit, O., & Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5), 603–621.
Ledoit, O., & Wolf, M. (2004a). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365–411.
Ledoit, O., & Wolf, M. (2004b). Honey, I shrunk the sample covariance matrix. The Journal of Portfolio Management, 30(4), 110–119.
Ledoit, O., & Wolf, M. (2012). Nonlinear shrinkage estimation of large-dimensional covariance matrices. The Annals of Statistics, 40(2), 1024–1060.
Levy, H., & Levy, M. (2014). The benefits of differential variance-based constraints in portfolio optimization. European Journal of Operational Research, 234(2), 372–381.
Lisi, F., & Corazza, M. (2008). Clustering financial data for mutual fund management. In C. Perna & M. Sibillo (Eds.), Mathematical and Statistical Methods in Insurance and Finance (pp. 157–164). Milan: Springer.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.
Merton, R. (1980). On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics, 8, 323–361.
Nanda, S., Mahanty, B., & Tiwari, M. (2010). Clustering Indian stock market data for portfolio management. Expert Systems with Applications, 37(12), 8793–8798.
Scherer, B. (2011). A note on the returns from minimum variance investing. Journal of Empirical Finance, 18(4), 652–660.
Tan, P.-N., Steinbach, M., & Kumar, V. (2006). Introduction to data mining. London: Pearson.
Tobin, J. (1958). Liquidity preference as behavior towards risk. The Review of Economic Studies, 25(2), 65–82.
Tola, V., Lillo, F., Gallegati, M., & Mantegna, R. N. (2008). Cluster analysis for portfolio optimization. Journal of Economic Dynamics and Control, 32(1), 235–258.
Tu, J., & Zhou, G. (2011). Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies. Journal of Financial Economics, 99(1), 204–215.
Xu, R., & Wunsch, D. (2005). Survey of clustering algorithms. IEEE Transactions on Neural Networks, 16(3), 645–678.
Acknowledgments
We thank Michael Hanke, Kourosh Marjani Rasmussen, the Guest Editors Nalan Gulpinar, Xuan V. Doan and Arne K. Strauss, and two anonymous referees for helpful comments. Special thanks also to conference participants of the APMOD 2014 at the University of Warwick and seminar participants at the University of Oxford and the Technical University of Denmark.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bjerring, T.T., Ross, O. & Weissensteiner, A. Feature selection for portfolio optimization. Ann Oper Res 256, 21–40 (2017). https://doi.org/10.1007/s10479-016-2155-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-016-2155-y