Abstract
The earliest documented analytical approach to portfolio selection is Markowitz’s mean–variance analysis, which attempts to find the portfolio with optimal performance by considering the tradeoff between return and risk. The performance of mean–variance analysis has been the subject of many studies and compared to other portfolio construction approaches such as a naïve equally-weighted allocation scheme. In recent years, several approaches have been proposed to improve the mean–variance model by reducing the sensitivity of the portfolio selection process in order achieve robust performance. Although robust portfolio optimization has been one of the most researched methods for improving portfolio robustness, the performance of robust portfolios has not been the major focus of studies. In this paper, a comprehensive analysis on robust portfolio performance is presented for equity portfolios constructed in the U.S. market during the period 1980 and 2014, and results confirm the advantage of robust portfolio optimization for controlling uncertainty while efficiently allocating investments.
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Notes
The industry returns are available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
Portfolios with smaller annualized volatility are not considered since the GMV portfolio often shows annualized standard deviation above 10% for estimation periods of 1 year or longer.
The calculation involved in estimating the estimation error covariance matrix is derived in Stubbs and Vance (2005).
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.
Bloomfield, T., Leftwich, R., & Long, J. B. (1977). Portfolio strategies and performance. Journal of Financial Economics, 5(2), 201–218.
Broadie, M. (1993). Computing efficient frontiers using estimated parameters. Annals of Operations Research, 45(1), 21–58.
Ceria, S., & Stubbs, R. A. (2006). Incorporating estimation errors into portfolio selection: Robust portfolio construction. Journal of Asset Management, 7(2), 109–127.
Chopra, V. K., & Ziemba, W. T. (1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. 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. Journal of Portfolio Management, 33(1), 10–24.
Cohen, K. J., & Pogue, J. A. (1967). An empirical evaluation of alternative portfolio-selection models. Journal of Business, 40(2), 166–193.
DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/\(N\) portfolio strategy? Review of Financial Studies, 22(5), 1915–1953.
Fabozzi, F. J., Gupta, F., & Markowitz, H. M. (2002). The legacy of modern portfolio theory. Journal of Investing, 11(3), 7–22.
Fabozzi, F. J., Huang, D., & Zhou, G. (2010). Robust portfolios: Contributions from operations research and finance. Annals of Operations Research, 176, 191–220.
Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., & Focardi, S. M. (2007a). Robust portfolio optimization. Journal of Portfolio Management, 33, 40–48.
Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., & Focardi, S. M. (2007b). Robust portfolio optimization and management. Hoboken, New Jersey: Wiley.
Fan, J., Fan, Y., & Lv, J. (2008). High dimensional covariance matrix estimation using a factor model. Journal of Econometrics, 147(1), 186–197.
Frost, P. A., & Savarino, J. E. (1988). For better performance: Constrain portfolio weights. Journal of Portfolio Management, 15(1), 29–34.
Garcia, C. B., & Gould, F. J. (1987). A note on the measurement of risk in a portfolio. Financial Analysts Journal, 43(2), 61–69.
Goldfarb, D., & Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of Operations Research, 28(1), 1–38.
Grauer, R. R., & Shen, F. C. (2000). Do constraints improve portfolio performance? Journal of Banking and Finance, 24(8), 1253–1274.
Hansen, L. P., & Sargent, T. J. (2008). Robustness. Princeton: Princeton University Press.
Haugen, R. A., & Baker, N. L. (1991). The efficient market inefficiency of capitalization-weighted stock portfolios. Journal of Portfolio Management, 17(3), 35–40.
Jensen, M. C. (1968). The performance of mutual funds in the period 1945–1964. Journal of Finance, 23(2), 389–416.
Jorion, P. (1992). Portfolio optimization in practice. Financial Analysts Journal, 48(1), 68–74.
Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2013). Composition of robust equity portfolios. Finance Research Letters, 10(2), 72–81.
Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2014). Recent developments in robust portfolios with a worst-case approach. Journal of Optimization Theory and Applications, 161(1), 103–121.
Kim, W. C., Kim, J. H., & Fabozzi, F. J. (2016). Robust equity portfolio management + website: Formulations, implementations, and properties using MATLAB. Hoboken: Wiley.
Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2017). Robust factor-based investing. Journal of Portfolio Management, 43(5), 157–164.
Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356–371.
Linsmeier, T. J., & Pearson, N. D. (2000). Value at risk. Financial Analysts Journal, 56(2), 47–67.
Maginn, J. L., Tuttle, D. L., McLeavey, D. W., & Pinto, J. E. (2007). Managing investment portfolios: A dynamic process (3rd ed.). Hoboken: Wiley.
Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
Michaud, R. O. (1989). The Markowitz optimization enigma: Is “optimized” optimal? Financial Analysts Journal, 45, 31–42.
Qian, E. E., Hua, R. H., & Sorensen, E. H. (2007). Quantitative equity portfolio management: Modern techniques and applications. Boca Raton: CRC Press.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21–42.
Roll, R. (1992). A mean/variance analysis of tracking error. Journal of Portfolio Management, 18(4), 13–22.
Scherer, B. (2007). Can robust portfolio optimization help to build better portfolios? Journal of Asset Management, 7, 374–387.
Sargent, T. J. (2014). Rational expectations and ambiguity (corrected). Financial Analysts Journal, 70(2), 14–19.
Siegel, J. J. (1992). The equity premium: Stock and bond returns since 1802. Financial Analysts Journal, 48(1), 28–38.
Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119–138.
Sortino, F. A., & Price, L. N. (1994). Performance measurement in a downside risk framework. Journal of Investing, 3(3), 59–64.
Stubbs, R. A., & Vance, P. (2005). Computing return estimation error matrices for robust optimization. New York: Axioma Inc.
Tütüncü, R. H., & Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132(1–4), 157–187.
Acknowledgements
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2016R1C1B1014492).
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Kim, J.H., Kim, W.C., Kwon, DG. et al. Robust equity portfolio performance. Ann Oper Res 266, 293–312 (2018). https://doi.org/10.1007/s10479-017-2739-1
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DOI: https://doi.org/10.1007/s10479-017-2739-1