Robust portfolios: contributions from operations research and finance

• Ahn, D. H., Boudoukh, J., Richardson, M., & Whitelaw, R. F. (1999). Optimal risk management using options. Journal of Finance, 54, 359–375.

  Google Scholar 

• Aït-Sahalia, Y., & Brandt, M. W. (2001). Variable selection for portfolio choice. Journal of Finance, 56, 1297–1351.

  Google Scholar 

• Alexander, G. J., & Baptista, A. M. (2002). Economic implications of using a mean-VaR model for portfolio selection: a comparison with mean-variance analysis. Journal of Economic Dynamics and Control, 26, 1159–1193.

  Google Scholar 

• Alexander, G. J., & Baptista, A. M. (2004). A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model. Management Science, 50, 1261–1273.

  Google Scholar 

• Anderson, T. W. (1984). An introduction to multivariate statistical analysis (2nd ed.). New York: Wiley.

  Google Scholar 

• Ang, A., Bekaert, G., & Liu, J. (2005). Why stocks may disappoint. Journal of Financial Economics, 76, 471–508.

  Google Scholar 

• Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228.

  Google Scholar 

• Avramov, D. (2004). Stock predictability and asset pricing models. Review of Financial Studies, 17(3), 699–738.

  Google Scholar 

• Barberis, N. (2000). Investing for the long run when returns are predictable. Journal of Finance, 55, 225–264.

  Google Scholar 

• Basak, S., & Shapiro, A. (2001). Value-at-risk management: optimal policies and asset prices. Review of Financial Studies, 14, 371–405.

  Google Scholar 

• Bawa, V. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2, 95–121.

  Google Scholar 

• Bawa, V. S., Brown, S. J., & Klein, R. W. (1979). Estimation risk and optimal portfolio choice. Amsterdam: North-Holland.

  Google Scholar 

• Ben-Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of Operations Research, 23, 769–805.

  Google Scholar 

• Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations Research Letters, 25, 1–13.

  Google Scholar 

• Ben-Tal, A., Margalit, T., & Nemirovski, A. N. (2002). Robust modeling of multi-stage portfolio problems. In H. Frenk, K. Roos, T. Terlaky, & S. Zhang (Eds.), High performance optimization (pp. 303–328). Dordrecht: Kluwer.

  Google Scholar 

• Berger, J. O. (1985). Statistical decision theory and Bayesian analysis. New York: Springer.

  Google Scholar 

• 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.

  Google Scholar 

• Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48, 28–43.

  Google Scholar 

• Boyle, P. P., Siu, T. K., & Yang, H. (2002). Risk and probability measures. Risk, 15(7), 53–57.

  Google Scholar 

• Brandt, M. W. (2004, forthcoming). Portfolio choice problems. Handbook of financial econometrics, Ait-Sahalia, Y. & L. P. Hansen (Eds.).

• Broadie, M. (1993). Computing efficient frontiers using estimated parameters. Annals of Operations Research, 45, 21–58.

  Google Scholar 

• Brown, S. J. (1976). Optimal portfolio choice under uncertainty. Ph.D. dissertation, University of Chicago.

• Brown, S. J. (1978). The portfolio choice problem: comparison of certainty equivalence and optimal Bayes portfolios. Communications in Statistics—Simulation and Computation, 7, 321–334.

  Google Scholar 

• Brown, D. B., & Sim, M. (2008, forthcoming). Satisfying measures for analysis of risky positions. Management Science.

• Calafiore, G. C. (2007). Ambiguous risk measures and optimal robust portfolios. SIAM Journal on Optimization, 18(3), 853–877.

  Google Scholar 

• Ceria, S., & Stubbs, R. A. (2006). Incorporating estimation errors into portfolio selection: robust portfolio construction. Journal of Asset Management, 7(2), 109–127.

  Google Scholar 

• Chincarini, L. B., & Kim, D. (2006). Quantitative equity portfolio management. New York: McGraw-Hill.

  Google Scholar 

• Chopra, V. K., & Ziemba, W. T. (1993). The effects of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management, 19(2), 6–11.

  Google Scholar 

• Costa, O. L. V., & Paiva, A. C. (2002). Robust portfolio selection using linear-matrix inequalities. Journal of Economic Dynamics and Control, 26(6), 889–909.

  Google Scholar 

• Cremers, K. J. M. (2002). Stock return predictability: a Bayesian model selection perspective. Review of Financial Studies, 15(4), 1223–1249.

  Google Scholar 

• Delage, E., & Ye, Y. (2008, forthcoming). Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research.

• Dembo, R., & Rosen, D. (2000). The practice of portfolio replication. Algo Research Quarterly, 3(2), 11–22.

  Google Scholar 

• DeMiguel, V., & Nogales, F. J. (2008, forthcoming). Portfolio selection with robust estimation. Operations Research.

• DeMiguel, V., Garlappi, L., & Uppal, R. (2008, forthcoming). Optimal versus naive diversification: how inefficient is the 1/N portfolio strategy? Review of Financial Studies.

• Duchin, D., & Levy, H. (2009, forthcoming). Markowitz versus the Talmudic portfolio diversification strategies. Journal of Portfolio Management.

• El Ghaoui, L., & Lebret, H. (1997). Robust solutions to least-squares problems with uncertain data. SIAM Journal on Matrix Analysis and Applications, 18, 1035–1064.

  Google Scholar 

• El Ghaoui, L., Oks, M., & Oustry, F. (2003). Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Operations Research, 51, 543–556.

  Google Scholar 

• Elliott, R. J., & Siu, T. K. (2008, forthcoming). On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy. Annals of Operations Research.

• Embrechts, P., Klüppelberg, C., & Mikosch, T. (1997). Modelling extremal events for insurance and finance. Berlin: Springer.

  Google Scholar 

• Fabozzi, F. J., Gupta, F., & Markowitz, H. M. (2002). The legacy of modern portfolio theory. Journal of Investing, 11(3), 7–22.

  Google Scholar 

• Fabozzi, F., Focardi, S. M., & Kolm, P. N. (2006). Incorporating trading strategies in the Black-Litterman framework. Journal of Trading, Spring, 28–36.

  Google Scholar 

• Fabozzi, F. J., Kolm, P. N., Pachamanova, D., & Focardi, S. M. (2007). Robust portfolio optimization and management. Hoboken: Wiley.

  Google Scholar 

• Föllmer, H., & Schied, A. (2002). Convex measures of risk and trading constraints. Finance and Stochastics, 6(4), 429–447.

  Google Scholar 

• Föllmer, H., Schied, A., & Weber, S. (2008). A robust preference and robust portfolio choice, Preprint.

• Frittelli, M., & Rosazza Gianin, E. (2002). Putting order in risk measures. Journal of Banking and Finance, 26(7), 1473–1486.

  Google Scholar 

• Garlappi, L., Uppal, R., & Wang, T. (2007). Portfolio selection with parameter and model uncertainty: a multi-prior approach. Review of Financial Studies, 20(1), 41–81.

  Google Scholar 

• Goldfarb, D., & Iyengar, G. (2003a). Robust convex quadratically constrained programs. Mathematical Programming, 97, 495–515.

  Google Scholar 

• Goldfarb, D., & Iyengar, G. (2003b). Robust portfolio selection problems. Mathematics of Operations Research, 28, 1–38.

  Google Scholar 

• Grinold, R. C., & Kahn, R. N. (2000). Active portfolio management (2nd ed.). New York: McGraw-Hill.

  Google Scholar 

• Guidolin, M., & Timmermann, A. (2008). International asset allocation under regime switching, skew and kurtosis preferences. Review of Financial Studies, 21(2), 889–935.

  Google Scholar 

• Gul, F. (1991). A theory of disappointment aversion. Econometrica, 59(3), 667–686.

  Google Scholar 

• Hall, J. A., Brorsen, B. W., & Irwin, S. H. (1989). The distribution of futures prices: a test of the stable Paretian and mixture of normals hypothesis. Journal of Financial and Quantitative Analysis, 24, 105–116.

  Google Scholar 

• Hansen, L. P., & Sargent, T. J. (2008). Robustness. Princeton: Princeton University Press.

  Google Scholar 

• Harvey, C. R., Liechty, J., Liechty, M., & Müller, P. (2003). Portfolio selection with higher moments. Working Paper, Duke University.

• Holton, G. (1997). Subjective value-at-risk. Financial Engineering News, August.

• Hong, Y., Tu, J., & Zhou, G. (2007). Asymmetries in stock returns: statistical tests and economic evaluation. Review of Financial Studies, 20, 1547–1581.

  Google Scholar 

• Huang, D., Zhu, S. S., Fabozzi, F. J., & Fukushima, M. (2008). Portfolio selection with uncertain exit time: a robust CVaR approach. Journal of Economic Dynamics and Control, 32(2), 594–623.

  Google Scholar 

• Huber, R. J. (2003). Robust statistics. New York: Wiley.

  Google Scholar 

• Jobson, J. D., & Korkie, B. (1980). Estimation for Markowitz efficient portfolios. Journal of the American Statistical Association, 75, 544–554.

  Google Scholar 

• Jobson, J. D., Korkie, B., & Ratti, V. (1979). Improved estimation for Markowitz portfolios using James-Stein type estimators. Proceedings of the American Statistical Association, Business and Economics Statistics Section, 41, 279–284.

  Google Scholar 

• Jorion, P. (1986). Bayes-Stein estimation for portfolio analysis. Journal of Financial and Quantitative Analysis, 21, 279–292.

  Google Scholar 

• Jorion, P. (1991). Bayesian and CAPM estimators of the means: implications for portfolio selection. Journal of Banking and Finance, 15, 717–727.

  Google Scholar 

• Jorion, P. (2006). Value-at-risk: the new benchmark for managing financial risk (3rd ed.). New York: McGraw-Hill.

  Google Scholar 

• Kacperczyk, M. (2007). Asset allocation under distribution uncertainty. Working paper, University of British Columbia.

• Kan, R., & Zhou, G. (2007). Optimal portfolio choice with parameter uncertainty. Journal of Financial and Quantitative Analysis, 42, 621–656.

  Google Scholar 

• Kandel, S., & Stambaugh, R. F. (1996). On the predictability of stock returns: an asset-allocation perspective. Journal of Finance, 51, 385–424.

  Google Scholar 

• Klein, R. W., & Bawa, V. S. (1976). The effect of estimation risk on optimal portfolio choice. Journal of Financial Economics, 3, 215–231.

  Google Scholar 

• Kleshchelskiy, I., & Vincentz, N. (2007). Robust equilibrium yield curves. Working paper, Washington University.

• Knight, F. (1921). Risk, uncertainty and profit. Boston: Houghton Mifflin.

  Google Scholar 

• Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37, 519–531.

  Google Scholar 

• Konno, H., & Koshizuka, T. (2005). Mean-absolute deviation model. IIE Transactions, 37, 893–900.

  Google Scholar 

• 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, 603–621.

  Google Scholar 

• Litterman, B. (2003). Modern investment management: an equilibrium approach. New York: Wiley.

  Google Scholar 

• Lutgens, F. (2004). Robust portfolio optimization. Ph.D. dissertation, University of Maastricht.

• Lutgens, F., & Schotman, P. (2006). Robust portfolio optimization with multiple experts. Working paper, University of Maastricht.

• Maccheroni, F., Marinacci, M., & Rustichini, A. (2006). Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica, 74(6), 1447–1498.

  Google Scholar 

• MacKinlay, A. C., & Pástor, L̆. (2000). Asset pricing models: implications for expected returns and portfolio selection. Review of Financial Studies, 13, 883–916.

  Google Scholar 

• Maenhout, P. J. (2004). Robust portfolio rules and asset pricing. Review of Financial Studies, 17, 951–983.

  Google Scholar 

• Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7, 77–91.

  Google Scholar 

• Markowitz, H. M. (1959). Portfolio selection: efficient diversification of investments. New Jersey: Wiley.

  Google Scholar 

• Maronna, R. A., Martin, D. R., & Yohai, V. J. (2006). Robust statistics: theory and methods. New York: Wiley.

  Google Scholar 

• Merton, R. (2003). Thoughts on the future: theory and practice of investment management. Financial Analyst Journal, 59(1), 17–23.

  Google Scholar 

• Meucci, A. (2005). Risk and asset allocation. Berlin: Springer.

  Google Scholar 

• Mori, H. (2004). Finite sample properties of estimators for the optimal portfolio weight. Journal of Japan Statistical Society, 34, 27–46.

  Google Scholar 

• Natarajan, K., Pachamanova, D., & Sim, M. (2008a). Incorporating asymmetric distribution information in robust value-at-risk optimization. Management Science, 54(3), 573–585.

  Google Scholar 

• Natarajan, K., Sim, M., & Uichanco, J. (2008b). Tractable robust expected utility and risk models for portfolio optimization, Working paper, National University of Singapore.

• Natarajan, K., Pachamanova, D., & Sim, M. (2009, forthcoming). Constructing risk measures from uncertainty sets. Operations Research.

• Ortobelli, S., Rachev, S. T., Stoyanov, S., Fabozzi, F. J., & Biglova, A. (2005). The proper use of risk measures in portfolio theory. International Journal of Theoretical and Applied Finance, 8(8), 1107–1133.

  Google Scholar 

• Pástor, L̆. (2000). Portfolio selection and asset pricing models. Journal of Finance, 55, 179–223.

  Google Scholar 

• Pástor, L̆., & Stambaugh, R. F. (2000). Comparing asset pricing models: an investment perspective. Journal of Financial Economics, 56, 335–381.

  Google Scholar 

• Peel, D., & McLachlan, G. J. (2000). Robust mixture modeling using the t distribution. Statistics and Computing, 10, 339–348.

  Google Scholar 

• Pinar, M. C. (2007). Robust scenario optimization based on downside-risk measure for multi-period portfolio selection. OR Spectrum, 29(2), 295–309.

  Google Scholar 

• Pinar, M. C., & Tütüncü, R. (2005). Robust profit opportunities in risk financial portfolios. Operations Research Letters, 33(4), 331–340.

  Google Scholar 

• Popescu, I. (2007). Robust mean-covariance solutions for stochastic optimization. Operations Research, 55(1), 98–112.

  Google Scholar 

• Qian, E., Hua, R., & Sorensen, E. (2007). Quantitative equity portfolio management: modern techniques and applications. New York: Chapman & Hall.

  Google Scholar 

• Rachev, S. T., Ortobelli, S., Stoyanov, S., Fabozzi, F. J., & Biglova, A. (2008a). Desirable properties of an ideal risk measure in portfolio theory. International Journal of Theoretical and Applied Finance, 11(1), 19–54.

  Google Scholar 

• Rachev, S. T., Hsu, J. S. J., Bagasheva, B. S., & Fabozzi, F. J. (2008b). Bayesian methods in finance. New Jersey: Wiley.

  Google Scholar 

• Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21–41.

  Google Scholar 

• Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26(7), 1443–1471.

  Google Scholar 

• Rockafellar, R. T., Uryasev, S., & Zabarankin, M. (2006). Optimality conditions in portfolio analysis with generalized deviation measures. Mathematical Programming, 108, 515–540.

  Google Scholar 

• Roy, A. D. (1952). Safety first and the holding of assets. Econometrica, 20(3), 431–449.

  Google Scholar 

• Rustem, B., Becker, R. G., & Marty, W. (2000). Robust min-max portfolio strategies for rival forecast and risk scenarios. Journal of Economic Dynamics and Control, 24, 1591–1621.

  Google Scholar 

• Shen, R., & Zhang, S. (2008). Robust portfolio selection based on a multi-stage scenario tree. European Journal of Operational Research, 191(3), 864–887.

  Google Scholar 

• Siu, T. K., Tong, H., & Yang, H. (2001). Bayesian risk measures for derivatives via random Esscher transform. North American Actuarial Journal, 5(3), 78–91.

  Google Scholar 

• Stambaugh, R. F. (1997). Analyzing investments whose histories differ in length. Journal of Financial Economics, 45, 285–331.

  Google Scholar 

• Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proceedings of the third Berkeley symposium on mathematical statistics and probability (vol. 1, pp. 197–206). Berkeley: University of California Press.

  Google Scholar 

• Steinbach, M. C. (2001). Markowitz revisited: mean-variance models in financial portfolio analysis. SIAM Review, 43(1), 31–85.

  Google Scholar 

• Stoyanov, S. V., Rachev, S. T., & Fabozzi, F. J. (2007). Optimal financial portfolios. Applied Mathematical Finance, 14(5), 403–438.

  Google Scholar 

• Strzalecki, T. (2008). Axiomatic foundations of multiplier preferences. Working paper, Harvard University.

• Ter Horst, J., De Roon, F., & Werker, B. (2006), Incorporating estimation risk in portfolio choice. In P. Duffhues & L. Renneboog (Eds.), Advances in corporate finance and asset pricing, Emerald Group Publishing.

• Tu, J., & Zhou, G. (2004). Data-generating process uncertainty: what difference does it make in portfolio decisions? Journal of Financial Economics, 72, 385–421.

  Google Scholar 

• Tu, J., & Zhou, G. (2008). Being naive about naive diversification: can investment theory be consistently useful? Working paper, Washington University.

• Tu, J., & Zhou, G. (2009, forthcoming). Incorporating economic objectives into Bayesian priors: portfolio choice under parameter uncertainty. Journal of Financial and Quantitative Analysis.

• Tütüncü, R., & Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132, 157–187.

  Google Scholar 

• Uppal, R., & Wang, T. (2003). Model misspecification and underdiversification. Journal of Finance, 58(6), 2465–2486.

  Google Scholar 

• Wang, Z. (2004). A shrinkage approach to model uncertainty and asset allocation. Review of Financial Studies, 18(2), 673–705.

  Google Scholar 

• Whittle, P. (1990). Risk-sensitive optimal control. New York: Wiley.

  Google Scholar 

• Whittle, P. (1996). Optimal control: basics and beyond. New York: Wiley.

  Google Scholar 

• Xia, Y. (2001). Learning about predictability: the effect of parameter uncertainty on dynamic asset allocation. Journal of Finance, 56, 205–246.

  Google Scholar 

• Young, M. R. (1998). A minimax portfolio selection rule with linear programming solution. Management Science, 44, 673–683.

  Google Scholar 

• Zellner, A., & Chetty, V. K. (1965). Prediction and decision problems in regression models from the Bayesian point of view. Journal of the American Statistical Association, 60, 608–616.

  Google Scholar 

• Zhou, G. (2008). On the fundamental law of active portfolio management: what happens if our estimates are wrong? Journal of Portfolio Management, 34(3), 26–33.

  Google Scholar 

• Zhou, G. (2009, forthcoming) Beyond Black-Litterman: letting the data speak. Journal of Portfolio Management.

• Zhu, S. S., & Fukushima, M. (2008, forthcoming). Worst-case conditional value-at-risk with application to robust portfolio management. Operations Research.

Download references