Robust portfolios: contributions from operations research and finance

In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard mean-variance objective, but also in terms of two of the most popular risk measures, mean-VaR and mean-CVaR developed recently. In addition, we review optimal estimation methods and Bayesian robust approaches.

[1]  Andrew Alford Managing,et al.  Quantitative Equity Portfolio Management , 2008 .

[2]  Geoffrey J. McLachlan,et al.  Robust mixture modelling using the t distribution , 2000, Stat. Comput..

[3]  Alexander Schied,et al.  Convex measures of risk and trading constraints , 2002, Finance Stochastics.

[4]  Lorenzo Garlappi,et al.  Portfolio Selection with Parameter and Model Uncertainty ∗ , 2003 .

[5]  Robert A. Stubbs,et al.  Incorporating estimation errors into portfolio selection: Robust portfolio construction , 2006 .

[6]  Melvyn Sim,et al.  Satisficing Measures for Analysis of Risky Positions , 2009, Manag. Sci..

[7]  Alexandre M. Baptista,et al.  Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis , 2002 .

[8]  N. Barberis.  Investing for the Long Run When Returns are Predictable , 2000 .

[9]  H. Konno,et al.  Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market , 1991 .

[10]  Ioana Popescu,et al.  Robust Mean-Covariance Solutions for Stochastic Optimization , 2007, Oper. Res..

[11]  B. Rustem,et al.  Robust min}max portfolio strategies for rival forecast and risk scenarios , 2000 .

[12]  Lorenzo Garlappi,et al.  Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach , 2004 .

[13]  Laurent El Ghaoui,et al.  Robust Solutions to Least-Squares Problems with Uncertain Data , 1997, SIAM J. Matrix Anal. Appl..

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

[15]  Shuzhong Zhang,et al.  Robust portfolio selection based on a multi-stage scenario tree , 2008, Eur. J. Oper. Res..

[16]  Mustafa Ç. Pinar,et al.  Robust profit opportunities in risky financial portfolios , 2005, Oper. Res. Lett..

[17]  Frank Lutgens,et al.  Robust Portfolio Optimization with Multiple Experts , 2007 .

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

[19]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[20]  A. Roy.  SAFETY-FIRST AND HOLDING OF ASSETS , 1952 .

[21]  Robert C. Merton,et al.  Thoughts on the Future: Theory and Practice in Investment Management , 2003 .

[22]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[23]  Michael W. Brandt.  Portfolio Choice Problems , 2010 .

[24]  Stoyan V. Stoyanov,et al.  Optimal Financial Portfolios , 2005 .

[25]  R. Stambaugh,et al.  Analyzing Investments Whose Histories Differ in Length , 1997 .

[26]  Raman Uppal,et al.  Model Misspecification and Under-Diversification , 2002 .

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

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

[29]  Tak Kuen Siu,et al.  Bayesian Risk Measures for Derivatives via Random Esscher Transform , 2001 .

[30]  C. Patel.  Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy? , 2009 .

[31]  Eric H. Sorensen,et al.  Quantitative Equity Portfolio Management: Modern Techniques and Applications , 2007 .

[32]  H. Föllmer,et al.  Robust Preferences and Robust Portfolio Choice , 2009 .

[33]  William H. Sackley.  Incorporating Trading Strategies in the Black-Litterman Framework , 2006 .

[34]  Frank Lutgens,et al.  Robust Portfolio Optimization with Multiple Experts , 2004 .

[35]  Guofu Zhou,et al.  Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty , 2008, Journal of Financial and Quantitative Analysis.

[36]  Donald Goldfarb,et al.  Robust convex quadratically constrained programs , 2003, Math. Program..

[37]  Svetlozar T. Rachev,et al.  Bayesian methods in finance , 2008 .

[38]  Reha H. Tütüncü,et al.  Robust Asset Allocation , 2004, Ann. Oper. Res..

[39]  Robert J. Elliott,et al.  On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy , 2010, Ann. Oper. Res..

[40]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[41]  Pascal J. Maenhout.  Robust Portfolio Rules and Asset Pricing , 2004 .

[42]  K. J. Martijn Cremers,et al.  Stock Return Predictability: A Bayesian Model Selection Perspective , 2000 .

[43]  Guofu Zhou,et al.  Data-generating process uncertainty: What difference does it make in portfolio decisions? , 2004 .

[44]  A. Meucci.  Risk and asset allocation , 2005 .

[45]  Tak Kuen Siu,et al.  Risk and probability measures , 2002 .

[46]  Zhenyu Wang,et al.  A Shrinkage Approach to Model Uncertainty and Asset Allocation , 2005 .

[47]  Tomasz Strzalecki,et al.  Axiomatic Foundations of Multiplier Preferences , 2009 .

[48]  Francisco J. Nogales,et al.  Portfolio Selection With Robust Estimation , 2007, Oper. Res..

[49]  William N. Goetzmann,et al.  Active Portfolio Management , 1999 .

[50]  A. Roy.  Safety first and the holding of assetts , 1952 .

[51]  Dessislava A. Pachamanova,et al.  Robust Portfolio Optimization , 2007 .

[52]  Melvyn Sim,et al.  Constructing Risk Measures from Uncertainty Sets , 2009, Oper. Res..

[53]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[54]  S. Irwin,et al.  The Distribution of Futures Prices: A Test of the Stable Paretian and Mixture of Normals Hypotheses , 1989, Journal of Financial and Quantitative Analysis.

[55]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[56]  Yihong Xia.  Learning About Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation , 2000 .

[57]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[58]  Robert B. Litterman,et al.  Global Portfolio Optimization , 1992 .

[59]  Stephen J. Brown.  The portfolio choice problem: Comparison of certainty equivalence and optimal bayes portfolios , 1978 .

[60]  M. Fukushima,et al.  Portfolio selection with uncertain exit time: A robust CVaR approach , 2008 .

[61]  Guofu Zhou,et al.  On the Fundamental Law of Active Portfolio Management , 2008 .

[62]  Stan Uryasev,et al.  Optimality conditions in portfolio analysis with general deviation measures , 2005, Math. Program..

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

[64]  Michael W. Brandt,et al.  Variable Selection for Portfolio Choice , 2001 .

[65]  Mustafa Ç. Pinar,et al.  Robust scenario optimization based on downside-risk measure for multi-period portfolio selection , 2007, OR Spectr..

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

[67]  Alexandre M. Baptista,et al.  A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model , 2004, Manag. Sci..

[68]  Philippe Jorion.  Bayesian and CAPM estimators of the means: Implications for portfolio selection , 1991 .

[69]  Marc C. Steinbach,et al.  Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis , 2001, SIAM Rev..

[70]  Melvyn Sim,et al.  TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION , 2009 .

[71]  Hiroshi Konno.  Mean-absolute deviation model , 2005 .

[72]  Stephen J. Brown,et al.  Estimation risk and optimal portfolio choice , 1980 .

[73]  Masao Fukushima,et al.  Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management , 2009, Oper. Res..

[74]  Arkadi Nemirovski,et al.  Robust Modeling of Multi-Stage Portfolio Problems , 2000 .

[75]  Andrew W. Alford,et al.  Quantitative Equity Portfolio Management , 2008 .

[76]  B. Werker,et al.  Incorporating Estimation Risk in Portfolio Choice , 2002 .

[77]  H. Markowitz,et al.  The Legacy of Modern Portfolio Theory , 2002 .

[78]  D. Rosen,et al.  The Practice of Portfolio Replication 1 , 2000 .

[79]  Massimo Marinacci,et al.  AMBIGUITY AVERSION, ROBUSTNESS, AND THE VARIATIONAL , 2006 .

[80]  Byung Ha Lim,et al.  A Minimax Portfolio Selection Rule with Linear Programming Solution , 1998 .

[81]  Nicolas Vincent,et al.  Robust Equilibrium Yield Curves , 2007 .

[82]  Jerzy Neyman,et al.  Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability : held at the Statistical Laboratory, University of California, December, 1954, July and August, 1955 , 1958 .

[83]  Massimo Guidolin,et al.  International Asset Allocation Under Regime Switching, Skew and Kurtosis Preferences , 2007 .

[84]  John Liechty,et al.  Portfolio selection with higher moments , 2004 .

[85]  Arkadi Nemirovski,et al.  Robust Convex Optimization , 1998, Math. Oper. Res..

[86]  Melvyn Sim,et al.  Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization , 2008, Manag. Sci..

[87]  Yinyu Ye,et al.  Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems , 2010, Oper. Res..

[88]  O. Costa,et al.  Robust portfolio selection using linear-matrix inequalities , 2002 .

[89]  Harunori Mori,et al.  FINITE SAMPLE PROPERTIES OF ESTIMATORS FOR THE OPTIMAL PORTFOLIO WEIGHT , 2004 .

[90]  Hans Frenk,et al.  High performance optimization , 2000 .

[91]  Stoyan V. Stoyanov,et al.  THE PROPER USE OF RISK MEASURES IN PORTFOLIO THEORY , 2005 .

[92]  Faruk Gul.  A Theory of Disappointment Aversion , 1991 .

[93]  P. Whittle.  Risk-Sensitive Optimal Control , 1990 .

[94]  Arnold Zellner,et al.  Prediction and Decision Problems in Regression Models from the Bayesian Point of View , 1965 .

[95]  M. Best,et al.  On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results , 1991 .

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

[97]  Arkadi Nemirovski,et al.  Robust solutions of uncertain linear programs , 1999, Oper. Res. Lett..

[98]  Laurent El Ghaoui,et al.  Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach , 2003, Oper. Res..

[99]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[100]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[101]  H. L. Le Roy,et al.  Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV , 1969 .

[102]  Guofu Zhou.  Beyond Black–Litterman: Letting the Data Speak , 2009, The Journal of Portfolio Management.

[103]  M. Frittelli,et al.  Putting order in risk measures , 2002 .

[104]  Guofu Zhou,et al.  Asymmetries in Stock Returns: Statistical Tests and Economic Evaluation , 2003 .

[105]  Guofu Zhou,et al.  Being Naive about Naive Diversification: Can Investment Theory be Consistently Useful , 2008 .

[106]  F. Fabozzi.  Robust Portfolio Optimization and Management , 2007 .

[107]  Paul Damien,et al.  Asset Allocation Under Distribution Uncertainty , 2011 .

[108]  Peter Whittle,et al.  Optimal Control: Basics and Beyond , 1996 .

[109]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .

[110]  Donald Goldfarb,et al.  Robust Portfolio Selection Problems , 2003, Math. Oper. Res..

[111]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[112]  F. Knight.  The economic nature of the firm: From Risk, Uncertainty, and Profit , 2009 .

[113]  Doron Avramov,et al.  Stock Return Predictability and Asset Pricing Models , 2003 .

[114]  J. Jobson,et al.  Estimation for Markowitz Efficient Portfolios , 1980 .

[115]  Mark Broadie,et al.  Computing efficient frontiers using estimated parameters , 1993, Ann. Oper. Res..

[116]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[117]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[118]  Suleyman Basak,et al.  Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices , 1999 .

[119]  C. O'Connor.  An introduction to multivariate statistical analysis: 2nd edn. by T. W. Anderson. 675 pp. Wiley, New York (1984) , 1987 .

[120]  R. Stambaugh,et al.  On the Predictability of Stock Returns: An Asset-Allocation Perspective , 1995 .

[121]  H. Levy,et al.  Markowitz Versus the Talmudic Portfolio Diversification Strategies , 2009, The Journal of Portfolio Management.

[122]  Bob Litterman,et al.  Modern Investment Management: An Equilibrium Approach , 2003 .

[123]  Dong-Hyun Ahn,et al.  Optimal Risk Management Using Options , 1997 .

[124]  John Matatko,et al.  Estimation risk and optimal portfolio choice , 1980 .

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

[126]  Stoyan V. Stoyanov,et al.  DESIRABLE PROPERTIES OF AN IDEAL RISK MEASURE IN PORTFOLIO THEORY , 2008 .

[127]  Giuseppe Carlo Calafiore,et al.  Ambiguous Risk Measures and Optimal Robust Portfolios , 2007, SIAM J. Optim..

[128]  V. Bawa.  OPTIMAL, RULES FOR ORDERING UNCERTAIN PROSPECTS+ , 1975 .