The Regularization Aspect of Optimal-Robust Conditional Value-at-Risk Portfolios

In portfolio management, Robust Conditional Value - at - Risk (Robust CVaR) has been proposed to deal with structured uncertainty in the estimation of the assets probability distribution. Meanwhile, regularization in portfolio optimization has been investigated as a way to construct portfolios that show satisfactory out-ofsample performance under estimation error. In this paper, we prove that optimal- Robust CVaR portfolios possess the regularization property. Based on expected utility theory concepts, we explicitly derive the regularization scheme that these portfolios follow and its connection with the scenario set properties.

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

[2]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

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

[4]  V. K. Chopra.  Improving Optimization , 1993 .

[5]  Martin Schweizer,et al.  Variance-Optimal Hedging in Discrete Time , 1995, Math. Oper. Res..

[6]  J. Mossin.  EQUILIBRIUM IN A CAPITAL ASSET MARKET , 1966 .

[7]  F. Delbaen.  Coherent risk measures , 2000 .

[8]  Peter A. Frost,et al.  An Empirical Bayes Approach to Efficient Portfolio Selection , 1986, Journal of Financial and Quantitative Analysis.

[9]  Alexander Shapiro,et al.  Lectures on Stochastic Programming: Modeling and Theory , 2009 .

[10]  M. Teboulle,et al.  AN OLD‐NEW CONCEPT OF CONVEX RISK MEASURES: THE OPTIMIZED CERTAINTY EQUIVALENT , 2007 .

[11]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[12]  Raman Uppal,et al.  A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms , 2009, Manag. Sci..

[13]  Hans-Jakob Lüthi,et al.  Robust risk management , 2012, Eur. J. Oper. Res..

[14]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

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

[16]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

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

[18]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

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

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

[21]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[22]  S. Ross.  The arbitrage theory of capital asset pricing , 1976 .

[23]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

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

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