A mean-CVaR-skewness portfolio optimization model based on asymmetric Laplace distribution

In the presence of uncertainty of asset returns, choosing an appropriate risk measure and determining the optimal weights of assets in a portfolio remain formidable and challenging problems. In this paper, we propose and study a mean-conditional value at risk-skewness portfolio optimization model based on the asymmetric Laplace distribution, which is suitable for describing the leptokurtosis, fat-tail, and skewness characteristics of financial assets. In addition, skewness is added into the portfolio optimization model to meet the diverse needs of investors. To solve this multi-objective problem, we suggest a simplified model with exactly the same solution. This modified model greatly reduces the complexity of the problem. Therefore, the mean-conditional value at risk-skewness model can be correspondingly solved. In order to illustrate the method, we provide an application concerning the portfolio allocation of 19 constituent stocks of S&P 500 index using our model. We show that this model could make important contributions to research on investment decision making.

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

[2]  S. Uryasev.  Probabilistic constrained optimization : methodology and applications , 2000 .

[3]  K. Podgórski,et al.  Asymmetric laplace laws and modeling financial data , 2001 .

[4]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[5]  Eric Jondeau,et al.  Entropy Densities: With an Application to Autoregressive Conditional Skewness and Kurtosis , 2001 .

[6]  Ramesh K. S. Rao,et al.  Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence , 1989, Journal of Financial and Quantitative Analysis.

[7]  Fred D. Arditti.  Another Look at Mutual Fund Performance , 1971, Journal of Financial and Quantitative Analysis.

[8]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

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

[10]  P. Samuelson.  The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments , 1970 .

[11]  Kristiaan Kerstens,et al.  Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach , 2007, Manag. Sci..

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

[13]  Fred D. Arditti.  RISK AND THE REQUIRED RETURN ON EQUITY , 1967 .

[14]  G. Pflug.  Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk , 2000 .

[15]  Hiroshi Konno,et al.  A mean-absolute deviation-skewness portfolio optimization model , 1993, Ann. Oper. Res..

[16]  Yasuhiro Yamai,et al.  Value-at-risk versus expected shortfall: A practical perspective , 2005 .

[17]  Samuel Kotz,et al.  The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance , 2001 .

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

[19]  D. Tasche,et al.  Expected Shortfall: a natural coherent alternative to Value at Risk , 2001, cond-mat/0105191.

[20]  Maria Grazia Speranza,et al.  Conditional value at risk and related linear programming models for portfolio optimization , 2007, Ann. Oper. Res..

[21]  Andreas Behr,et al.  Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models , 2009 .

[22]  William W. Hogan,et al.  Toward the Development of an Equilibrium Capital-Market Model Based on Semivariance , 1974, Journal of Financial and Quantitative Analysis.