Combined forecasts in portfolio optimization: A generalized approach

Abstract In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean–variance–skewness model with 11 objective functions. Returns and return errors for each asset obtained using different forecasting techniques, are combined in optimal proportions so as to minimize the mean absolute forecast error. These proportions are then used in constructing six criteria related to the mean, variance and skewness of return forecasts of assets in the future and forecasting errors of returns of assets in the past. The obtained multi-objective model is scalarized by using the conic scalarization method which guarantees to find all non-dominated solutions by considering investor preferences in non-convex multi-objective problems. The obtained scalar problem is solved by utilizing F-MSG algorithm. The performance of the proposed approach is tested on a real case problem generated on the data derived from Istanbul Stock Exchange. The comparison is conducted with respect to different levels of investor preferences over return, variance, and skewness and obtained results are summarized.

[1]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[2]  Desheng Dash Wu,et al.  Enterprise risk management: a DEA VaR approach in vendor selection , 2010 .

[3]  Tsong-Yue Lai.  Portfolio selection with skewness: A multiple-objective approach , 1991 .

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

[5]  Rafail N. Gasimov,et al.  A multiobjective faculty-course-time slot assignment problem with preferences , 2007, Math. Comput. Model..

[6]  P. Fishburn.  Mean-Risk Analysis with Risk Associated with Below-Target Returns , 1977 .

[7]  Desheng Dash Wu,et al.  A risk analysis model in concurrent engineering product development. , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[8]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[9]  J. M. Bates,et al.  The Combination of Forecasts , 1969 .

[10]  Kathrin Klamroth,et al.  Introducing oblique norms into multiple criteria programming , 2002, J. Glob. Optim..

[11]  Bruce E. Hansen,et al.  Least-squares forecast averaging , 2008 .

[12]  S. Shapiro,et al.  A Comparative Study of Various Tests for Normality , 1968 .

[13]  Rafail N. Gasimov,et al.  Stability and Duality of Nonconvex Problems via Augmented Lagrangian , 2002 .

[14]  Andrzej P. Wierzbicki,et al.  Reference Point Methods in Vector Optimization and Decision Support , 1998 .

[15]  Yusif Simaan.  Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model , 1997 .

[16]  Desheng Dash Wu,et al.  Introduction to the Special Section on “Optimizing Risk Management: Methods and Tools” , 2009 .

[17]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[18]  James C. T. Mao,et al.  Models of Capital Budgeting, E-V VS E-S , 1970, Journal of Financial and Quantitative Analysis.

[19]  Desheng Dash Wu,et al.  Enterprise risk management: coping with model risk in a large bank , 2010, J. Oper. Res. Soc..

[20]  P. Yu.  A Class of Solutions for Group Decision Problems , 1973 .

[21]  Refail Kasimbeyli,et al.  A Nonlinear Cone Separation Theorem and Scalarization in Nonconvex Vector Optimization , 2009, SIAM J. Optim..

[22]  Alexander M. Rubinov,et al.  On augmented Lagrangians for Optimization Problems with a Single Constraint , 2004, J. Glob. Optim..

[23]  Yazid M. Sharaiha,et al.  Heuristics for cardinality constrained portfolio optimisation , 2000, Comput. Oper. Res..

[24]  Stanley Zionts,et al.  Multiple Criteria Decision Making in the New Millennium , 2001 .

[25]  C. Granger,et al.  Experience with Forecasting Univariate Time Series and the Combination of Forecasts , 1974 .

[26]  Refail Kasimbeyli,et al.  The modified subgradient algorithm based on feasible values , 2009 .

[27]  R. Clemen.  Combining forecasts: A review and annotated bibliography , 1989 .

[28]  S. Liu,et al.  Mean-variance-skewness model for portfolio selection with transaction costs , 2003, Int. J. Syst. Sci..

[29]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[30]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[31]  Kathrin Klamroth,et al.  An MCDM approach to portfolio optimization , 2004, Eur. J. Oper. Res..

[32]  Rafail N. Gasimov,et al.  The analytic hierarchy process and multiobjective 0-1 faculty course assignment , 2004, Eur. J. Oper. Res..

[33]  An-Sing Chen,et al.  Using investment portfolio return to combine forecasts: A multiobjective approach , 2001, Eur. J. Oper. Res..

[34]  R. N. Gasimov.  Characterization of the Benson proper efficiency and scalarization in nonconvex vector optimization , 2001 .

[35]  Desheng Dash Wu,et al.  Enterprise risk management: small business scorecard analysis , 2009 .

[36]  Refail Kasimbeyli,et al.  Multiobjective Programming and Multiattribute Utility Functions in Portfolio Optimization , 2009, INFOR Inf. Syst. Oper. Res..

[37]  E. Adam,et al.  An empirical evaluation of alternative forecasting combinations , 1987 .

[38]  Tugba Saraç,et al.  A multi-objective programming approach to 1.5-dimensional assortment problem , 2007, Eur. J. Oper. Res..

[39]  R. L. Winkler,et al.  Averages of Forecasts: Some Empirical Results , 1983 .

[40]  Kaisa Miettinen,et al.  On scalarizing functions in multiobjective optimization , 2002, OR Spectr..

[41]  Kin Keung Lai,et al.  Neural network-based mean-variance-skewness model for portfolio selection , 2008, Comput. Oper. Res..

[42]  Ignacy Kaliszewski,et al.  A modified weighted tchebycheff metric for multiple objective programming , 1987, Comput. Oper. Res..

[43]  David L. Olson,et al.  Supply chain risk, simulation, and vendor selection , 2008 .

[44]  C. Yalçin Kaya,et al.  On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian* , 2006, J. Glob. Optim..

[45]  W. B. Gearhart.  Compromise solutions and estimation of the noninferior set , 1979 .

[46]  Rafail N. Gasimov,et al.  Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming , 2002, J. Glob. Optim..