An exact algorithm for factor model in portfolio selection with roundlot constraints

We consider in this article a factor model in portfolio selection with roundlot constraints. Mathematically, this model leads to a quadratic integer programming problem. We exploit the separable structure of the model in order to derive Lagrangian bounds. A branch-and-bound algorithm based on Lagrangian relaxation and continuous relaxation is then developed for solving this model. Computational results are reported for test problems with up to 150 securities.

[1]  W. Ogryczak,et al.  LP solvable models for portfolio optimization: a classification and computational comparison , 2003 .

[2]  Barr Rosenberg,et al.  Extra-Market Components of Covariance in Security Returns , 1974, Journal of Financial and Quantitative Analysis.

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

[4]  Daniel Bienstock,et al.  Computational study of a family of mixed-integer quadratic programming problems , 1995, Math. Program..

[5]  André F. Perold,et al.  Large-Scale Portfolio Optimization , 1984 .

[6]  Hiroshi Konno.  PORTFOLIO OPTIMIZATION OF SMALL SCALE FUND USING MEAN-ABSOLUTE DEVIATION MODEL , 2003 .

[7]  W. Sharpe.  A Simplified Model for Portfolio Analysis , 1963 .

[8]  R. Mansini,et al.  An exact approach for portfolio selection with transaction costs and rounds , 2005 .

[9]  Andriy Demchuk,et al.  Portfolio Optimization with Concave Transaction Costs , 2002 .

[10]  X. Zhou,et al.  Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework , 2000 .

[11]  M. Thapa,et al.  Notes: A Reformulation of a Mean-Absolute Deviation Portfolio Optimization Model , 1993 .

[12]  W. Sharpe.  Portfolio Theory and Capital Markets , 1970 .

[13]  Hiroshi Konno,et al.  Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints , 2001, Math. Program..

[14]  W. Sharpe,et al.  Mean-Variance Analysis in Portfolio Choice and Capital Markets , 1987 .

[15]  Maria Grazia Speranza,et al.  Heuristic algorithms for the portfolio selection problem with minimum transaction lots , 1999, Eur. J. Oper. Res..

[16]  Wlodzimierz Ogryczak,et al.  Multiple criteria linear programming model for portfolio selection , 2000, Ann. Oper. Res..

[17]  Harry M. Markowitz,et al.  Portfolio Analysis with Factors and Scenarios , 1981 .

[18]  Hiroshi Konno,et al.  Integer programming approaches in mean-risk models , 2005, Comput. Manag. Sci..

[19]  W. Michalowski,et al.  Extending the MAD portfolio optimization model to incorporate downside risk aversion , 2001 .

[20]  Duan Li,et al.  Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation , 2000 .

[21]  D. Bunn.  Stochastic Dominance , 1979 .

[22]  Hiroshi Konno,et al.  MEAN-ABSOLUTE DEVIATION PORTFOLIO OPTIMIZATION MODEL UNDER TRANSACTION COSTS , 1999 .

[23]  Hiroshi Konno,et al.  Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints , 2002, J. Glob. Optim..

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

[25]  Daniel Bienstock,et al.  Computational Study of a Family of Mixed-Integer Quadratic Programming Problems , 1995, IPCO.

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

[27]  Siddhartha S. Syam.  A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals , 1998, Eur. J. Oper. Res..

[28]  S. Yitzhaki.  Stochastic Dominance, Mean Variance, and Gini's Mean Difference , 1982 .

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

[30]  Duan Li,et al.  OPTIMAL LOT SOLUTION TO CARDINALITY CONSTRAINED MEAN–VARIANCE FORMULATION FOR PORTFOLIO SELECTION , 2006 .

[31]  Raymond Hemmecke,et al.  Nonlinear Integer Programming , 2009, 50 Years of Integer Programming.

[32]  J. Mulvey.  Financial optimization: Incorporating transaction costs in models for asset allocation , 1993 .

[33]  H. Markowitz.  Mean—Variance Analysis , 1989 .

[34]  Harry M. Markowitz,et al.  Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions , 2005, Oper. Res..

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

[36]  Hans Kellerer,et al.  Selecting Portfolios with Fixed Costs and Minimum Transaction Lots , 2000, Ann. Oper. Res..

[37]  Yves Crama,et al.  Simulated annealing for complex portfolio selection problems , 2003, Eur. J. Oper. Res..

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