Multiperiod portfolio investment using stochastic programming with conditional value at risk

Stagewise stochastic (integer) programming with CVaR for multiperiod portfolio investment are proposed.Heuristic moment matching method is utilized to generate scenarios for our models.The targets are the 50 listed companies with the greatest market capitalization in Taiwan.The SPSP model earn significantly positive return with the superior predictive ability test.The compact and general settings of the SPSP model achieved the annualized returns of 13.09% and 12.06%, respectively, which are higher than that of the buy-and-hold rule (9.95%). Display Omitted This paper proposes the portfolio stochastic programming (PSP) model and the stagewise portfolio stochastic programming (SPSP) model for investing in stocks in the Taiwan stock market. The SPSP model effectively reduces the computational resources needed to solve the PSP model. Additionally, the conditional value at risk (CVaR) is used as a risk measure in the models. In each period of investment, 200 scenarios are generated to solve the SPSP model. The experimental data set consists of the 50 listed companies with the greatest market capitalization in the Taiwan stock exchange, and the experimental interval began on January 3, 2005 and ended on December 31, 2014, consisting of 2484 trading periods (days) in total. The experimental results show that the SPSP model is insensitive to small variation of the portfolio size and the historical period for estimating statistics. The portfolio size of the SPSP model can be set with two cases: M = M c and M ź Mc. When M = M c , the M invested target stocks have been predetermined. When M ź Mc, a set of Mc candidate stocks are given, but the M real target stocks have not been decided. The average annualized returns are 13.09% and 12.06% for the two portfolio settings, respectively, which are higher than that of the buy-and-hold (BAH) rule (9.95%). In addition, because the CVaR is considered, both portfolio settings of the SPSP model exhibit higher Sharpe and Sortino ratios than the BAH rule, indicating that the SPSP model provides a higher probability to earn a positive return. The superior predictive ability test is performed to illustrate that the SPSP model can avoid the data-snooping problem.

[1]  Ashraf Chaudhry,et al.  The Efficacy of the Sortino Ratio and Other Benchmarked Performance Measures Under Skewed Return Distributions , 2008 .

[2]  Jack L. Treynor,et al.  MUTUAL FUND PERFORMANCE* , 2007 .

[3]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[4]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[5]  B. WETSt,et al.  STOCHASTIC PROGRAMS WITH FIXED RECOURSE : THE EQUIVALENT DETERMINISTIC PROGRAM , 2022 .

[6]  Hercules Vladimirou,et al.  A dynamic stochastic programming model for international portfolio management , 2008, Eur. J. Oper. Res..

[7]  S. Zenios,et al.  CVaR models with selective hedging for international asset allocation , 2002 .

[8]  Werner Römisch,et al.  Scenario tree modeling for multistage stochastic programs , 2009, Math. Program..

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

[10]  Michal Kaut,et al.  A Heuristic for Moment-Matching Scenario Generation , 2003, Comput. Optim. Appl..

[11]  John R. Birge,et al.  Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs , 1985, Oper. Res..

[12]  Chang-Biau Yang,et al.  Stock Investment with Stochastic Programming , 2014 .

[13]  Michal Kaut,et al.  A copula-based heuristic for scenario generation , 2014, Comput. Manag. Sci..

[14]  F. Sortino,et al.  Performance Measurement in a Downside Risk Framework , 1994 .

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

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

[17]  Pieter Klaassen,et al.  Comment on "Generating Scenario Trees for Multistage Decision Problems" , 2002, Manag. Sci..

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

[19]  R. Wets.  Stochastic Programs with Fixed Recourse: The Equivalent Deterministic Program , 1974 .

[20]  Dimitris Bertsimas,et al.  Robust multiperiod portfolio management in the presence of transaction costs , 2008, Comput. Oper. Res..

[21]  P. J. Green,et al.  Probability and Statistical Inference , 1978 .

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

[23]  Michal Kaut,et al.  Shape-based scenario generation using copulas , 2011, Comput. Manag. Sci..

[24]  Patrizia Beraldi,et al.  Generating scenario trees: A parallel integrated simulation-optimization approach , 2010, J. Comput. Appl. Math..

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

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

[27]  David S. Watkins,et al.  Fundamentals of matrix computations , 1991 .

[28]  David L. Woodruff,et al.  Pyomo: modeling and solving mathematical programs in Python , 2011, Math. Program. Comput..

[29]  Alexander Shapiro,et al.  Lectures on Stochastic Programming - Modeling and Theory, Second Edition , 2014, MOS-SIAM Series on Optimization.

[30]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals , 1980 .

[31]  Kjetil H yland.  Generating Scenario Trees for Multistage Decision Problems , 2016 .

[32]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[33]  A. Madansky.  Inequalities for Stochastic Linear Programming Problems , 1960 .

[34]  D. Dickey,et al.  Testing for unit roots in autoregressive-moving average models of unknown order , 1984 .

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

[36]  H. White,et al.  A Reality Check for Data Snooping , 2000 .

[37]  Georg Ch. Pflug,et al.  Scenario tree generation for multiperiod financial optimization by optimal discretization , 2001, Math. Program..

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

[39]  John R. Birge,et al.  Introduction to Stochastic programming (2nd edition), Springer verlag, New York , 2011 .

[40]  David S. Watkins,et al.  Fundamentals of Matrix Computations: Watkins/Fundamentals of Matrix Computations , 2005 .

[41]  Laureano F. Escudero,et al.  An effective heuristic for multistage linear programming with a stochastic right-hand side , 2014, Comput. Oper. Res..

[42]  P. Hansen.  A Test for Superior Predictive Ability , 2005 .