Constrained Index Tracking under Loss Aversion Using Differential Evolution

Index tracking is concerned with forming a portfolio that mimics a benchmark index as closely as possible. Traditionally, this implies that the returns between the index and the portfolio should differ as little as possible. However, investors might happily accept positive deviations (ie, returns higher than the index’s) while being particularly concerned with negative deviations. In this chapter, we model these preferences by introducing loss aversion to the index tracking problem and analyze the financial implications based on a computational study for the US stock market. In order to cope with this demanding optimization problem, we use Differential Evolution and investigate some calibration issues.

[1]  M. C. Jensen.  The Performance of Mutual Funds in the Period 1945-1964 , 1967 .

[2]  P. Pope,et al.  Discovering Errors in Tracking Error , 1994 .

[3]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[4]  J. List.  Neoclassical Theory Versus Prospect Theory: Evidence from the Marketplace , 2003 .

[5]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[6]  Christopher R. Blake,et al.  The Persistence of Risk-Adjusted Mutual Fund Performance , 1995 .

[7]  R. Thaler.  Toward a positive theory of consumer choice , 1980 .

[8]  Dietmar Maringer,et al.  Portfolio management with heuristic optimization , 2005 .

[9]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[10]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[11]  Hiroshi Konno,et al.  Index-plus-alpha tracking under concave transaction cost , 2005 .

[12]  Dietmar Maringer,et al.  Index tracking with constrained portfolios , 2007, Intell. Syst. Account. Finance Manag..

[13]  H. Zimmermann,et al.  A linear model for tracking error minimization , 1999 .

[14]  Alex Frino,et al.  The Index Tracking Strategies of Passive and Enhanced Index Equity Funds , 2005 .

[15]  Moshe Levy,et al.  Prospect Theory: Much Ado About Nothing? , 2002, Manag. Sci..

[16]  R. Roll,et al.  A Mean/Variance Analysis of Tracking Error , 1992 .

[17]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

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

[19]  D. Maringer.  Risk Preferences and Loss Aversion in Portfolio Optimization , 2008 .