Portfolio Selection with Skewness: A Comparison and a Generalized Two Fund Separation Result

The main aim of this contribution is to compare existing and newly developed techniques for geometrically representing mean-variance-skewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based on the shortage function on the other hand. Moreover, we explain the working of these different methodologies in detail and provide graphical illustrations. Inspired by these illustrations, we prove a generalization of the well-known two fund separation theorem from traditional mean-variance portfolio theory.

[1]  G. Mitra,et al.  Mean-risk models using two risk measures: a multi-objective approach , 2007 .

[2]  Kristiaan Kerstens,et al.  Geometric representation of the mean-variance-skewness portfolio frontier based upon the shortage function , 2011, Eur. J. Oper. Res..

[3]  Arun J. Prakash,et al.  Portfolio selection and skewness: Evidence from international stock markets , 1997 .

[4]  Chorng-Shyong Ong,et al.  Enhanced Index Investing Based on Goal Programming , 2007 .

[5]  H. M. Kat,et al.  Fund of hedge funds portfolio selection: A multiple-objective approach , 2005 .

[6]  Konstantinos P. Anagnostopoulos,et al.  A portfolio optimization model with three objectives and discrete variables , 2010, Comput. Oper. Res..

[7]  Jaap Spronk,et al.  Multicriteria Decision Aid/Analysis in Finance , 2005 .

[8]  I. Daubechies,et al.  Sparse and stable Markowitz portfolios , 2007, Proceedings of the National Academy of Sciences.

[9]  Ben-Chang Shia,et al.  Multinational Portfolio Construction Using Polynomial Goal Programming and Lower Partial Moments , 2007 .

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

[11]  Xiang Li,et al.  Mean-variance-skewness model for portfolio selection with fuzzy returns , 2010, Eur. J. Oper. Res..

[12]  Sigrid Müller,et al.  Moment preferences and polynomial utility , 1987 .

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

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

[15]  Laurent Cantaluppi,et al.  Efficiency Ratio , 2000 .

[16]  Horace Ho,et al.  Building a Hedge Fund Portfolio with Kurtosis and Skewness , 2007 .

[17]  R. Hafner,et al.  Optimal investments in volatility , 2008 .

[18]  John Liechty,et al.  Portfolio selection with higher moments , 2004 .

[19]  Georges Dionne,et al.  Performance analysis of a collateralized fund obligation (CFO) equity tranche , 2009, New Facets of Economic Complexity in Modern Financial Markets.

[20]  Victor DeMiguel,et al.  Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? , 2009 .

[21]  Yue Qi,et al.  Portfolio Selection in the Presence of Multiple Criteria , 2008 .

[22]  W. Briec,et al.  Single-Period Markowitz Portfolio Selection, Performance Gauging, and Duality: A Variation on the Luenberger Shortage Function , 2002 .

[23]  Charles Audet,et al.  A New Multi-objective Approach for the Portfolio Selection Problem with Skewness , 2007 .

[24]  Brice V. Dupoyet,et al.  Effect of intervalling and skewness on portfolio selection in developed and developing markets , 2008 .

[25]  Kristiaan Kerstens,et al.  Portfolio selection in multidimensional general and partial moment space , 2010 .

[26]  Constantin Zopounidis,et al.  Bank asset liability management programming techniques: an overview , 2004 .

[27]  Shouyang Wang,et al.  Portfolio Selection and Asset Pricing , 2002 .

[28]  Miguel Ángel Canela,et al.  Portfolio selection with skewness in emerging market industries , 2007 .

[29]  Sebastián Lozano,et al.  TSD-consistent performance assessment of mutual funds , 2008, J. Oper. Res. Soc..

[30]  Bertrand B. Maillet,et al.  Hedge Funds Portfolio Selection with Higher-order Moments: A Non-parametric Mean-Variance-Skewness-Kurtosis Efficient Frontier , 2006 .

[31]  P. Boyle,et al.  Portfolio Selection with Skewness , 2005 .

[32]  R. Flôres,et al.  Finding a maximum skewness portfolio--a general solution to three-moments portfolio choice , 2004 .

[33]  Nicolas Papageorgiou,et al.  Optimal fund of funds asset allocation: Hedge funds, CTAs, and REITs , 2006 .

[34]  Ryan J. Davies.  Funds of Hedge Funds Portfolio Selection , 2008 .

[35]  M. Rockinger,et al.  Optimal Portfolio Allocation Under Higher Moments , 2004 .

[36]  Chenchuramaiah T. Bathala.  Skewness Persistence with Optimal Portfolio Selection , 2003 .

[37]  M. Anson.  Handbook of Alternative Assets , 2002 .

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

[39]  Hsin-Hung Chen,et al.  Value-at-Risk Efficient Portfolio Selection Using Goal Programming , 2008 .