Using medians in portfolio optimization

Some new portfolio optimization models are formulated by adopting the sample median instead of the sample mean as the investment efficiency measure. The median is a robust statistic, which is less affected by outliers than the mean, and in portfolio models this is particularly relevant as data are o...

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Bibliographic Details
Published inThe Journal of the Operational Research Society Vol. 66; no. 5; pp. 720 - 731
Main Author Benati, Stefano
Format Journal Article
LanguageEnglish
Published London Taylor & Francis 01.05.2015
Palgrave Macmillan
Palgrave Macmillan UK
Taylor & Francis Ltd
Subjects
Business and Management
Decision making
Diversification
finance
General Paper
General Papers
Linear programming
Management
mixed-integer linear programming
Normal distribution
Operations research
Operations Research/Decision Theory
Optimization
Portfolio management
portfolio models
Random variables
risk management
robust statistics
Studies
portfolio models
risk management
mixed-integer linear programming
finance
robust statistics
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Summary:Some new portfolio optimization models are formulated by adopting the sample median instead of the sample mean as the investment efficiency measure. The median is a robust statistic, which is less affected by outliers than the mean, and in portfolio models this is particularly relevant as data are often characterized by attributes such as skewness, fat tails and jumps, which may strongly bias the mean estimate. As in mean/variance optimization, the portfolio problems are formulated as finding the optimal weights, for example, wealth allocation, which maximize the portfolio median, with risk constrained by some risk measure, respectively, the Value-at-Risk, the Conditional Value-at-Risk, the Mean Absolute Deviation and the Maximum Loss, for a whole of four different models. All these models are formulated as mixed integer linear programming problems, which, at least for moderate sized problems, are efficiently solved by standard software. Models are tested on real financial data, compared to some benchmark portfolios, and found to give good results in terms of realized profits. An important feature is greater portfolio diversification than that obtained with other portfolio models.
ISSN:0160-5682
1476-9360
DOI:10.1057/jors.2014.57