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Data Envelopment Analysis Models of Investment Funds

This paper develops theory missing in the sizeable literature that uses data envelopment analysis to construct return : risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification, coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference. | ISSN 0143-4543 14 9 5 University of Aberdeen Business Schoo Data Envelopment Analysis Models of Investment Funds By John D. Lamb and Kai-Hong Tee Discussion Paper 2010-01 August 2010 Editor Dr W David McCausland www.abdn.ac.uk business Data envelopment analysis models of investment funds John D. Lamb University of Aberdeen Business School Aberdeen AB24 3QY Kai-Hong Tee Loughborough University Business School Loughborough LE11 3TU This paper develops theory missing in the sizeable literature that uses data envelopment analysis to construct return risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period. It discusses possible shortcomings of the procedure and offers directions for future research. DATA ENVELOPMENT ANALYSIS INVESTMENT FUND DIVERSIFICATION COHERENT RISK MEASURE RETURNS TO SCALE STOCHASTIC DOMINANCE I Introduction Data envelopment analysis dea is a method for estimating the technical efficiency of several decision-making units DMUs given several inputs and several outputs. Typically the efficiency can be written in the form weighted sum of outputs weighted sum of inputs 1 In contrast to other methods of estimating technical efficiency DEA does not use fixed weights. Instead it chooses the best nonnegative weights for each DMU subject to the constraint that given those weights no DMU has efficiency greater than 100 . Thus DEA gives nonsubjective .