Incorporating multiple risk and return measures in portfolio analysis: A DEA approach

Abstract

Classical portfolio analysis typically considers standard deviation of returns as the risk measure and the average return as the return measure. This is probably the right approach to portfolio analysis when the returns are normal or when the utility function of the investor is quadratic. However, in case neither of these assumptions hold, one needs to explicitly incorporate, one needs to explicitly incorporate multiple risk and return measures in the portfolio analysis. Our study proposes the use of DEA (Data Envelopment Analysis) to incorporate multiple risk returns in portfolio analysis. To verify our approach, we do a detailed construction of efficient frontier for various input and output preferences of the user and find that efficient frontier almost always consists of the securities found by the DEA analysis. We also explore why this is not always the case. Further, we find the correlation between the rankings as given by DEA and various other prominen ratios, such as Sharpe and Sortino ratios. We find that the various rankings are quite similar to each other. We explore the reason where and why the DEA ranking is different from the rankings given by other ratios.