Abstract
Institutional and individual investors have always been interested in identifying those mutual funds that appear to outperform the market more often than not. Identification of such funds is not difficult as a simple comparison against the market index allows individual fund performance to be evaluated on an absolute basis. However, this approach is insufficient for investors to make a comparison between funds with different return and risk levels.
Entrenched in finance literature is the Sharpe measure and coefficient of variation, techniques that utilize both the standard deviation (a measure of risk) and expected return (a measure of return). This thesis proposes using a new methodology, Data Envelopment Analysis, to evaluate mutual funds on a relative basis.
Data Envelopment Analysis (DEA) is widely used to analyse the relative efficiencies of decision-making units (DMUs) that are similar in nature. There are two important versions of DEA, namely, Deterministic Data Envelopment Analysis (DDEA) developed to consider deterministic input and output variables, and Stochastic Data Envelopment Analysis (SDEA) used extensively when input or output variables are random in nature.
This thesis applies a simulation approach to SDEA based on EXCEL/@RISK, which provides a variety of informative statistical measures about the stochastic properties of the efficiency figure. The approach is illustrated by analyzing the relative performance of the largest United States equity mutual funds towards the end of the 20th century using historical data to identify significantly efficient and inefficient funds. The model is validated using an extensive window analysis where the results obtained by the SDEA model are compared with the traditional mean-variance approaches preferred in the past. This introduces to the portfolio performance evaluation literature a new tool for evaluating relative (as opposed to absolute) fund performance.