Statistical inference and efficient portfolio investment performance

Two main methods have been used in mutual funds evaluation. One is portfolio evaluation, and the other is data envelopment analysis (DEA). The history of portfolio evaluation dates from the 1960s with emphasis on both expected return and risk. However, there are many criticisms of traditional portfolio analysis which focus on their sensitivity to chosen benchmarks. Imperfections in portfolio analysis models have led to the exploration of other methodologies to evaluate fund performance, in particular data envelopment analysis (DEA). DEA is a non-parametric methodology for measuring relative performance based on mathematical programming. Based on the unique characteristics of investment trusts, Morey and Morey (1999) developed a mutual funds efficiency measure in a traditional mean-variance model. It was based on Markowitz portfolio theory and related the non-parametric methodologies to the foundations of traditional performance measurement in mean-variance space. The first application in this thesis is to apply the non-linear programming calculation of the efficient frontier in mean variance space outlined in Morey and Morey (1999) to a new modern data set comprising a multi-year sample of investment funds. One limitation of DEA is the absence of sampling error from the methodology. Therefore the second innovation in this thesis extends Morey and Morey (1999) model by the application of bootstrapped probability density functions in order to develop confidence intervals for the relative performance indicators. This has not previously been achieved for the DEA frontier in mean variance space so that the DEA efficiency scores obtained through Morey and Morey (1999) model have not hitherto been tested for statistical significance. The third application in this thesis is to examine the efficiency of investment trusts in order to analyze the factors contributing to investment trusts’ performance and detect the determinants of inefficiency. Robust-OLS regression, Tobit models and Papke-Wooldridge (PW) models are conducted and compared to evaluate contextual variables affecting the performance of investment funds. From the thesis, new and original Matlab codes designed for Morey and Morey (1999) models are presented. With the Matlab codes, not only the results are obtained, but also how this quadratic model is programming could be very clearly seen, with all the details revealed.