Methods for solving problems in financial portfolio construction, index tracking and enhanced indexation

Abstract

The focus of this thesis is on index tracking that aims to replicate the movements of an index of a specific financial market. It is a form of passive portfolio (fund) management that attempts to mirror the performance of a specific index and generate returns that are equal to those of the index, but without purchasing all of the stocks that make up the index. Additionally, we consider the problem of out-performing the index - Enhanced Indexation. It attempts to generate modest excess returns compared to the index. Enhanced indexation is related to index tracking in that it is a relative return strategy. One seeks a portfolio that will achieve more than the return given by the index (excess return). In the first approach, we propose two models for the objective function associated with choice of a tracking portfolio, namely; minimise the maximum absolute difference between the tracking portfolio return and index return and minimise the average of the absolute differences between tracking portfolio return and index return. We illustrate and investigate the performance of our models from two perspectives; namely, under the exclusion and inclusion of fixed and variable costs associated with buying or selling each stock. The second approach studied is that of using Quantile regression for both index tracking and enhanced indexation. We present a mixed-integer linear programming of these problems based on quantile regression. The third approach considered is on quantifying the level of uncertainty associated with the portfolio selected. The quantification of uncertainty is of importance as this provides investors with an indication of the degree of risk that can be expected as a result of holding the selected portfolio over the holding period. Here a bootstrap approach is employed to quantify the uncertainty of the portfolio selected from our quantile regression model.