Return predictability and its implications for portfolio selection

Abstract

This thesis inquires into a range of issues in return predictability and its implications. First, the thesis investigates estimation bias in predictive regressions. This research stresses the importance of accounting for the bias when studying predictability. To tackle the problem of biased estimation, a general and convenient method based on the jackknife technique is proposed. The proposed method reduces the bias for both single- and multiple-regressor models and for both short- and long-horizon regressions. Compared with the existing bias-reduction methods in the literature, the proposed method is more stable, robust and flexible. More importantly, it can successfully reduce the estimation bias in long-horizon regressions, whereas the existing bias-reduction methods in the literature cease to work. The effectiveness of the proposed method is demonstrated by simulations and empirical estimates of common predictive models in finance. Empirical results show that the significant predictive variables under ordinary least squares become insignificant after adjusting for the finite-sample bias. These results cast doubt on conclusions drawn in earlier studies on the return predictability by these variables. Next, this thesis examines the predictability of return distributions. It provides detailed insights into predictability of the entire stock and bond return distributions in a quantile regression framework. The difficulty experienced in establishing predictability of the conditional mean through lagged predictor variables does not imply that other parts of the return distribution cannot be predicted. Indeed, many variables are found to have significant but heterogenous effects on the return distributions of stocks and bonds. The thesis establishes a quantile-copula framework for modelling conditional joint return distributions. This framework hinges on quantile regression for marginal return distributions and a copula for the return dependence structure. The framework is shown to be flexible and general enough to model a joint distribution while, at the same time, capturing any non-Gaussian characteristics in both marginal and joint returns. The thesis then explores the implications of return distribution predictability for portfolio selection. A distribution-based framework for portfolio selection is developed which consists of the joint return distribution modelled by the quantile-copula approach and an objective function accommodating higher-order moments. Threshold-accepting optimisation technique is used for obtaining optimal allocation weights. This proposed framework extends traditional moment-based portfolio selection in order to utilise the whole predicted return distribution. The last part of the thesis studies nonlinear dynamics of cross-sectional stock returns using classification and regression trees (CART). The CART models are demonstrated to be a valuable alternative to linear regression analysis in identifying primary drivers of the stock returns. Moreover, a novel hybrid approach combining CART and logistic regression is proposed. This hybrid approach takes advantage of the strengths in both CART and linear parametric models. An empirical application to cross-sectional stock return prediction shows that the hybrid approach captures return dynamics better than either a standalone CART or a logistic model.