Modelling equity returns in South Africa: a data mining approach to the variable selection problem in asset pricing

Abstract

This study demonstrates the use of data mining techniques for variable selection in the construction of macroeconomic time-series models. The Arbitrage Pricing Theory (APT) provides a broad based framework for modelling equity returns, but a significant drawback is that the theory itself says nothing about the identity and the number of variables necessary to adequately price returns. Variable selection is a common modelling problem for which the APT represents an acute example. This study borrows two computationally efficient variable selection algorithms from the field of data science, Least-Angle Regression and Random Forests, and demonstrates their efficacy at the selection of relevant variables that lead to appropriate multifactor time-series models for the JSE All-Share index and the JSE Industry indices. The resultant time-series models for the JSE All-Share index show good in-sample fit and perform better than a naïve model in test periods. The resultant models for the JSE Industry indices show a large degree of variation in training period model fit, but overall they suggest that the variables selected for modelling by the feature selection techniques are appropriate. There is strong evidence that the variables selected by the feature selection techniques are both period and industry dependent. Period and industry dependence implies that the subset of variables that comprise the true return generating process for JSE equity indices is not constant, which is symptomatic of an adaptive framework for returns.