Predicting stock returns and assessing prediction performance

We use regression methods to predict the expected monthly return on stocks and the covariance matrix of returns, the predictor variables being a company's ‘fundamentals’, such as dividend yield and the history of previous returns. Predictions are evaluated out of sample for shares traded on the London Stock Exchange from 1976 to 2005. We explore and evaluate many modelling and inferential approaches, including the use of weighted regression, discounted regression, shrinkage of regression coefficients and the transformation to normality of predictor variables. We also investigate alternative covariance matrix models, such as a two-index model and a shrinkage model. Using suitable statistics to enable the out-of-sample performance of competing methodologies to be compared is crucial, and we develop some new statistics and a graphical aid for this purpose. What is original in this paper is an evaluation of many modelling and inferential procedures for which conflicting claims have been made in the literature and the development of new measures of portfolio performance.