Modelling the Equity Risk Premium in the Long Term

Abstract

The main thrust of this paper is to develop a novel approach to modelling the ex ante or expected equity risk premium from share price and dividend information. The starting point involves modelling the stochastic nature of the dividend series and using this to derive the corresponding functional form of the share price. Using the (estimated) parameters of the dividend equations in conjunction with the share price equations we are able to solve implicitly for the expected risk premium. We then go on to model the ex ante risk premium as a mean reverting Ornstein-Uhlenbeck process with a time dependent mean. Our results show clearly that the ex ante equity risk premium is mean reverting towards a long term mean. We also investigate whether the ex post risk premium reverts to the ex ante risk premium by using a naive model (viz. ex post risk premium is equal to the ex ante risk premium plus a forecast error) and a more general specification based on an Ornstein-Uhlenbeck process. Our results suggest that this more general specification offers superior explanatory and forecasting power when compared to the naive model, and is a potentially valuable procedure for purposes such as security analysis and utility regulation where estimates of the ex ante risk premium are a crucial component of estimating expected rates of return.