Modelling the market in a risk-averse world: the case of South Africa

Abstract

In this paper, descriptive models of real returns on the South African market portfolio are developed and analysed. The ‘market portfolio’ is taken to comprise listed equity and government bonds, aggregated in proportion to their market capitalisation from time to time. The models have the attributes that, conditionally on information at the start of a year:
– the real return on the market portfolio during that year is normally distributed; and
– the market price of risk during that year is reasonably greater than zero.
For the purpose of predictive modelling, the best of the models considered was found to be a linear function of the risk-free rate. For that purpose it was decided to use ex-ante estimates of expected returns. This led to bias in the observed mean returns, which negates the rational expectations hypothesis. In the light of the literature on the subject, this is considered acceptable for these purposes.

KEYWORDS Market portfolio, risk aversion, South Africa, bias