Risk estimation for shares on the Johannesburg Stock Exchange using transfer function modeling

Ian K Craig,Mike T Bendixen

doi:10.4102/sajbm.v29i1.765

Abstract

This study investigates whether the estimation of the systematic risk component or the beta of shares on the Johannesburg Stock Exchange (JSE) can be improved using transfer function or MARIMA modeling. Two propositions are tested. Transfer function modeling will result in estimates of systematic risk which are different from those obtained using conventional OLS regression methods. Transfer function models will provide forecasting results which are better than those provided by betas estimated in the conventional way. Proposition I cannot be tested using conventional inferential tests as the standard errors of estimate of the betas estimated from MARIMA modeling cannot, in general, be measured. It is found however that 16.9% of the MARIMA beta estimates fall outside the 95% confidence intervals of the respective OLS regression beta estimates. Similar results are obtained when the OLS regression betas are compared to the University of Cape Town (UCT) Financial Risk Service and BFA-NET beta estimates. Proposition 2 can in general not be supported as the MARIMA and OLS regression forecasts are found not to be statistically significantly different. Cross correlations between index and share returns are in many cases found not to be statistically significant. In such cases one is probably better off using OLS regression. Resulting beta estimates should be used with caution.

Highlights

The Capital Asset Pricing Model (CAPM), developed by Sharpe (1964), Lintner (1965) and others, and the market model (Markowitz, 1959; Sharpe, 1963), are widely used products of Capital Market Theory
Transfer function modeling will result in estimates of systematic risk which are different from those obtained using conventional Ordinary Least Squares (OLS) regression methods
Statistically testing the first proposition, which states that transfer function modeling will result in estimates of systematic risk which are different from those obtained using conventional OLS regression methods, cannot be achieved using conventional inferential tests

Summary

Introduction

The Capital Asset Pricing Model (CAPM), developed by Sharpe (1964), Lintner (1965) and others, and the market model (Markowitz, 1959; Sharpe, 1963), are widely used products of Capital Market Theory These models essentially relate returns to the systematic risk taken to achieve such returns. The estimation of the systematic risk component of shares have been the focus of many researchers in the field of financial economics. It is traditionally estimated from the market model (Bodie, Kane & Marcus, 1996: 279) which postulates a simple linear relationship between the return on the share and the return on the market. In the CAPM framework, excess returns (deviations from the risk free rate) would typically be used in the regressions

Methods

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Conclusion