The arbitrage pricing theory in South Africa : an empirical study of the effect of pre-specified risk factors on share prices on the Johannesburg Stock Exchange.

Abstract

This study tests the Arbitrage Pricing Theory on the Johannesburg stock Exchange (JSE). Following the McElroy and Burmeister (1988) approach of pre-specifying a factor structure to be tested, a possible set of factors was selected on the basis of a priori theoretical and empirical evidence that they could affect share prices. All combinations of these factors were separately tested against mining and industrial shares listed on the JSE. Two sets of tests were performed, firstly, a multivariate nonlinear regression with cross-equation restrictions as a test of the APT model and secondly, a seemingly unrelated regression model. The APT test results for mining shares show that the model with gold price risk and residual market risk and the model with growth rate risk and residual market risk had the highest adjusted-R2 values. However these factors were not priced APT factors since they were not significantly different from zero. Two one-factor models yielded priced APT factors. These were the model including the gold price risk and another model with growth rate risk. Whilst these were both priced APT factors, the gold price risk model was better fitted. Four models were selected from the APT tests on industrial shares, on the basis of high adjusted-R2 values and factors which were significantly different from zero. They included the following risk factors: gold price risk and residual market risk; foreign exchange risk and residual market risk; inflation risk and residual market risk; default premium risk, gold price risk and residual market risk. The seemingly unrelated regression models had very similar adjusted-R2 values and indicated that the APT did not appear to explain the variation in share returns any better or worse than the seemingly unrelated regression model. The adjusted-R2 values for individual shares and the signs of the factor risk-premiums appear to be reasonable. The residual market risk factor was significantly different from zero for both the mining and industrial share samples, indicating that further work is required to identify the APT factors operating on the JSE.