“van Rensburg P (2002), “Market Segmentation on the Johannesburg Stock Exchange II”, Journal of Studies in Economics and Econometrics, vol 26, no 1, 83-99″

Abstract: Given the reclassification of the Johannesburg Stock Exchange (JSE) sector indices that occurred in March 2000, this paper updates the factor analytic procedure conducted by van Rensburg and Slaney (1997). It is found that the new Financial-Industrial (CI21) and Resources (CI11) indices may be used as observable proxies for the first two principal components extracted from the covariance matrix of JSE returns. Consequently, it is suggested that these indices replace the Industrial and All-Gold index in future applications of the two factor arbitrage pricing theory (APT) model. Prior research is extended by considering the implications of the dichotomy in the return generating processes underlying JSE financial-industrial and resource stocks for the estimation of security betas. It is mathematically demonstrated that this dichotomy implies that the cross-sectional correlation matrix of the market model’s residual errors is not diagonal. As a result, conventionally conducted market model regressions are characterised by the problem of omitted variable bias and downwardly biased t statistics. A remedial procedure is proposed, which may serve as a general correction for omitted variable bias in ordinary least squares regression analysis when using panel data. Finally, it is pointed out that the All-Share Index, conventionally employed as the market proxy in South African beta estimation, is not mean-variance efficient given the opportunity for offshore investment. This implies that the capital asset pricing model, as conventionally specified by South African academics does not hold on the JSE.

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