Market Betas on the JSE: Factor selection, estimation and empirical evaluation

Master Thesis


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University of Cape Town

This paper examines the nature and significance of market betas on the Johannesburg Stock Exchange (JSE). The identity of market betas is determined by means of Principal Component Analysis (PCA) performed on the returns of the FTSE/JSE Africa Index Series. A scree test shows two factors necessary for inclusion in the appropriate Arbitrage Pricing Theory (APT) model. Based on the promax rotated factor loadings, it is argued that the Financials (J580) and Basic Materials (J510) indices ought be used as the appropriate observable index proxies for the first and second factors respectively. Regarding the estimation of beta, this paper makes the case for the use of Reduced Major Axis (RMA) regression over the traditional Ordinary Least Squares (OLS) approach. A number of characteristics are assessed when arriving at this conclusion. Importantly, it is shown that the traditional OLS regression method chronically underestimates the magnitude of the beta parameter whereas RMA regression does not. In addition, it is shown that, while OLS beta values are more stable in absolute terms than RMA beta values, the RMA values are more stable when adjusted for their magnitude. This paper does not make use of a thin trading filter to narrow the sample of stocks for empirical evaluation. Instead, an examination is made of the significance of beta values at the point at which they are estimated. This is accomplished by means of a rolling window of regressions. It is shown that, while most stocks do exhibit betas which are consistently significant over their listing period, many stocks do not. Some stock returns result in almost no significant beta values while some others exhibit beta values which are significant for only a portion of their listing period. It is shown that a median beta p-value value of 5% is an appropriate 'significance filter' for limiting the sample of stocks to only those significant for the majority of their listing period. Using only these stocks, an empirical evaluation of beta is conducted using portfolios sorted on both OLS and RMA beta values. It is found that neither beta measure explains the cross-section of returns in the case of resource stocks. However, in the case of non-resource stocks the results show a clear divergence between the methods. In the case of OLS sorted portfolios, the results show a negative relationship between beta and returns. This surprising and counterintuitive result has also been arrived at by other researchers and is the opposite of what the APT would predict. However, in the case of RMA sorted portfolios, this pattern reverses itself, showing a positive relationship between beta and returns. For some holding periods, this is shown to be significant, providing evidence in support of the APT. As a result it is demonstrated that OLS regression not only underestimates the magnitude of beta, but that it distorts the results of empirical tests. On this basis it is argued that RMA regression ought replace OLS regression as the preferred method of beta estimation for the JSE.