The capital-asset pricing model reconsidered: tests in real terms on a South African market portfolio comprising equities and bonds

Abstract

This paper extends previous work of the authors to reconsider the capital-asset pricing model (CAPM) in South Africa in real terms. As in that work, the main question this study aimed to answer remains: Can the CAPM be accepted in the South African market for the purposes of the stochastic modelling of investment returns in typical actuarial applications? To test the CAPM in real terms, conventional and index-linked bonds were included both in the composition of the market portfolio and in tests of the securities market line. For the investigation, quarterly total returns from the FTSE/JSE all-share index listed on the JSE Securities Exchange from 30 September 1964 to 31 December 2010 were used, together with yields on government bonds and consumer price indices over the same period. As expressed in the securities market line, the CAPM suggests that higher systematic risk, as measured by beta, is associated with higher expected returns, and that the relationship between expected return and beta is linear. In this investigation the above-mentioned predictions of the CAPM were tested for the South African market. Regression tests both of the zero-beta and standard versions of the CAPM were made, using both prior betas and in-period betas. Hotelling’s test was also applied, as well as a regression analysis. These tests were made for individual periods as well as for all periods combined.

Keywords: Beta; bonds; capital-asset pricing model; excess return; South Africa