Reviving Beta Another Look at the Cross-section of Average Returns on the JSE

1. Reviving BetaAnother Look at the Cross-section of Average Returns on the JSE Christo Auret & Daniel Page

2. Introduction • Van Rensburg and Robertson (2003a), Basiewicz and Auret (2009) and Strugnell, Gilbert and Kruger (2011) found that there is both a significant size and value premium present on the cross-section of average returns on the JSE • Van Rensburg and Robertson (2003a) concluded that their findings presented an ‘unambiguous empirical contradiction of the CAPM’ • Cohen, Polk and Vuolteenaho (2002) considered a variation of estimating beta that utilised ‘cash-flow’ return and found that the cash-flow beta successfully explained both the size and value premium

3. Central Hypotheses • The study to be conducted utilises the cash-flow beta of Cohen, Polk and Vuolteenaho (2002) and will test whether the cash flow beta can successfully explain the cross-sectional variation in average returns on the JSE • A number of sub-hypotheses are considered: • Is their a significant size and value effect on the JSE using the buy-and-hold portfolio return estimation methodology of Cohen, Polk and Vuolteenaho (2002)? • Does the cash flow beta succeed in explaining the cross-sectional variation in share returns? • Does the cash flow beta subsume the size and value effect? • Does the conventionally measured CAPM beta present a negative relationship with share returns consistent with the findings of Van Rensburg and Robertson (2003a) and Strugnell, Gilbert and Kruger (2011)?

4. Data and Methodology • The sample period is from January 1995 – June 2009 • There are two sets of tests employed: • Overlapping OLS regression in order to evaluate the evolution of the cash flow beta over time • Panel Data cross-sectional regressions using GMM/Dynamic panels

5. Overlapping OLS • Initially size and value portfolios are sorted at 3 year, 5 year and 7 year intervals mimicking long-term buy-and-hold investors that rebalance portfolios 5, 3 and 2 times over the sample period • Size portfolios are sorted into one of three portfolios based on the previous years average log of market cap • Value portfolio are sorted based on the previous years median B/M • Average equally-weighted total returns are estimated for each the strategies/portfolio • A price filter is applied to all strategies in order to consider potential illiquidity

6. Overlapping OLS • The cash flow returns are estimated for each portfolio using the formulae: • ROEi,t is defined as the arithmetic book-value per share return at time t while ROEm,tis the arithmetic book value return of the value weighted market proxy • ρis the average historical discounted dividend yield of the JSE

7. Results: Value 5 year No restriction 100c restriction 75c restriction 50c restriction

8. Results • The results indicate that there seems to be a pervasive value premium for all three strategies namely for rebalancing that is conducted every 3, 5 and 7 years • The results further show that the value effect is still significant even when applying varying liquidity/price filters • For each of the portfolios, rolling window cash flow betas are estimated (rolling window OLS regressions using 60 months of historical returns) in order to examine the evolution of cash flow betas over time

9. 5 year Rolling window cash flow beta No restriction 100c restriction 75c restriction 50c restriction

10. Results • The above diagrams indicate that when betas are estimated using the ROE of the respective portfolios and the ROE of the market, the cash flow betas tend to match the long-term returns of both the value and growth portfolios • These findings are consistent with those of Cohen, Polk and Vuolteenaho (2002) • The same was done for size portfolios and the results also indicate that the cash flow beta seems to track the returns of the small cap and large cap portfolios

11. Size 5 year return – 100c filter 5 year rolling window cf beta – 100c filter 5 year rolling window cf beta – 50c filter 5 year return – 50c filter

12. Cross-Sectional Regressions • The central hypothesis of this study considers the cross-sectional variation of average returns • Using the methodology similar to that employed by Cohen, Polk and Vuolteenaho (2002), portfolios are sorted yearly and held for a period of 60 months post sort • The result is a cross-sectional panel of 11 separate sorts over the sample period • Initially univariate sorts are conducted on size and value separately. Shares are sorted into nine portfolios based on the previous years average log of market cap and eight portfolios based on the median B/M • For each of the cross-sectional regressions GMM/Dynamic Panel data estimations are used in order to account for the potential estimation error induced by both the time-series and cross-sectional structure of the data

13. Results – Value Sort • The results of the dynamic panel data GMM regressions are consistently in favour of the cash flow beta • The CAPM beta is significant, yet always negative • The regressions indicate that there is a significant value effect on the cross-section of average returns on the JSE • The cash flow beta performs well as it is significantly positive throughout and even subsumes the B/M as an explanatory variable

14. Results – Size Sort • The results of the size sorted portfolios are once again less promising than those of the value sort • The CAPM beta is once again significantly negative • There seems to be a significant size effect present on the cross-section of average returns • The cash flow beta performs best when considered alone • However when including the other variables, the cash flow beta loses its significance and changes signs

15. Multivariate Sort • In order to truly test the explanatory power of the cash flow beta, a multivariate test has been constructed where portfolios are sorted simultaneously on size and value • Nine portfolios are formed average size and median B/M • As before, portfolios are formed yearly and held for a period of sixty months and equally weighted average returns are calculated

16. Results – Size and Value Sort • The multivariate sort provides the most promising evidence in favour of the cash flow beta • The CAPM beta is consistently negative • The cash flow beta is significantly positive in all cases • There seems to be a significant and independent size and value effect • Most interestingly, the cash flow beta in the final regression does not subsume B/M which still remains positive and significant, yet it seems to over power the size variable as the size premium is still significant at the 10% level, yet its sign has changed to positive

17. Concluding Remarks • The cash-flow beta seems to do a better job at explaining the cross-sectional in average share returns on the JSE consistent with the findings of Cohen, Polk and Vuolteenaho (2002) • The evidence dictates that there is both a significant size and value premium present on the JSE consistent with evidence presented by Van Rensburg and Robertson (2003a), Basiewicz and Auret (2009) and Strugnell, Gilbert and Kruger (2011) • The evidence is more in favour of the cash-flow beta explaining the value effect as opposed to the small-size premium • The CAPM beta fails to explain the cross-sectional variation in share returns and in cross-sectional regressions consistently maintains a negative coefficient as was found in the studies conducted by Van Rensburg and Robertson (2003a) and Strugnell, Gilbert and Kruger (2011)