Revisiting the risk-return relation in the South African stock market

Revisiting the risk-return relation in the South African stock market Author F. Darrat, Ali, Li, Bin, Wu, Leqin Published 0 Journal Title African Journal of Business Management Coyright Statement 0 Academic Journals Inc. The attached file is reroduced here in accordance with the coyright olicy of the ublisher. Please refer to the journal's website for access to the definitive, ublished version. Downloaded from htt://hdl.handle.net/007/4994 Link to ublished version htt://www.academicjournals.org/ajbm/abstracts/abstracts/abstracts0/nov/darrat%0et %0al.htm Griffith Research Online htts://research-reository.griffith.edu.au

African Journal of Business Management Vol.6 (46),. 4-45, November 0 Available online at htt://www.academicjournals.org/ajbm DOI: 0.5897/AJBM.86 ISSN 993-833 0 Academic Journals Full Length Research Paer Revisiting the risk-return relation in the South African stock market Ali F. Darrat, Bin Li * and Leqin Wu 3 College of Business, Louisiana Tech University, Ruston, Louisiana, U.S.A. Deartment of Accounting, Finance and Economics, Griffith Business School, Griffith University, Queensland 4, Australia. 3 MB Century, Richlands, Brisbane, Queensland, Australia. Acceted 8 Setember, 0 We investigate the risk-return relation in the South African stock market using data covering the eriod from 973 to 0. Prior research for several countries reveals high sensitivity of the results to data details and models used. Therefore, our analysis of the risk-return nexus in South Africa are based on three different data frequencies (weekly, monthly and quarterly) and are derived from three different generalized autoregressive conditional heteroskedasticity (GARCH) models in addition to a lain vanilla time-series aroach. Similar to the findings of Glosten et al. in 993 and Harvey in 00, our results fail to suort a significantly ositive risk-return relationshi in South Africa across various data frequencies and model secifications, and this conclusion survives further robustness checks using different sub-eriods and index data. Our results further suggest that the recent global financial crisis may have altered market dynamics and distorted the risk-return relation in the South African stock market. Key words: Risk-return relationshi, volatility models, conditional variance, South African stock market. INTRODUCTION The trade-off between risk and return in stock markets is an imortant subject in finance theory. In the seminal aer of Merton (980), he argues that the conditional exected stock return is ositively related to the conditional variance as in: E [ R ] = µ + γvar [ R ], () t t+ t t + where γ should be ositive since it measures the effect of the conditional variance on returns (corresonding to the coefficient of relative risk aversion of a reresentative investor), and µ is a constant and should reduce to zero. However, the emirical research is indecisive on the ositive risk/return nexus exected by the underlying theory. In articular, while French et al. (987), Cambell and Hentschel (99), and Ghysels et al. (005) reort ositive relationshis; yet such relations rove statistically weak. In fact, Cambell (987) and Nelson (99) suort significantly negative relationshis. As Glosten et al. (993) and Harvey (00) argue the emirical results aear to be highly sensitive to the choice of models and estimation methods. Most revious emirical studies on the risk/return relation focus on the U.S. and Euroean markets. In this aer, we investigate the risk/return relationshi in the South African stock market as different markets dislay diverse atterns of return and volatility. The Johannesburg Stock Exchange (JSE) began trading in 887 and it is the largest stock exchange in Africa. The JSE has about 47 listed comanies with a market caitalization of US $855.7 billion as of 0 according to Standard and Poor's Global Stock Markets Factbook, making the JSE among the to 0 largest stock exchange worldwide. *Corresonding author. E-mail: b.li@griffith.edu.au. Tel: +6 7 373 577. South Africa is also ranked the first out of 39 countries for its regulation of securities exchanges (World Economic Forum Cometiveness Reort, 00 to 0).

4 Afr. J. Bus. Manage. Only a few studies examine the risk/return link in South Africa and, similar to research on other markets, these studies reort mixed results. Rautsoane (009) find a ositive relation for the majority of industry indexes but this conclusion is refuted by Mandimika and Chinzara (00) at the industry and market levels. This aer examines the risk/return relation in the South African stock market over the eriod from January, 973 to December 30, 0. In light of the known sensitivity of the available evidence on the risk/return relation to model secifications and data details, we derive our results from various models and three different data frequencies (weekly, monthly and quarterly). Two main findings are worth highlighting. First, consistent with et al. (993) and Harvey (00), our results do not uniformly suort a significant ositive risk/return relation in South Africa across models and data frequencies. Second, there is evidence suggesting that the recent global financial crisis has significantly imacted the nature of the risk/return relation in the South African market. The rest of the aer is organized as follows. Section describes the data. Section 3 reorts the results from the generalized autoregressive conditional heteroskedasticity (GARCH)-M model, while Section 4 does the same under a lain-vanilla time-series model. Section 5 discusses robustness checks, and Section 6 concludes. DATA Our data, culled from Data Stream, are for the total stock return index in South Africa (Code: TOTMKSA) covering January, 973 to December 30, 0 (0,05 daily observations). We comute the weekly returns by using every Wednesday rice, monthly returns by using the rice of the last trading day of that month, and we comute quarterly returns by using the rice at the end of each quarter. Table assembles the summary statistics for the market returns at the three time frequencies. The statistics include the mean, median, minimum, maximum, standard deviation, skewness, kurtosis, and autocorrelations. As the table suggests, the returns are somewhat negatively skewed and the monthly returns aear to be normally distributed. The table also shows that the first-order autocorrelations are not very large (less than 0.0 for all the frequencies). The Ljung-Box Q statistics are significant for high frequency data (weekly) but not for low frequency data (monthly and quarterly) (Table ). THE RISK/RETURN RELATIONSHIP UNDER GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY (GARCH) SPECIFICATIONS Model secifications Research on volatility models ioneered by Engle (98) and Bollerslev (986) has oularized the use of generalized autoregressive conditional heteroskedasticity (GARCH) models for analyzing the risk/return relation. Similar to our use of three different data frequencies to enhance the robustness of the results, we also emloy three different variants of GARCH (,q) models to ensure robust findings on the nature of the risk/return relationshi in South Africa. We select the otimal lags, q in all models based on Akaike information criterion (AIC). For illustrative urose, we discuss the following case for = and q=. The mean equation to be estimated for all the four GARCH models is, R = µ + γvar [ R ] + ε. () t+ t t+ t+ The variance rocess of the corresonding GARCH (Model ) is secified as: Var = ω + αε + βvar, (3) garch garch t t t ε = R µ γvar. To ensure efficient estimations, garch where t t t we emloy the maximum likelihood method to estimate the arameters, µ, γ, ω, α, β in all models. Since ositive and negative residuals may have different imacts on future volatilities, the exonential GARCH (EGARCH) of Nelson (99) allows the asymmetric effect of good and bad news on conditional variances. The conditional variance of the EGARCH (,) model (Model ) can be written as: lnvar Var c ε ε Var Var, (4) egarch egarch t t t = ω + β ln t + + α egarch egarch t t π Where c is a arameter that catures the effects that asymmetric ositive and negative shocks, ε t, have on conditional variance, and ε / Var N(0,). t t Another well-known asymmetric model is the GJR model roosed by Glosten et al. (993). The GJR model is a simle extension of GARCH with an additional term added to account for ossible asymmetries. In the GJR (,), the conditional variance (Model 3) takes the form: Var = ω + βvar + αε + cs ε, (5) gjr gjr t t t t t α + c when the return = ), and by α when where the squared residual is multilied by is below its conditional exectation ( St the return is above or equal to the exected value ( t 0 there is leverage effect, we would exect c > 0. EMPIRICAL RESULTS S = ). If We assemble our results from the three GARCH models 3 and three data frequencies in Table. The table gives the coefficient estimates and the corresonding Most rior emirical research on the risk/return nexus emloys monthly data. For robustness, besides monthly observations, we also use shorter (weekly) and longer (quarterly) data frequencies. 3 We assume normally distributed errors. The estimates would remain consistent even without this assumtion rovided the mean and variance equations are correctly secified (Bollerslev and Wooldridge, 99).

Darrat et al. 43 Table. Summary statistics of stock market returns in South Africa Frequency Mean Median Std. Dev. Min Max Skewness Kurtosis ρ ρ ρ 3 Q() Q- Significance Weekly 0.0034 0.004 0.03-0. 0.4-0.68 4.9 0.0 0.05 0.05 3.56 0.00 Monthly 0.046 0.093 0.07-0.39 0.8-0.95 3.55 0.03 0.00 0.05 0.60 0.56 Quarterly 0.0438 0.0463 0. -0.4 0.45-0.44.88 0.0-0.7 0.05 3.7 0.3 This table rovides the mean, median and standard deviation, minimum, maximum and skewness and kurtosis of stock market returns in South Africa in local currency. The table also shows the coefficients of autocorrelation and the Ljung-Box Q statistics for lags. The samle starts from January, 973 to December 30, 0. Table. The Risk-return relation under various GARCH secifications. Frequency Weekly GARCH (,q) EGARCH (,q) GJR-GARCH (,q) µ γ LLR µ γ LLR µ γ q q q LLR 0.00.886 0.003** >-0.00** 0.003** 0.534 45 454 (.5) (0.99) (07.53) (-07.53) (.99) (0.36) 48 Monthly Quarterly 0.03** 0.707 0.06** <0.00* 0.04** 0.37 6 606 (.98) (0.54) (6.64) (.67) (.4) (0.8) 0.030.375 0.08** -0.003** -0.07 4.840 6 3 (.58) (.8) (3.95) (-.56) (-0.) (.04) 63 6 This table shows estimates of the risk-return relation, E [ R ] = µ + γvar [ R ] with the GARCH, EGARCH, and GJR. Estimators of the t t + t t + conditional variance are given by equations (3) to (5). The coefficients and the corresonding Bollerslev and Wooldridge s (99) robust t- statistics (in arentheses) are shown. LLR denotes the log likelihood ratio., q are the otimal lag numbers chosen based on AIC, with the maximum lags for both and q being three lags. ** and * denote significance at the five and ten ercent levels, resectively. Bollerslev and Wooldridge s (99) robust t-statistics. The results suggest that lags = and q= generate the best models. Across the three data frequencies, the estimated risk aversion coefficients γ are not statistically significant in the GARCH and GJR model. In contrast, the risk aversion coefficients roved ositive and significant in the EGARCH model but only for the monthly data. However, the EGARCH results from the weekly and quarterly data, although significant, are erversely negative imlying high risk is associated with low return. In sum, the results reorted in Table from different models and data frequencies do not consistently suort a significantly ositive relation between risk and return in South Africa. The results aear highly sensitive to the models and data frequencies used. THE RISK-RETURN RELATIONSHIP UNDER A PLAIN VANILLA TIME-SERIES MODEL Literature on the risk/return nexus reveals some interest in the relation between stock returns and the ast realized variance of stock returns. Following et al. (005) and Bali et al. (009), we use a lain vanilla time-series model to investigate the relation between returns and their conditional variance. That is: R = µ + γ E ( σ ) + ε, (6) t+ t t+ t + where Et ( σ t + ) is a conditional variance of the market ortfolio as reresented by the one-eriod lagged realized variance obtained from daily market returns, and is an error term. We comute the conditional ε t + variance using daily returns as follows: σ =, (7) S k t rs s= where σ t is the realized variance of stock market return, S k is the number of trading days in the eriod and r s is the market return on day s. Table 3 reorts the time-series regression estimates from Equation (6) for the weekly, monthly and quarterly frequencies. The deendent variable is one eriod ahead

44 Afr. J. Bus. Manage. Table 3. The Risk-Return Relation under the Plain- Vanilla Secification Frequency Weekly Monthly Quarterly Plain-vanilla model µ γ R 0.003** 0.044 0.00% (.9) (0.36) 0.04** 0.87 0.04% (3.60) (0.38) 0.04** 0.67 0.05% (3.) (0.34) This table shows estimates from R µ γ E ( σ ) ε t+ t t + t+ = + +, where E ( σ ) t t + is a conditional variance of the market ortfolio as aroximated by the one-eriod lagged realized variance obtained from daily market returns and ε t + is an error term. R is the R squared statistic. The Newey-West adjusted t- statistics with four lags are in arentheses below the arameter estimates. and the indeendent variables are a constant and the realized variance within the eriod. The Newey-West adjusted t-statistics are laced in arentheses below the arameter estimates. Similar to our findings from the GARCH models, these results from the lain vanilla timeseries aroach do not suort the resence of a significant and ositive relation between risk and return in South Africa. Similar to the findings in several rior studies (Ghysels et al., 005; Bali et al., 009), the exlanatory ower of the estimated lain vanilla timeseries model is rather feeble. FURTHER ROBUSTNESS TESTS Our evidence thus far suggests the absence of a ositive and significant relation between risk and return in the South African market. This lack of evidence seems consistent across several models and various data frequencies. In this section, we investigate if other factors may have contaminated our results and led to biased conclusions. Given the lengthy time san of our samle (almost 40 years), a structural break is conceivable which could render the results susect 4. We slit our samle eriod in two different manners. First, the recent global financial crisis that began in 007 may have imacted market dynamics worldwide, including South Africa. Therefore, we deleted the otentially turbulent ost-007 crisis suberiod and re-estimated our models over the re-crisis 4 To conserve sace, we confine our test of structural break to the common monthly data frequency. sub-eriod. We reort the results in Tables 4 and 5. Under the GARCH and GJR models, the results from the re-crisis data are similar to those derived earlier from the full eriod. However, the results from the EGARCH model suort a significant and ositive risk/return relationshi. Thus, according to the EGARCH aaratus, the global financial crisis may have weakened the risk/return relation in the South African market. Of course the global financial crisis is not the only imortant event in the ast four decades that could have contaminated our results. Thus, we follow Farley et al. (975) and divide our samle at the midoint to examine the risk/return relation in the two sub-eriods 5. The results, also shown in Tables 4 and 5, are similar in the first sub-eriod to those in the re-crisis eriod. However, in the second sub-eriod, the EGARCH model no longer indicates a ositive risk/return relation. In fact, this relationshi became significantly negative in the second half of the eriod. It is further ossible that the results may be susect due to our use of the total return index rather than the rice index (the latter excludes dividends). To check this ossibility, we re-estimate our models on the basis of the rice index and reort the results in Tables 4 and 5. Again, the results ersist in rejecting a significantly ositive risk/return relation. Contrary to our findings from the total return index data (Table 3), the results from the rice index under the EGARCH model indicate the resence of a significantly negative risk/return relationshi in South Africa. Such a erverse outcome reveals some caution in using the rice index since it ignores dividends that are an imortant comonent of returns in addition to caital gains. Finally, results reorted in Table 4 from the lain-vanilla time-series model over different samle eriods and from the rice index do not fare any better and they too fail to uncover a significantly ositive relation between risk and return. In sum, our results from a multitude of models, data frequencies, index data, and samle eriods consistently suggest the absence of a credible ositive risk/return relation in the South African stock market. Conclusion This aer examines the risk/return relation in the South African stock market using data from 973 to 0 at three different frequencies (weekly, monthly and quarterly) and using various GARCH models as well as the lain vanilla time-series aroach. We do not find a significantly ositive risk/return relation across data frequencies and models used. This conclusion generally 5 One virtue of slitting the samle at the midoint when testing for structural instability is to maximize the test efficiency by having sufficient degrees of freedom in both sub-eriods (Farley et al., 975).

Darrat et al. 45 Table 4. Robustness Tests (GARCH secifications). Samle Excluding GFC GARCH (,q) EGARCH (,q) GJR-GARCH (,q) µ γ LLR µ γ LLR µ γ q q q LLR 0.03 0.8 0.07** <0.00** 0.04 0.594 59 56 (.40) (0.44) (7.55) (0.74) (.57) (0.3) 59 973:-99: 993:-0: Using rice index 0.008.53 0.08** <0.00** 0.008.535 87 86 (0.6) (0.7) (4.80) (.03) (0.5) (0.7) 0.04** 0.674 0.008** -0.00** 3 0.03** 0.099 330 30 (.69) (0.6) (7.84) (-7.84) (.73) (0.0) 0.0* 0.443 0.005** >-0.00** 0.0* 0.77 6 604 (.68) (0.34) (67.73) (-67.73) (.67) (0.3) 87 335 6 Table 5. Robustness tests (lain-vanilla model). Samle Excluding GFC 973:-99: 993:-0: Using rice index Plain-Vanilla Model µ γ R (%) 0.04** 0.575 (3.9) (0.69) 0.03** 0.84 (.0) (0.7) 0.05** -0.594 (3.3) (-0.76) 0.0** 0.33 (.75) (0.3) 0.4 0.30 0.7 0.0 GFC denotes the recent global financial crisis. Using rice index means the returns are calculated based on the rice index rather than the total return index. ersists desite the use of various sub-eriods and different index data. That finding is erhas not that surrising since many studies for other countries have also concluded that the risk/return relation is tenuous at best (Glosten et al., 993; Harvey, 00). We have further resented some evidence that the recent global financial crisis may have altered market dynamics and distorted the risk/return relation. This is because our results from the EGARCH model estimated over the recrisis eriod suort the resence of a significantly ositive risk/return relation in South Africa. ACKNOWLEDGEMENT We thank the Editor and two anonymous reviewers for several helful comments. The usual disclaimer alies. Bin Li is grateful for financial suort from Griffith University under the 0 Griffith University New Researcher Grant, Project Number 40730 REFERENCES Bali TG, Demirtas K, Levy H (009). Is there an intertemoral relation between downside risk and exected returns? J. Financ. Quant. Anal. 44:883-909. Bollerslev T (986). Generalized autoregressive conditional heteroskedasticity. J. Econ. 3:307-37. Bollerslev T, Wooldridge JM (99). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econ. Rev. :43-7. Cambell JY (987). Stock returns and the term structure. J. Financ. Econ. 8:373-399. Cambell JY, Hentschel L (99). No news is good news: an asymmetric model of changing volatility in stock returns. J. Financ. Econ. 3:8-38. Engle RF (98). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987-008. Farley JU, Hinich MJ, McGuire TW (975). Some comarisons of tests for a shift in the sloes of a multivariate linear time series model. J. Econom. 3:97-38. French KR, Schwert W, Stambaugh RF (987). Exected stock returns and volatility. J. Financ. Econ. 9:3-9. Ghysels E, Santa-Clara P, Valkanov R (005). There is a risk-return trade-off after all. J. Financ. Econ. 76:509-548. Glosten LR, Jagannathan R, Runkle DE (993). On the relation between exected value and the volatility of the nominal excess return on stocks. J. Financ. 48:779-80. Harvey CR (00). The secification of conditional exectations. J. Em. Financ. 8:573-638. Mandimika NZ, Chinzara Z (00). Risk-return tradeoff and the behavior of volatility on the South African stock market: evidence from both aggregate and disaggregate data. Rhodes University Working Paer 98. Merton RC (980). On estimating the exected return on the market. J. Financ. Econ. 8:33-36. Nelson DB (99). Conditional heteroskedasticity in asset returns: a new aroach. Econometrica 59:347-370. Rautsoane L (009). The risk-return relationshi in the South Africa stock market. South African Reserve Bank, Working Paer.