Volatility dynamics and the risk-return relationship in South Africa: A GARCH approach
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DOIhttp://dx.doi.org/10.21511/imfi.18(2).2021.09
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Article InfoVolume 18 2021, Issue #2, pp. 106-117
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This study is aimed at investigating the volatility dynamics and the risk-return relationship in the South African market, analyzing the FTSE/JSE All Share Index returns for an updated sample period of 2009–2019. The study employed several GARCH type models with different probability distributions governing the model’s innovations. Results have revealed strong persistent levels of volatility and a positive risk-return relationship in the South African market. Given the elaborate use of the GARCH approach of risk estimation in the existing finance literature, this study highlighted several weaknesses of the model. A noteworthy property of the GARCH approach was that the innovation distributions did not affect parameter estimation. Analyzing the GARCH type models, this theory was supported by the majority of the GARCH test results with respect to the volatility dynamics. On the contrary, it was strongly unsupported by the risk-return relationship. More specifically, it was found that while the innovations of the EGARCH (1, 1) model could account for the volatile nature of financial data, asymmetry remained uncaptured. As a result, misestimating of risks occurred, which could lead to inaccurate results. This study highlighted the significance of the innovation distribution of choice and recommended the exploration of different nonnormal innovation distributions to aid with capturing the asymmetry.
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JEL Classification (Paper profile tab)C22, C58, G32
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References18
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Tables9
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Figures0
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- Table 1. Descriptive statistics of the ALSI returns
- Table 2. Heteroscedasticity tests for the ALSI returns
- Table 3. ML parameter estimates of the GARCH (1, 1) for different innovation distributions
- Table 4. ML parameter estimates of GJR-GARCH for different innovation distributions
- Table 5. ML parameter estimates of EGARCH with different innovation distributions
- Table 6. ML parameter estimates of APARCH with different innovation distributions
- Table 7. Preliminary test results for the innovations of the EGARCH
- Table 8. ML parameter estimates for GARCH-M with different innovation distributions
- Table 9. ML parameter estimates for EGARCH-M with different innovation distributions
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- Adu, G., Alagidede, P., & Karimu, A. (2015). Stock return distribution in the BRICS. Review of Development Finance, 5(2), 98-109.
- Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.
- Brooks, C. (2014). Introductory Econometrics for Finance. New York: Cambridge University Press.
- Ding, X., Granger, C. W. J., & Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83-106.
- Engle, F. R. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.
- Engle, R. F., Lilien, D., & Robins, R. (1987). Estimating time varying risk premia in the term structure: the ARCH-M model. Econometrica, 55, 391-407.
- Feng, L., & Shi, Y. (2017). A simulation study on the distributions of disturbances in the GARCH model. Cogent Economics and Finance, 5(1), 1-19.
- Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48(5), 1779-1801.
- Ilupeju, Y. E. (2016). Modelling South Africa’s market risk using the APARCH model and heavy-tailed distributions. (Master’s thesis). University of KwaZulu-Natal. Durban. South Africa.
- Jensen, M. J., & Maheu, J. M. (2018). Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis. Journal of Risk and Financial Management, 11(52), 1-29.
- JIN, X. (2017). Time-varying return-volatility relation in international stock markets. International Review of Economics and Finance, 51, 157-173.
- Khan, F., Rehman, S., Khan, H., & Xu, T. (2016). Pricing of risk and volatility dynamics on an emerging stock market: evidence from both aggregate and disaggregate data. Economic Research-Ekonomska Istrazivanja, 29(1), 799-815.
- Mandimika N. Z., & Chinzara, Z. (2012). Risk-return trade-off and behaviour of volatility on the South African stock market: evidence from both aggregate and disaggregate data. South African Journal of Economics, 80(3), 345-365.
- Mangani R. (2008). Modelling return volatility on the JSE Securities Exchange of South Africa. African Finance Journal, 10(1), 55-71.
- Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59, 347-370.
- Park, S.Y., Ryu, D., & Song, J. (2017). The dynamic conditional relationship between stock market returns and implied volatility. Physica A, 482, 638-648.
- Spierdijk, L. (2016). Confidence intervals for ARMA–GARCH Value-at-Risk: The case of heavy tails and skewness. Computational Statistics and Data Analysis, 100, 545-559.
- Yu, J. H., Kang, J., & Park, S. (2019). Information availability and return volatility in the bitcoin Market: Analysing differences of user opinion and interest. Information Processing and Management, 56, 721-732.