Volatility forecasting in small and mid-cap shares using EWMA and GARCH (1,1) models
Abstract
Considerable changes in share price returns are immediately followed by considerable changes of similar share price returns. Furthermore, inconsiderable changes in share price returns are immediately followed by inconsiderable changes of the same share price returns. The EWMA and GARCH (1, 1) models are used for volatility forecasting in small and mid-cap shares because of their shared trait in volatility clustering. The EWMA model is a derivative of the moving average family and the GARCH (1, 1) model is a derivative of the autoregressive conditional heteroscedasticity family. The weakness of the historical standard deviation is that the model assigns similar share price weights to all share price returns, whereas the EWMA and GARCH (1, 1) models inclusion to the study is to highlight the aforementioned weakness of the historical standard deviation. This is by using the EWMA and GARCH (1, 1) models to assign greater share price weight to recent share price returns and lesser share price weight to distant share price returns. Therefore, this study is aimed to investigate the preferable model to forecast volatility between the EWMA and GARCH (1, 1) models in small and mid-cap shares.
The EWMA and GARCH (1, 1) models were used for volatility forecasting for small and mid-cap shares as a result of the underwhelming performance of small and mid-cap shares that indicated a high risk investment. Rising government debt, the dissatisfying performance of GDP and an unreliable South African electricity public utility named Eskom were among factors that influenced the underperformance of small and mid-cap shares. Additionally, failure to preserve effective and ethical leadership with regards to successful corporate operations and governing outcomes over the last decade also had an influence on the performance of small and mid-cap companies. The COVID-19 pandemic outbreak, best described as an extreme global event also led to economic instability during 2020.
Based on the context of volatility forecasting within this study, volatility forecasting for small and mid-cap shares using the EWMA and GARCH (1, 1) models were conducted in order to support the empirical objectives. The results from the empirical objectives found that COVID-19 was an extreme event as it had a low probability of occurring, however, whenever it took place, it led to great damage to the global economy. Equally weighted share price returns that were evident using the historical standard deviation signified the use of the EWMA and GARCH (1, 1) models. The mid-cap optimal lambda was of a more considerable size than that of the small-cap shares. This was because of the considerable share price weighting since each weight was a constant multiplier of the prior day’s weight.
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According to the study’s findings, it was preferable to make use of both models since they track a relative similar volatility of share price returns in small and mid-cap shares. Whenever there was an extreme event such as the COVID-19, the EWMA and GARCH (1, 1) models captured and recorded the event and changes in the optimal lambda were evident for small and mid-cap shares respectively. The outbreak of COVID-19 in South Africa proved to have been impactful as small and mid-cap companies endured a steep decline in share price returns. Share price returns were at their lowest in the period under analysis. Meanwhile, share price volatility was at its highest indicating the negative relationship between share price returns and share price volatility. The inverse relationship was evident from EWMA and GARCH (1, 1) as well as the historical standard deviation.
In order to achieve the primary objective, which is to forecast volatility in small and mid-cap shares using the EWMA and GARCH (1, 1) models, an event study methodology was used to examine a data sample of small and mid-cap shares between 1 January 2010 and 31 July 2020, using daily data. A descriptive comparison between the EWMA, GARCH (1, 1) and the historical standard deviation models was conducted with the inclusion of determining the optimal lambda. The use of the EWMA and GARCH (1, 1) models added to the importance of providing a holistic view of their advantages and disadvantages respectively. The advantages for the EWMA include the model’s ability to continuously update its forecast in volatility, subject to new information availability, and reacting quicker not to the shock itself but in the role of recovering the marketplace while absorbing the shock. The disadvantage entails the failure to capture the asymmetry of volatility. Meanwhile, the advantage of the GARCH (1, 1) model is to readjust at a quick rate to the repercussions of the shocks in the financial markets, however, computational expensiveness disadvantages the model as only a select few, namely, investors, analysts, and traders could access its affordability.
The study recommends the use of other volatility forecasting models that would further elaborate on the weakness of the historical standard deviation and disclose findings that were not analysed under the EWMA and GARCH (1, 1) models. In addition, it is recommended to include the concept of mispricing of small and mid-cap shares amid the COVID-19 pandemic. The managerial implication would be to use the EWMA and GARCH (1, 1) models at the same time, as it was evident that both models tracked a relative movement of share price volatility.