Robustness of the GARCH Model

The generalized autoregressive conditional heteroskedasticity (GARCH) model is an econometric model for analyzing stock market volatility. The GARCH model is used to estimate the variance of a return, using past returns as an input into a model. It is a popular tool for measuring risk in financial markets, as it can capture the time-varying nature of risk.

There is a large volume of literature that deals with the application of the GARCH model in trading. Reference [1] stood out by bringing a new perspective. It examined the robustness of the GARCH model by asking the following questions,

  1. Which rolling GARCH specification produces the most accurate volatility forecast?
  2. Does more frequent model refitting improve portfolio Information Ratio?
  3. How does the size of the training window affect the strategy performance?
  4. Is the base model strategy performance stable with regards to different historical volatility estimators?

After several sensitivity tests, the authors concluded,

Referring to the main hypothesis we can say that we were not able to obtain robust abnormal returns with comparison to the equity benchmark strategies. Further empirical findings support this statement. We found out that (see Table 8) across four GARCH model specifications considered, the strategy based on the threshold GARCH (fGARCH – TGARCH extension) was the most attractive one producing the highest value of Information Ratio, the highest annualized returns and the lowest maximum drawdown. … The more frequent model refitting did not improve portfolio’s Information Ratio – not as it was initially expected. Regarding the size of the training window, we were unable to conclude that the longer or shorter one necessarily improves or diminishes Information Ratio. In our research based on the data used we obtained that there is no direct relationship – and the optimal training window size is within 126 and 252 trading days range. The performance of strategies under different volatility estimators differ considerably. The poor performance of the Garman-Klass and Parkinson estimators might be partially explained by relatively higher number of long signals generated during the overall seven-year downward volatility trend observed.

In short, the performance of the GARCH model is sensitive to system parameters and the length of historical data.

In our opinion, this article tackled a very important question in trading system design, which is robustness.

References

[1]  Oleh Bilyk, Paweł Sakowskia, Robert Ślepaczuka, Investing in VIX futures based on rolling GARCH models forecasts, University of Warsaw, Faculty of Economic Sciences, 2020

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