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How GARCH Adds Volatility Forecasts to an ARMA Trading Model

Article Quant Q&A · Author: Nobody
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Summary

The note distinguishes the roles of the ARMA and GARCH components in a return model used for directional trading. The ARMA conditional mean supplies the expected return and therefore drives a rule that goes long or short according to the forecast sign. GARCH models conditional variance: it estimates how large the next return’s deviation from that expected mean may be, rather than independently identifying the direction of the move.

That volatility estimate can support risk management, including Value at Risk calculations, and can help characterize changing dispersion and heavy-tailed shocks. The response also raises options trading as a possible use when both drift and volatility forecasts are useful, but offers no implementation details or evidence that such a strategy improves returns. The discussion is conceptual and does not evaluate the referenced strategy, its forecasts, or its costs. In particular, volatility forecasts do not guarantee better risk estimates, and model fit and distributional assumptions remain important.

Key ideas

  • The ARMA conditional mean provides the expected return used for a directional long or short signal.
  • GARCH estimates conditional variance and the likely size of deviations from the expected return.
  • Volatility forecasts can contribute to risk measures such as Value at Risk.
  • Modeling conditional variance may help describe changing volatility and non-normal shocks.
  • The note suggests options as a possible application but supplies no evidence of improved performance.

Tags

StatisticsVolatilityRisk managementBacktesting
Full text
# ARMA+GARCH day-trading strategy


# ARMA+GARCH day-trading strategy












I have a question regarding this particular post on quantstart:

https://www.quantstart.com/articles/ARIMA-GARCH-Trading-Strategy-on-the-SP500-Stock-Market-Index-Using-R

In it, he designs a day-trading strategy that uses a 500-day rolling forecast from an ARMA+GARCH model. If the model predicts negative returns then the stock is shorted, and if it predicts positive returns then it is longed.

My question is regarding to the use of the GARCH component. Since it (the strategy) only relies on the model's point forecasts, then in reality, the GARCH does not add much to the strategy itself right? Since, at least from my understanding, the point forecasts from an ARMA + GARCH would be exactly the same as an ARMA's.

Thanks in advance

## Answer by Fr1 (score 1, accepted)

https://quant.stackexchange.com/a/47016

Yes.

We should indeed say that the Garch part of the model does not help to predict the Direction of the movement (this is given by the expected drift of the Arma, which gives the conditional mean of the return process) but helps to predict the size of the deviation of the next period return from the expected Arma drift. It is a measure of the squared size of the difference between next period return and its conditional expectation based on the Arma conditional mean. Which is why it is so popular in the risk management. The garch part answer the question: provided that the next period return will be different (to some extent) from my conditional mean prediction, how much will it be different? So it becomes very useful if you want to compute a Value at Risk on your strategy.

To this purpose, notice that it may be good to model a Garch even if you are not interested in the Garch per se, because it will contribute to removing the asymmetric and fat-tailed nature of the distribution of the shocks.. in other words, in an ideal world, you will have innovations that will resemble more closely a symmetric distribution with little excess kurtosis, which will help a lot in the risk management part of the strategy.

Not to mention that, of course, if you implement a good Arma-Garch model, and you are in the position to give a good forecast of both the drift and volatility, then you could switch to option trading (instead of equity trading like described) in order to boost your returns.. but this is another story..

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.