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Currently studying about time series modelling of financial data and faced the known GARCH$(p,q)$ model for modelling volatility. We observe that big changes are followed by large changes and vice versa, as Mandelbrot said. But, in term of qualitative analysis, what are the main behavioral factors that lead to such pattern? Does volatility persistence oppose to EMH?

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    $\begingroup$ Volatility clustering is not inconsistent with the efficient market hypothesis that prices reflect all available information. A perfectly rational story for volatility clustering is that the arrival of big, market making moves forecasts the arrival of additional big, market moving news. For example if war breaks out in the Persian Gulf, you're more likely to see market moving news on oil supply disruptions etc.... $\endgroup$ – Matthew Gunn Oct 10 '18 at 15:24
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First, the semi strong form of the EMH (prices reflect all public information) corresponds to the returns being a martingale difference; GARCH is a martingale difference, so GARCH is compliant with the EMH.

Second, you can look into the stylized fact of financial returns called "leverage effect", in short it says that returns have a negative correlation with the changes of their volatilities. A way to look at this is:

  1. prices go down
  2. companies become more leveraged and thus riskier
  3. the prices fluctuate more
  4. as prices become more volatile the investors demand higher returns
  5. the prices go down
  6. repeat until prices go up and the reverse happens (less volatility)

An excellent book for this subject is Fan & Yao, 2017 The Elements of Financial Econometrics.

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Can you use the information from the GARCH model to time the market and make excess risk adjust returns.

If so, its against market efficiency.

You have to ask yourself,

What market? If you can correctly predict the VIX (or other volatility index) and trade on this yes.

The market, probability not!

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