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If we assume that, broadly speaking:

  • Assets in liquid markets are fairly priced to its value
  • Volatility is predictable (volatility clustering, GARCH, etc)
  • Investors are rewarded and earn a return for bearing risk

Then shouldn't it be possible to slot in your forecast of volatility, and compute implied returns of an asset?

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  • $\begingroup$ How does that differ from estimating a GARCH($p$, $q$) with constant mean? $\endgroup$ – Lisa Ann Jul 27 at 9:42
  • $\begingroup$ The "risk" that is rewarded with returns is not necessarily equal to volatility (for example it could be Beta that is rewarded, or multiple Betas, or covariance with consumption, etc.). Volatility unconnected with the economy, or which can trivially be diversified away is almost certainly NOT rewarded. $\endgroup$ – noob2 Jul 27 at 12:41
  • $\begingroup$ From how I am reading your question, you are saying: Given I can forecast volatility, can I say anything about future price? As far as I am thinking about it, the answer is of course: Yes. Yes, but. But, you can only forecast returns in absolute terms. $\endgroup$ – jason m Jul 27 at 15:31
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    $\begingroup$ Think about a simple model, where the price only has two options going up or going down. With your assumptions you can say something about the probabilities of going up or going down and something about the step sizes. But you can not determine, if the price will go up or down in the future. $\endgroup$ – Ami44 Jul 28 at 21:53

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