Hmm, I have to disagree with you there. I think you are conflating the non-normal nature of the distribution with stochastic/uncertain volatility. You can rescale the returns by the expected volatility (e.g. I rescale returns by the ATM implied vol for some studies) and that does create a historically-consistent set of returns. However, the resulting distribution will still be fat-tailed and skewed.
No, that was deliberate.
When someone has to go on CNN and claim there has been a 10 standard deviation event, is that because (a) there really has been a 10 standard deviation event [unlikely, there are too many of those to go around], (b) the distribution is non normal, or (c) because the standard deviation of the distribution is actually much higher today than yesterday?
It's a bit of a philosophical question, but is an unusually large return value because the distribution has massive kurtosis, or is it because the vol of the distribution has gone up? Is a negative skewed set of returns because the distribution has massive skew, or is it because the vol of the distribution tends to increase when the market is in an especially bearish mood?
Putting philosophy aside; the question is, how well does vol scaling do empirically? (Nice plot by the way). If I do the exercise of rescaling by recent vol across all the markets in my dataset (since an equivalent of VIX isn't available for everything), it nearly always reduce kurtosis and skew significantly. Sure it will never completely get rid of them, but that doesn't mean it isn't worth doing.
More importantly, the scaling by recent realised vol produces forecasts for trading strategies that have skew and kurtosis properties that are much nicer than the underlying. To take a simple example, the returns from a risk parity position which is short VIX looks a lot nicer than a flat short VIX position...
So I'm not saying you can get rid of this stuff completely, but it does a very good job of flattening things out to produce distributions that are much more pleasant to work with. And it's such a simple step, so why not?
GAT
PS Haven't used R for about 10 years, mostly python since then...
PPS It's ironic that I'm having this discussion at the same time as arguing with other people on the internet who say my trading strategies don't have enough [positive] skew, and I'm not allowed in the pure trend followers club as a result
