Correlation between Historical and Future Volatility
This isn’t a finished thought – just some bits of data from some things I’m pondering at the moment…
In this post I want to look at how well different periods of historical volatility are correlated to different periods of future volatility. Put another way, if I wanted to predict the daily volatility of the market over the next week, month, quarter, etc. would I want to look at the last week, month, quarter, etc. as my guide?
Click on the table below to zoom.
The table shows the correlation between different periods of historical and future volatility, since 1970.
For example, the daily volatility of any two days has been only 28% correlated with volatility of the subsequent two, but the daily volatility of any ten days has been 45% correlated to the subsequent two. In other words, looking at market volatility over the previous ten days has been a better guide for the amount of volatility to expect over the next two days.
We see the highest correlations in predicting the volatility of the next two weeks (10 days) to one month (21 days) using the last two weeks to one month.
I say this is an “unfinished thought” because simply looking at the volatility of period X and expecting it to continue into period Y is overly simplistic; there are more sophisticated ways to go about it.
But I do think this is a reasonable back-of-the-envelope approach. Want to know how much daily volatility to expect over the next one or two weeks? Look at the last two weeks. Volatility of the next month or quarter? Look at the last month. Etc, etc, etc.
Happy Trading,
ms
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Filed under: VIX & Volatility | 16 Comments
The largest numbers are in the middle of your chart: two weeks and a month compared to two weeks and a month.
What this suggests to me is that it takes that long for people to recover from shocks. A shock that creates high volatility will continue to reverberate through the market for 2-4 weeks. If there are no further shocks, by the end of that time things will have settled back down.
That seems like a human estimate of what to make of a shock. How long should we be afraid? It depends on the shock, of course, but 2-4 weeks seems like an understandable time.
RE to Blue: well said sir. That’s a very nice way to put these #’s into words. michael
In weather forecasting, that is known as the “naive” forecast: tomorrow’s weather will be the same as today’s. The interesting thing is that studies have shown that despite gazillions of $$ poured into forecasting technology, once you go beyond a period of roughly 24 hours out, you’re likely to be more accurate using the naive forecast than the one from the National Weather Service!
I suspect that the same effect applies to financial forecasting.
RE to CarlosR: well put and I agree in many instances, but I do think there are more effective approaches than this one for predicting vol. Here’s a long ago post that doesn’t directly speak to this, but is in the ballpark:
http://marketsci.wordpress.com/2008/07/28/the-vix-is-very-predictable/
michael
Michael,
Interesting thought, though I’m having trouble replicating some of the values in the table. Can you expand on the methodology you used to create the table?
My first thought after seeing the table was, “how stable are these correlations over time?” My preliminary tests indicate they’re not very stable, but they’re based on my guesses of your methodology.
Best,
Josh
RE to Josh: I’ll do my best.
First calc the log % change of each day on the S&P 500 index.
Assuming today = t, the historical lookback = h, and the future look ahead = f, for each day since 1970, calculate (a) the SD of daily log % changes from (t – h + 1) to t, and (b) the SD of daily log % changes from (t + 1) to (t + f).
Finally, calc the correlation between all values for (a) and (b).
Hope that helps!
michael
Very helpful, thanks!
Did you happen to catch Dr. Brett’s “bonus post” on pivot points? He posted it as a bonus to current readers for a limited time, so I don’t want to recreate it here, but it might have some useful food for thought for estimating future volatility.
Josh
RE to Josh: I didn’t catch it, but if you think it’s of value I’ll email the good doctor for it. thanks, michael
not sure why you would pursue this approach. Either even a cross-sectional crude risk model (let alone USE3) or a (serial) GARCH model (e.g. the recent “Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity” by Bollerslev et al.) will be more powerful and insightful.
RE to Gappy: as I hope I made clear in the post I agree with you (note bold lettered section). michael
ok. But even playing by these very restrictive rules, I have a couple of suggestions: i) re: reporting: correlation^2, i.e. R-squared is perhaps more meaningful and has closed-form F-test; besides 1-corr^2 is a valid metric between random variables; ii) the way n-day volatility is estimated makes all the difference. Do you use intraday returns, or end-of-day returns over the period in question? The choice of the estimator is also crucial, the reason being that you are estimating correlations between two estimates of volatility, but you are actually interested in the correlation between the true values of volatility; iii) if you yourself to data on market returns, you can identify persistence of correlation by test of hypothesis on the autocorrelation of squared market returns.
RE to Gappy: responses below…
1. fair enough, but a lot more people know have some idea what correlation means than r-squared, and I try to make the posts accessible to everyone (besides it doesn’t take any work to extrapolate the r2 val on your own).
2. good point. everything we do here at marketsci is close-to-close because it’s how we trade, so that’s the only vol I’m concerned with (and the vol. we examined here).
3. expect a follow up post shortly on this sans-hypothesis test. again, have to keep it accessible to the max number of folks, but there are other ways to make the point.
michael