Voronoi Tessellation

Was messing around with these last weekend. It basically generates some random points, builds the tessellation around them, then fills each cell with the average color.



Voronoi Evolution from dizzy pete on Vimeo.


Also made some static images

I signed up to twitter

Because I just wasn't spending enough time on the net as it is. Say hello if you are there too dizzy_pete.

Follow me if you're interested in stuff like cool pictures of skateboards and my thoughts about fellow passengers on the bus.

A volatility filter using historical vol

We have been looking at a way to improve risk adjusted returns by using a volatility filter. Although we could use VIX or equivalent, it turns out that historical volatility will work just as well, if not a little better.

You can see part 1 here Digging into the VIX, and part 2 here What can we use VIX for?

Although the mean return of how we slice things is zero, the distribution of returns is wider for higher readings of our relative measure of volatility. High volatility begets high volatility, at least for our purposes.

By staying out during periods of higher relative volatility, we aim to reduce drawdowns and the volatility of our returns, leading to better risk adjusted results.

A plus of using HV over some external measure like VIX is that it is readily available for any underlying. This means such a filtering technique can be applied to whatever it is we are trading.

Performance

Below is a table with two comparisons, the first compares the HV filter to buy and hold.  Although performance is generally better, we still get some pretty big drawdowns.

The second adds in a 200 period moving average, which is a reasonably strong way of protecting against downside. Again we can see lower volatility and smaller drawdowns with the addition of a vol filter.

I used a 3 month/63 day look back for our relative volatility measure. I haven’t really dug in to what happens when volatility remains elevated for extended periods of time.

I also did not experiment much with the threshold for where we draw the line on ‘high’ relative volatility. I use 0.6 as the cutoff because I originally split things into quintiles when making the first charts.

I also ran this for RUT and NDX over the same period

These results are all frictionless, don’t factor in dividends, return on cash, etc, etc. I don’t consider this viable as a standalone indicator, but something that can be used along side other factors like rotational strategies, or as a potential tool if you are looking for lower volatility.

The source is up here, feel free to have a play around with it and see how you go.

Thanks for reading, 'till next time.

What can we use the VIX for?

In part 1, we took a look at VIX and the relationship it had between historical volatility and realized volatility.

Continuing on, I thought I would take a look at next day returns and the VIX. There is a relationship between SPX and VIX in that when SPX drops, VIX typically rises. This leads the question: does a high VIX serve as a useful indicator of what might happen to SPX the next day?

A problem in answering this is quantifying what we mean by a "high" VIX. A VIX of 25 might be high if it has been under 20 for the last 3 months, but might be considered low if it has been around 30.

To deal with this I use a proportional measure based on its previous trading range. If it is at the top of its range, it gets a 1, and at the bottom it gets a 0. Anywhere in between it gets a number between 0 and 1.

I used data from 2000-2013 and a 252 period lookback, which is roughly 1 year, recording the next day return of SPX. I split this data into 5 groups, the first with relative VIX readings up to 0.2, the second between 0.2 and 0.4, and so on up to 1.0. Then I plotted the next day returns as a boxplot, giving the distribution of returns for a VIX reading in its relative quintile.

The box on the far left corresponds to the lowest relative VIX levels, while the box on the far right corresponds to the highest.

One thing that jumps out to me is that the mean of all these returns is more or less zero. Using this relative measure of VIX has no value as a predictor of next day returns, as whatever measure we use, a mean return of zero will see us end up flat (or in practice, probably down a bit). If there was a real edge, we would expect the mean return to be somewhere other than zero.

The second thing that I notice is the distribution of returns is a lot wider for the right most two boxes, which corresponds to relative VIX measure above 0.60, i.e. relatively higher volatility. Now this makes sense, as we would reasonably expect periods of higher volatility to have higher volatility.

It seems that high readings of VIX can serve as a useful predictor of higher periods of next day volatility, and for someone trying to implement a volatility filter, that could be quite useful.

Conclusion

To recap, we have seen that:

1) VIX is not very good at forecasting 30 day realized volatility.
2) Historical volatility can be a reasonable proxy for IV/VIX.
3) Higher periods of volatility do portend continued higher volatility, at least for the short term (1 day).

Note that 3 does contradict the mean reversion of volatility, because it is looking at the next day returns only. Over a longer period we would certainly expect it mean revert, otherwise we'd be experiencing some very, very bumpy rides ...

Also, I did similar analysis using RUT & RVX and NDX & VXN, both of which had very similar results. We will take a look at them in the next post where we use the findings from this post and the previous to implement a volatility filter.

Code for this post and the previous is up: here

Digging into the VIX

I wanted to revisit using some sort of volatility filter for systematic trading. In particular, if we are trading SPX, can we somehow use the VIX to produce better risk adjust returns? This is not about trading volatility, but more about using additional "out of band" data in our systems.

I thought I would take a look at the VIX, what is it, and can it help us?

In theory, the VIX is the market consensus of what future 30 day realized volatility of SPX will actually be, as derived from option prices of SPX. Anyone who watches or trades SPX has seen that a drop in SPX usually results a rise in VIX, or the IV in SPX option chains.

Occasionally this relationship breaks down, which can be a useful as an indicator in itself, but I had a sneaking suspicion that the VIX would have more in common with historical vol than what realized vol turns out to be over the next 30 calendar days. That is, the VIX is not particularly useful as a longer term forward looking indicator of volatility, at least no more than current historical volatility.

I did a bit of data gathering and calculated realized and historical volatility for SPX. I used 21 periods when calculating vols as the VIX covers 30 calendar days, which is roughly a month, and there are roughly 21 trading days in an average month.

First of all, we can take a look in hindsight at how well the VIX forecast of volatility matched the actual realized volatility over the next 21 days.

In this chart, the red line is what realized volatility turned out to be, going forward from a given day. It is impossible to know this in advance, so we are engaging in some serious data snooping, for educational purposes only. The teal line is the VIX. Below them is a plot of VIX - SPX realized vol, and flagrant abuse of gradients.

You can see that the VIX gives an estimate that is typically higher than what actually eventuated, a well-known phenomenon, which for convenience I will put in "The Volatility Risk Premium" basket.

There is one big divergence around the end of July, 2011, when the VIX was significantly underestimating what realized vol would actually turn out to be.  In August 2011 there was a large selloff and you can see the VIX jumped to a rather ebullient level.

If we moved the red line forward 21 periods, we would get historical volatility, that is, the actually volatility that occurred over the last 21 trading periods.

We can see the relationship is much closer. The VIX still generally reflects a premium over historical volatility, but big moves in the underlying SPX correlate to big moves in VIX/IV.

Relations

The correlations between these three measures, IV, RV and HV are worth taking a look at. This is using data from January 2000 up to about the end of January 2013:

There is a 91% correlation between historical volatility and VIX. This is higher than the correlation between HV and RV, and HV is really just RV shifted back 21 periods. It seems the relation between VIX and HV is something quite strong.

Now because these are all measures of very similar things, we might expect high correlation. Another metric we could use too look at the relationship is R-Squared.

We can see a relatively strong relationship between historical vol and IV/VIX, at 0.60. The relationship between IV and realized vol is looking a lot weaker.

Conclusion

From all of this, I concluded that the VIX is not a particularly useful indicator of 30 day future realized volatility. However, it is a reasonable estimate of what historical volatility was.

As it turns out, this is not particularly useful, as we can easily calculate historical volatility. It does mean that we can flip things around, and use historical volatility as a reasonable proxy for VIX or market expectations of future realized volatility.

This will turn out to be quite useful, as we may find ourselves trading instruments that do not have nice, readily available VIX equivalents, but that is a topic for a subsequent post.

So ends part 1. These posts turned out very long so I decided to split them up, part 2 should be available here.

The R code for this and the next post is up here.