Volatility Clusters -

Summary:

  • Volatility clusters, which means it can be, to some degree, predicted
  • that means that a big part of your returns can be predicted, since
  • Returns
  • Geometric Return = Arithmetic Return – Volatility^2/2

Volatility Clusters. The concept often causes strange reactions in people.

So many think the market is totally unpredictable, that no part of the market’s behavior can be forecasted. I believe this is essentially true for returns, but it’s not true for how choppy and bouncy those returns are. Volatility is partially predictable because it clusters.

At one level, I think this suspicion comes from so little being written on this topic1 and a lot written on market randomness. There are papers exploring the volatility clustering, but they are always very mathematical, normally using very fancy equations and very fancy words like stochastic, kurtosis, GARCH, autocorrelation, heteroskedastic, etc., and often behind academic paywalls (just look at the footnotes in wikipedia ).

Volatility Isn’t Tangible

Volatility is kind of like electricity where we can understand it, but because our senses don’t often experience it, you need a bit more to truly understand how it works. You can’t really see electricity, you can’t really hear it, you can’t smell it, and you can’t taste it.

You can feel electricity, but usually through a shock. Volatility is also normally experienced through a shock.

And I think this is why we struggle with the idea that volatility clusters. We don’t really pay attention to small levels of volatility. We just don’t sense it. We also look past upwards volatility. There is no pain, so we don’t really view it as volatility. But downward volatility, that shock we feel. It leaves a scar, and it feels often like it came out of nowhere.

But it didn’t.

Let’s see why, and since it’s so important for your senses to experience this, I’m going to show you that you can see it if you’re looking in the right place.

Polls

To see how volatility clusters, I’m going to show two graphs. One is a real investing asset over at least a decade of time. The other is a randomly generated data set. The random data will be randomly distributed with a Laplace distribution with the exact same standard deviation as the real data set. I chose the Laplace distribution for reasons I will get into in a later post, but for now, just know it better mirrors actual randomness in stocks than a normal distribution because it has fatter tails.

The charts show the absolute value of the daily returns. This way, our eyes can’t focus on up vs. down. We’re just looking to see how much the investment moves each day. Big moves, tall bars. Short moves, short bars. Nothing is directional, everything is a measure of absolute change.

Let’s test if you can identify charts where volatility clusters. Choose the graph you think represents an actual investment.

Set 1

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Set 2

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Set 3

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Set 4

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Set 5

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Set 6

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Answers

Notice that wasn’t very hard. It’s fairly easy to see that the absolute movement in an investment isn’t random, that it clusters together.

Here are the real charts:

Set 1: The top chart is the S&P 500 from 1990 to 2021 Set 2: The bottom chart is Exxon from 1965 to 1985 Set 3: The bottom chart is TLT from 2002 to 2021 Set 4: The bottom chart is GLD from 1968 to 2017 Set 5: The top chart is Apple From 2001 to 2021. Set 6: The bottom chart is the Dow Jones Industrial Average from 1900 to 1940

Deeper Dive

Ok, now that you know you know volatility clustering exists and that your eyes can see it, let’s dive deeper.

Wide Valleys

Notice that there are long wide valleys where there are never any spikes. The price changes are low for years and years. A random sample couldn’t possibly go a full year without a single day registering a move of 2 percent (twice the long term standard deviation), yet there are countless examples of this behavior.

Calculations are my own.

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Very clearly we see that low volatility clusters, and these environments can last for years.

Mountain Peaks

Also notice how there are clustered peaks. Groupings where the volatility climbs and peaks out and then fades away, creating little mountains on the chart.

Random volatility doesn’t do this. Sure, you may get a few places that have a similar look, but nothing so prominent.

Calculations are my own.

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It’s very clear that high volatility clusters together, and isn’t spread out evenly through time like random data.

Changes Aren’t Instantaneous

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Calculations are my own.

When the random sample has a spike, the next samples usually register back down around a “normal” level. The spike is simply a single spike. It’s random and the next values are not also elevated (go back and look at any of the random samples above for an example).

Yet market data never drops right back down to a normal volatility level after a spike. It may head back downwards towards a normal level after a spike, but it does so in a slow bleed over time, not right away.

Secondly, notice that the spikes in the market data don’t arise out of nowhere like they can in random data. The volatility always climbs first going into a big spike. It’s not a purely random black swan type event with no prior signal as it often feels.

1987 Volatility

I want to dive into the specifics of 1987 to emphasize this point clearly. I purposefully didn’t include 1987 in any of the poll questions above because I wanted to give the random data a fighting chance to fool you. But let’s look at it now.

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Calculations are my own.

The crash of 1987 is often represented as an event which came out of nowhere. A random day which couldn’t possibly be understood or anticipated. But is this really true?

Notice that volatility in 1987 was rising for days into Black Monday. The days before October 19th moved an enormous amount. They had very high volatility. The days before Black Monday had already set historical precedents.

Watch this video from the classic show Wall Street Week. Look at how the prior couple weeks were described the day before the crash.

Calculations are my own.

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So even the largest single day percent drop on record for the US stock exchanges, wasn’t really as random as it seems (notice too the reference to prior 3 straight years of low volatility).

Recent volatility was very very high going into that weekend. Black Monday didn’t come out of nowhere. Yes, the volatility came on quickly, but the weeks leading up to black Monday had already started to scream that volatility was high.

Volatility was clustering.

2020 COVID Crash

Calculations are my own.

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What about the 2020 COVID crash? Surely that came out of nowhere. Well not really. In some ways it was was slower than 1987.

Notice the low volatility at the start of the year and then the rise in late February, before the real fireworks arrived in the middle of March. February 24th was a bit sudden, but there clearly was a volatility regime change on from low to high a couple of weeks before the major volatility arrived.

High volatility doesn’t come out of nowhere. It builds, which means it doesn’t need to take you by surprise if you are paying attention.

Autocorrelation of Volatility

I’ve kept numbers out of this discussion until now, but I’m sure some of you want some actual stats to support these claims. So, to keep this as simple as possible I will show the correlation of absolute returns from one day to the next.

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Calculations are my own.

Day to Day correlation shows a statistical relationship between one day’s absolute return to the next. If the absolute return from the prior day correlates with the absolute return on the following day, it means future volatility depends at some level on prior volatility. If the correlation is near zero, then there isn’t any predative behavior. And if, by some chance the correlation is negative, it means volatility is somewhat mean reverting.

As we’d expect, the random data show no correlation from one day to the next. But the real data paints a very different picture. It shows the next day’s absolute return is partially correlated with the present day’s absolute return. 2

Today’s volatility holds information about tomorrow’s volatility.

Average of Past

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Calculations are my own.

Let’s expand this analysis. The prior example took a single value and tested it to see if it projects onto the next value. Single input values can be very choppy and well, random. So let’s smooth the input out a bit and take an average of the prior 5 days, and see how that average correlates with the next day’s absolute return.

Once again, absolutely not for the purely random data. But even more emphatically yes for the market data.3

The future volatility dependent on past volatility.

Aspects of the Market are Predictable

Now if you want to, you can go find academic papers on this topic4 and learn far more about Hurst coefficients and other ways to measure how volatility clusters. I’m going to leave that to those papers as it will probably put most people to sleep. What I wanted to do here was let you see with your own eyes how volatility clusters; see that it doesn’t come out of nowhere, and it doesn’t just disappear at the drop of a hat. Furthermore I want you to see that simple mathematical calculations prove that prior volatility does in fact partially predict future volatility.

Is it perfect. No. There is still randomness here. It’s just not pure randomness. The past informs us about the future.

You can make an educated prediction for near-term volatility.

Investing Revelation

Now pair this knowledge with your already strong understanding of the geometric return. Notice that half the equation for determining your long term wealth is actually fairly predictable.

Geometric Return = Arithmetic Return – Volatility 2 /2

Not everything in markets is purely random and unpredictable. Today’s volatility influences future volatility. When you fully grasp this concept, it will change your view of investing forever.

Footnotes

1-My friends at the Munity Fund have a great article on this concept that is very accessible to everyone.

2-I included individual stocks to show that while they may show less tendency for volatility to cluster, it still happens.

3-Correlatoin is a ratio of variances, so in a way the square root of the correlation tells you the ratio of correlation between standard deviation, which for many of these would be over 50%.

4-Maybe the most accessible technical source is Mandelbrot’s book, The (Mis)Behavior of Markets.

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