# From The Small To The Big: Earthquakes, Avalanches, & High-Frequency Trading

Submitted by World Complex blog,

I've been talking about scale invariance a lot lately. I became interested in the topic quite a few years ago in the context of geological phenomena like earthquakes and avalanches. The Gutenberg-Richter law describing the size-frequency relationship for earthquakes was one of the first natural laws based on scale invariance, but interest in the topic really picked up with the Bak et al. paper in 1987 (pdf - may only be a temporary link).

The cause for this relationship is still foggy, as is the physical mechanism between the small and large earthquakes. The best proposed explanation is that the scale-invariant distibution of events allows for the most efficient flow of energy (and information) through the system (but it isn't clear why that should be so).

So back in the early '90s I was estimating recurrence intervals estimates for certain hazardous events and I started trying to work out a methodology for detecting scale invariance in the geologic record. Using the Gutenberg-Richter Law, you can estimate the likelihood of a large earthquake in an area based on the number of small earthquakes. There were interesting implications for areas where the recurrence interval of large earthquakes is longer than the local recorded history (as in much of Canada). At the time, there were seismic hazard maps produced by the USGS which showed significant earthquake risk in zones which mysteriously ended right at the Canadian border.

One of my classmates in my undergrad days (we're back in the 80s, now) studied the correlation between microquakes and fluid injection at oil extraction operations in southwestern Ontario. The oil companies were surprisingly cooperative until they understood the point of the research, after which they started to withhold data.

And here is the mystery. The principle of scale invariance in earthquakes would suggest that increasing the number of small earthquakes should increase the number of large earthquakes at least in the short term. Yet our understanding of the dynamics of earthquakes tells us that lubricating the fault should allow stresses to be relieved through the small earthquakes, which in the long-run should reduce the chance of a large quake in the longer term. (This idea has been proposed at various times over the past fifty years, but for various obvious reasons, it has never been deliberately pursued).

By the early 2000s, other geophysicists (notably Didier Sornette, but there were others) had moved a portion of their data processing expertise into studying econometric time series. I made this move later as I gradually came to appreciate the key problem with developing quantitative techniques when the data were suspect. First of all, the measurements themselves are inaccurate. More importantly, our estimate of the timing of each observation was just that--an estimate. Most quantitative methods assume that the observations are evenly spaced in time. Failing that, they assume you know the timing of your observations. The consequences of errors in the timing are terrible, and frequently underestimated. The point is that it is difficult to develop excellent quantitative methods when the data are terrible.

The big advantage of working with economic time series--pricing data, in particular, is the elimination of the observational errors. When a transaction occurs, there is no doubt about either the price of the time--right down to the millisecond scale.

I started looking at market macrostructure--because (several years ago) nothing interesting ever happened on a scale of less than about an hour. Until just the past few years. Suddenly, strange, rich, unusual behaviours began to occur in individual stock prices, and even indices, on the millisecond scale. I didn't know what was causing it--but it sure was interesting.

Three seconds on the tilt-a-whirl.

This was the signature of onset of HFT. I was initially interested in it for entirely different reasons than most of you. After Crutchfield's (1994) paper (pdf) on emergence, I had been pondering the idea of how to recognize a fundamental change in a complex system. Again, my interest was in the earth system as a whole, and how to recognize whether or not new observations were pointing to a fundamental change in its mode of operation.

Given our understanding that the number of large avalanches is positively correlated to the number of small avalanches, it seems pretty clear that (as Nanex and Zerohedge has been saying) the damaged market microstructure is mirrored in the increasing number of flash crashes since Reg NMS. Unfortunately, our murky understanding of how the microstructure causes the macrostructural changes can be used by the regulatory authorities to avoid investigation. They can't see a smoking gun.

We would normally expect the micro-crashes to eventually relieve imbalances in the system, improving its long-run stability. (Perhaps this is how the SEC justifies the practice). But unlike earthquakes and avalanches, these uncountably many small crashes are not reducing the imbalances. One reason is that the cause of the imbalances is separate from HFT--the dollars keep being shoveled to the top of the mountain as fast as, if not faster, than HFT brings them cascading down. Another reason is that the trades (mostly) get unwound--so the exchanges push most of the snow back to the mountaintop after the avalanche.

HFT certainly benefits unfairly from the system, but isn't responsible for it. If anything, it is a symptom of corruption--but the cause of the corruption is elsewhere.

Accordingly, my modest proposal for dealing with HFT is this--nothing. Don't bust trades--let them stand. I'd be curious to see the response of the various Ivy-League endowment funds and pension funds when they suffer brutal, near-instantaneous, multi-billion-dollar losses. At a guess, I would probably hear the screaming up here. How would real companies, producing real products, react to a sudden monkey-hammering of their stock price, especially if it triggered debt covenants? Maybe they would all exit the market en masse. It might even force a real change.

## Comment viewing options

been waiting for another since May 2010, always the bridesmaid...

Earthquake Swarm In LA Is Sending A HUGE Message

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http://stateofthenation2012.com/?p=4676

Won't ever happen.

It's...it's...unAmerican!

Piles of money sliding down the hillside.  Good visual.

I suspect the sociopaths winning now won't want to change anything tho.

Sound good to me

Correlation=0... fail

"We would normally expect the micro-crashes to eventually relieve imbalances in the system, improving its long-run stability."

That is a normal expectation of an entropic system (one that desires lower engery states); and one where the pressures build and then relieve in dislocations.  I'm not so sure a "market" follows those basic rules, whether free or rigged.  What exactly is "pressure", and what is "relief"?   The spaghetti bowl graph of one of your "micro avalanches" might just be a collection of HFT algos stumbling into each other and triggering a chaotic war for bit, but on their time scales of milliseconds...    If so, to interpret that as a "market" edging towards collapse is maybe more than a small non-sequitur...

Agree....we are dealing with people which means fear and greed are the 2 drivers....a series of small crashes might just make folks scared of a big one and panic them so that the next small one starts to grow into 'the big one'....to paraphrase Red Foxx.

Interesting concept. There have been more then a few occasions when I was watching porn (chart, that is) and noticed sudden alterations in action. It's almost as though you can see when the algo's are working against each other or perhaps sellers/buyers, and when everyone is doing a merry jig to the promise land together.
You have to agree with the general premise of the article mind you, if you want efficient/effective markets you have to allow for the natural laws of pricing to occur. The fact there has been such an obvious effort to maintain an upward trajectory at all costs is an statement in itself. What's at stake here? Does anyone actually know the extent of the distortions that have been created?

An attempt to correlate a physical avalanche with "mining" cognitive expression via even behavioral economics is a stretch. No, correction... it's not a stretch, it's a Nudge. Cass and Samantha would be proud. Nice try. Next Hegelian synthetic solution provider to the "Flash Boyz" dilemma please take the stage.

This engineered HFT media planned demolition is about as staged as American Idol or Shark Tank. Whodathunk you can build instant SIFI scapegoats for the impending reset with 3D printers conveniently after the complete rebuilding of the primary dealers balance sheets. By the way, if you were flying a gold filled plane from Ukraine to China would you transfer to a Chinese code share flight in Kuala Lumpur?

Accordingly, my modest proposal for dealing with HFT is this--nothing. Don't bust trades--let them stand.

Well Goldman would be bankrupt if that happened... so it probably won't happen until GS mgmt is in jail.

I came to the conclusion that this will fix itself at some point. When the sharks have eaten all the minnows and the water is thick with blood, then the sharks will turn on one another and things will get very ugly.

Exactly. Great post. Make people responsible for their stupidity. I don't need busted trades to survive because I do risk management. If the trade goes bad, that is my problem.

Knight Trading was the best thing ever to happen. HFT volumes dropped instantly because they were scared they would have to wear the trade, Then the SEC said, not so much, and it was on again for all.

By having the SEC or the Feds forever backstopping things for the big boys it just sets us up for an eventual magnum crash since risk gets ignored.

Totally agree with the author's point of view...if you are getting the reward, then you also get the risk.

I said that long ago,  Your computer makes a Mistake, you live with it.. so be carefull what you alow your computer to Do...

now how many shares of stock at XYZ + .01% do you want times infinity again

There is never a shortage of excuses for regulatory agencies to do nothing in the face of massive frauds on the part of big participants in the markets.  This is another example.  I would suggest that, rather than seeking "automatic" solutions to market misbehavior, the regulators find their anatomy and start acting to preserve the integrity of the markets on behalf of the public and the institutional investors acting on their behalf.  An obvious solution to the high-frequency parasitism would be to reinstall the transaction taxes that, years ago were applied by New York State to Wall Street.  Only this time the tax should be applied at the federal level and include the placing of quote requests as taxable transactions.