Cockroach Theory and Levy Flight
Wednesday, August 11, 2010 at 2:30PMWritten by Michael Bigger. Follow me on Twitter.
Seth Godin wrote a fabulous blog post about a cool mathematical concept called the Levy flight that shows up in nature (Wikipedia: Levy Flight Description).
It also shows up in finance.
A journalist finds an interesting story to write about. Think about Merck and Vioxx. That was big business
news, and it stirred up emotions. Many people took a stance on both side of the issues related to this event. Writing about Vioxx generated good readership and sold advertising. Eventually, readers got bored with the story and moved on. Our journalist had to find other news. The journalist’s path follows a Levy flight from one random walk to a cluster followed by the same process over and over again, as depicted in the image (Source: Wikipedia).
Or you can think about it this way: the path between each cluster is a stochastic directional vector and the cluster is a manifestation of the cockroach theory. This theory states that if you find a roach in the cupboard, more than one is usually crawling in the same location. Using Godin’s example, once an animal finds food along its random walk, the animal will rummage in the same area because the likelihood of finding more food is elevated.
For traders, investors and algorithmic traders, a few things are of interest here:
- What is the relationship between a cluster and volatility?
- As journalists migrate from one story to the next, is tension being released on the system? Is that a form of catalyst (value trading and volatility trading)?
- What are the roles of traders or investors in these situations? Do they also become news amplifiers within the cluster? Do they contribute to the catalyst after the cluster disintegrates?
- When a news cluster starts forming, could monitoring social media, finance groups, or other venues help predict entry into a cluster or an exit from it?
- If so, could we use Internet message analysis to incorporate jump function into a Brownian process?
- If the cockroach theory is such an important part of behavior, do market participants under appreciate it?
- If so, how do we exploit it?
The Levy flight is worthy of further analysis. I can see a few ways to incorporate this concept into our algorithms right now.
When the next “Vioxx” crisis erupts, I will remember that journalists will eventually walk away and let it go. The news will subside as it always does. Benjamin Graham once said this: “This too shall pass.”
Since I wrote the original post, we’ve used this mental model to sell volatility on Goldman Sachs when the fraud scandal erupted in April 2010. You can read more about it here: Levy Flight, Truffle Diggers, and Goldman Sachs. The trade was highly profitable, and we unwound this trade in early July after the truffle diggers got bored and moved on to another story. The Gulf of Mexico became a much more powerful story to cover.
Recommended reading: Linchpin: Are You Indispensable? by Seth Godin (Amazon Affiliate Link).
Let me know what you think.
Reader Comments (9)
Interesting post, glad this caught my eye on the twitter feed... for the questions, i presume volatility related to the cluster is positively correlated; so taking as an example a stock which happens to fall in the cluster of (news event; earnings play; any catalyst) we can assume all focus is on it, thus increasing vol.
For traders and investors, could one theorize they cancel each other out? If yes, we can assume the short term traders will buy a stock after a dip of a bad e/r to scalp a few pennies, whereas the investor will dump after a disappointing long term outlook. Conversely however, when do investors and traders amplify this cluster volatility? An investor likes future potential of XYZ while a trader wants to chase the momo coming in?
I guess the only real question, as you point out, is how do arb this to our advantage, before the 1000-line a minute scannings computers do - OR, then again, how do we create a BETTER computer to do this for us:)
PS - i understand selling vol on GS was profitable... did the same trade on BP work just as well?
nice post bigger!! thanks for sharing this.
Great post again. I wonder how this relates to wheat currently? Lots of headline chasing.
PowerZero. Thank you.
You make great observations. I do believe that some people get information ahead of others. I read somewhere that usually translates into an increase in the frequency of internet messages. So at a minimum, I think it is important to keep the pulse on the companies you have a position on. We monitor message frequency on about 4500 companies at Bigger Capital. That is just too much information. We are implementing new messages algorithms to better sort these things.
I think the way I envision trading around the cluster is to increase position when you sense that market participants are starting to get bored with the story. If you are short volatility and can detect that something is going on (entering the cluster) , you might want to reduce the position or buy some gamma.
In the case of BP, it was easy to convince yourself that the company was toast. I did that and I even sold a call spread on it (small). I lost money. I should have stayed on the sideline at a minimum.
ppearlman. Thank you.
John. Thank you. I almost shorted your market on that huge spike but I stayed on the sideline because I don't know the wheat market. I do believe you are in a cluster and that too shall pass. You might want to look back and see how long do these episodes persist historically.
Interesting article. The Levy Flight phenomenon with regard to the markets has been discussed for some time (e.g. _Chaos and Order In the Capital Markets_). In addition to clustering it also drives fat-tail serial correlation events -- market moving events.
I just have a minor quibble. You wrote:
> When the next “Vioxx” crisis erupts, I will remember that journalists will eventually walk away and let it go. The news will subside as it always does. Benjamin Graham once said this: “This too shall pass.”
This is not quite true. It depends quite critically on the number of cockroaches and the nonlinear cascade effects. To continue the analogy: Sometimes when there are cockroaches in the pantry and you discover there isn't just one, as you work through the cluster you end up calling in the exterminator for the whole house. And for termites, the immediate reaction may not be a cluster at all but a pause and then whole-house fumigation.
More recently, what the last 4 years have shown is that the cockroaches in the credit/housing bubble have infested the entire structure, and the result has been not a V-shaped selloff-rebound but a prolonged slump (at least in residential investment and I expect in commercial RE investment as well).
I think we've got termites in the financial system and that whole system needs a fumigation aka systemic reform. But here's the critical thing: the journalists keep returning to that cluster. Just because they've left a particular issue at some point, doesn't mean that there isn't more food there to return to later. It's just that the appetite of the readers (or advertisers!) for more bad news may be limited.
Selling volatility and/or placing news-driven bets only works when you can be very confident that the downside damage can be (in Bernanke's words) "contained".
Wisdom Seeker,
You make interesting observations. Each situation is different. Let me give you two examples: Gm and Crocs. There was an intense news cluster surrounding GM but that did not give it value. If the company is bankrupt, it is bankrupt. On the other hand, Crocs was a totally different situation. In August of 2009 a journalist at The Washington Post declared the company bankrupt although it had very little debt and plenty of cash. It did not make sense and one could exploit the fallacy.
I ask many questions in this piece and I suggest that the Levy Flight deserves further analysis. We are experimenting with this concept and we are very excited about its potential.
The Random walk and the possibility of finding food, MUST [not Should] INCLUDE THIS IN THE EQUATION:
Who left the food at that point...
in order to the Sharks find it out?
Sharks will be Random no more...
they will come back for more...
BECAUSE THEY DO NOT THINK!!!
BUT... WHOEVER LEFT the food, [I call them The "Ones" ],
they sure know "the-why" food is there...
AND... they sure know, that will come a lot of more Sharks
AND... they sure know, when to leave no more food in that spot
AND... move it over ANOTHER PLACE.
So... where Sharks will go now?
Almost all of us are Sharks when trading...
or...
you are one of "The-Ones"???
So... The Random walk is true; that's why "The-Ones" know where/how to feed them.
EQUATION without The-Ones" is INCOMPLETE...
...and deserves further analysis!
Be Good and Healthy!
@francaselles
Thank you!