Awhile back, Rod pointed out in the comments section of the post about Thomas Cover's Universal Portfolio Method that information theorists seem to do conspicuously well in the market. A recent post by Ernest Chan documents the same idea. Here's a theory why.
The Evidence:
- John Kelly, inventor of the Kelly Formula, called Fortune's Formula for some of the apparent fortunes it has helped produce.
- Claude Shannon, the father of information theory, and Ed Thorp, whose returns rivaled those of Buffett and Soros. Claude Shannon also came up with the Shannon Method.
- Elwyn Berlekamp, whose college advisor was Claude Shannon and whose hedge fund had approximately 46% annual returns from 1990 to 2001.
- Berlekamp's fund apparently became part of the Medallion Fund, run by Jim Simons, Super Quant, cryptoanalyst (a subset of information theory) with 35% annual returns since 1989.
- David Shaw, computer scientist (which uses information theory heavily), Super Quant, whose annual returns average more than 20%.
- Thomas Cover, author of books on information theory, who started a hedge fund, bears watching, but as far as I can tell, his returns aren't in yet.
The Hypothesis. Information theorists are ideally suited to understanding the voting machine part of the market, where short term fluctuations are found. They aren't ideally suited to the weighing machine aspect, because they don't necessarily have an accounting background and a good grasp on the managerial aspects. Efficient Markets guys are typically economists and claim these fluctuations are "random," a product of a random walk. The information theorists know better, however, because randomness is an integral part of information theory. While many have an intuitive sense of what randomness is, it's the information theory guys that come up with the definitions of what randomness really is. Who better to identify randomness (or lack thereof): economists or those who spend their days thinking about it as well as how to produce it? (In defense of the abilities of economists, read this). The markets may be chaotic, or a complex system, but they are definately not random. It's my belief that the information theory will be used to precisely define how efficient a market is rather than an economist's conjecture that markets are efficient because "traders are rational." Anytime you tell them something is random, they sense it is not, and know they have an edge. They are drawn to games/markets like kids to candy.
More to the point, these guys spend their time figuring out ways to process signals, and find signals in noise. Find the signals, and you can predict them. Financial market data is nothing but another signal to these guys. They find patterns in data and use those patterns to compress the data. In Thomas Cover's words regarding his hedge fund philosophy:
Thus universal investment algorithms are a counterpart to the universal data compression algorithms used to compress voice, fax and computer files.
It's an information feed with an information entropy. The Kelly Formula has been completely hijacked in usage by the gambling community (fueled by Kelly himself), but was really started out as a way to deal with noise over long distance telephone lines. They investigate signal (information) correlations - who better to find correlations between market signals. Cryptography is a branch of information theory. The markets are simply a cipher to be cracked. Much of this is done with advanced mathematics, and these guys are well-equiped to easily understand the math behind derivatives. They are the rocket scientists of information mathematics, and mathematics is the science of pattern.
Third, they almost universally know computers and how to program them to put their ideas into action in the game/markets. They were some of the first to use computers and in some cases influenced computer development. Computers are perfect tools to implement their algorithms.
Update: In Berlekamp's own words:
No one who has made a legitimate fortune in the markets believes the efficient-market hypothesis. And conversely, no one who believes the efficient-market hypothesis has ever made a large fortune investing in the financial markets, unless she began with a moderately large fortune. Of the stories presented in Fortune's Formula, the case of Ed Thorp presents the greatest challenge to the efficient-market hypothesis. Poundstone devotes only a single paragraph to the even stronger cases of Ken Griffin, D. E. Shaw and Jim Simons, presumably because financial wizards as successful as these have always been unwilling to discuss their formulas in public.
Update II: Next come the physicists.
Indeed it seems that information theorists do very well in the market, especially Shannon and Berlekamp. Even though I pointed that out, and despite Ernie Chan's claims, I guess we may be missing the point here.
Shannon and Berlekamp are/were geniuses, the kind of people that can be insanely good at many things. Shannon was notorious before he came up with his seminal paper on information theory, and then when he published the paper he became a super-star. Berlekamp is known as the "greastest post-Shannon genius" for a reason. I believe that Information Theorists have an edge in that they possess a rather deep knowledge of probability theory in an applied setting: they study probability theory using practical applications which are rather varied. Maybe many geniuses in math are not particularly fascinated by "applied stuff" and shy away from anything which is remotely related to the real-world, like finance, in which the purpose is to make money, rather than pursue mathematical beauty. This might sound a bit weird, but I have some friends like that...
About Jim Simons: cryptoanalysis doesn't have much to do with Shannon's information theory, but rather, it has a lot to do with abstract algebra which seems to be the last thing to find application in finance. Simons is doubtlessly a very smart guy, but let's not get blinded by the "cult of genius": it's not Simons who makes money for Renaissance Tech, it's the people he hires... all those really smart guys who excel at many things. They don't have to be information theorists.
About David Shaw: he got into finance because he used to build supercomputers for a living in the mid-80s, the exact period when Wall Street started to see a competitive edge in massive computational power. He's into distributed computation, efficient and fast algorithms, and stuff. Not quite information theory, I'd say. Just like in Simons' case, D.E. Shaw makes money because of the brilliant people it hires, not because of Shaw's knowledge of information theory (I doubt he's an expert in that).
About Thomas Cover: well, he's the Information Theory God, no question whatsoever. I will be looking forwards to see how he performs. But since in his book he dedicated a full chapter to the markets, I believe he's got some good chances of coming out winning.
I am not saying that information theory is useless. Information theory is very important, but so is optimization, so is distributed computation, so is grid computing, etc
The guys who made money by doing statistical arbitrage for a living did succeed because they hired the best in different critical areas, not because they knew a lot of information theory.
Having a beautiful algorithm which takes too long is useless in a market place which is more and more burdened by hard real-time constraints.
Just my 2 cents...
Posted by: rod. | March 23, 2007 at 03:52 PM
I have posted my comment plus other stuff at:
http://stochastix.wordpress.com/2007/03/23/information-theorists-beat-the-market/
Posted by: rod. | March 23, 2007 at 05:08 PM
Rod,
Good post. I certainly didn't mean to imply information theory is the only way or even a way to succeed in the market - just reasons why information theorists could have an edge. I do think anyone with a signal processing, mathematical, physics or similar background can do just as well if they really apply themselves. Signal processing seems quite relevant as well.
Simon's Renaissance certainly takes this approach, hiring all sorts of geniuses from mathematicians to astrophysicists. Simon's firm is very secretive, so it's hard to judge what aspects of Simon's background has impacted the firm's results the most. Certainly his employees have been responsible for most of the money minting of recent vintage.
Shannon, as portrayed in Poundstone's book, Fortune's Formula, seems to be one of those tinkerers who just liked to be challenged. From building robots to roulette computers way ahead of his time, I suspect he was bored easily after solving something. As evidenced by the uncashed paychecks piled on his desk, money wasn't too important.
As far as having algorithm which takes too long, you are correct, but coming up with a money-making algorithm in the first place seems to me to be 90% of the challenge!
Posted by: Alan J | March 26, 2007 at 12:22 PM
Alan,
I guess my response was a bit "over-emphatic". You suggested that information theory people were doing good in the markets, and I came up with a huge text on that. My reply was broader, in the sense that the point I was trying to make is that there are many fields of knowledge which are relevant, and that sometimes one can be "fooled by randomness": by looking at 3 or 4 guys from information theory who did well, one might forget the 900 or 1000 that failed.
Success is great, but one usually learns more from stories of failure than from stories of success. Maybe that explains why I like so much all those big meltdowns: Enron, Amaranth, LTCM...
I suppose I am a bit like Shannon, only a hell less smart than him. Solving smth is the motivation, then it gets boring. If money motivated me above all, I'd have become an accountant, not a applied math kinda guy, ha ha ha
Posted by: rod. | March 26, 2007 at 05:04 PM
Rod,
We certainly don't hear of the information theorists that failed in the markets, however, I go back to your original comment that they seem unusually overrepresented in the small club of people that have successfully beaten the markets that we know of.
You are absolutely correct about failure as well. The thing about managing other people's money is that you don't typically get but one opportunity to fail, so it's best to learn from other's mistakes as much as possible rather than your own, which make Shaw's, Simon's, Berlekamp's and Thorp's relatively long-term achievements all the more remarkable.
As far as Shannon goes, I've left more than one uncashed paycheck on my desk, lol. I am always seeking out challenges and realize I need to get paid for solving some of them!
Posted by: Alan J | March 26, 2007 at 06:53 PM
I totally agree.
It reminds me of an old saying which went approx. like this:
"the key to success is to hide your failures and flaunt your achievements"
it sounds strange, but it works...
these highly successful guys get so much addulation that they start to believe in that whole bullsh*t. Everyone makes mistakes, and I would learn more from these top-notch dudes if they talked about what they did wrong other than what they did right, ha ha
because if you one does smth right, it's done...
if one does smth wrong, one learns and does it again and again until it comes right...
in the meantime, know-how has been gained. It's a shame that society does not promote the right for "creative failure"! Seriously!
Posted by: rod. | March 27, 2007 at 09:07 AM