*"A theory has only the alternative of being right or wrong. A model has a third possibility: it may be right, but irrelevant."*

**-Manfred Eigen
**

*"Models are what they are... people who model clothing, that's all."*

**-Kim Smith
**

*"Like dreams, statistics are a form of wish fulfillment."*

**-Jean Baudrillard
**

*Experience without theory is blind, but theory without experience is mere intellectual play."*

**-Immanuel Kant
**

*"The robot is going to lose. Not by much. But when the final score is tallied, flesh and blood is going to beat the damn monster."*

*-*Adam Smith

*"Nice fucking model"*

**-Michael Keaton**, *Beetlejuice*

Although the markets have been filled with uncertainty and it is still unclear of what exactly is going down, one cause for the recent volatility was revealed this week - the failure of "sophisticated" pricing models. In the past few weeks, the "marked to model" CDO's and CLO's have already shown the inability a model has in explaining reality. This week, Statistical Arbitrage funds did the same.

Statistical Arbitrage is a strategy that bets on temporary "mispricings" in securities. Traders usually pair up a long and short position and bet on a convergence to the mean. To further understand this, let's say that in the coin flipping market there are heads securities and tails securities securities and their value is determined by the number of flips a coin landed on heads and tails. If after 20 flips, there were 15 heads and 5 tails, a statistical arbitrageur would most like go short heads securities and long tails securities betting essentially that after 40 flips this would be closer to 20/20. Hedge funds do the same except with real securities and a ton of leverage. In addition, they leave computers to do most of the buying and selling.

"The program trading systems known as 'statistical arbitrage' have been running for years now and have become very popular. Some of them have made billions of dollars by exploiting small statistical abnormalities in the relationships between various stocks. But the problem is that the vast majority of these programs work based on an assumption of eventual convergence, so as more people do the same thing, the spreads between instruments begin to close and more leverage is required to get the same level of absolute return on the investment. These days, many of these strategies run from 3 to 10 times leverage (I've even heard of one which runs at 12 times leverage) meaning for every dollar they have invested, they have borrowed an additional 3 to 10 dollars and invested that as well."

Back in May, I warned about the dangers involved with reliance on "black-box" investing and trading models. I have long been leery of the deification that Quants and Physics PhD's have received on Wall Street in recent years. Applying for a analyst or trading job without a knowledge of C++ and applied math or physics is as hopeless a pursuit as a actually understanding Quantum Physics. Now don't get me wrong, I think most are very sophisticated and have added a great deal to the academic and practical field of finance, but until a physicist can produce an algorithm that with high probability predicts the winner of American Idol on the third night - or even the third from last night for that matter, I will feel uncomfortable with the idea of having them manage much of the world's wealth. Many hedge funds even actively sought to hire PhD's with no history or even knowledge of finance as they did not want any biases introduced into the equations. Those who are students of the markets know that in times of panic, the logic of mean reversion is not a high probability bet.

The failure of these StatArb funds is due to an enormous statistical blunder that is exogenous to the model itself. This error involved the omission of a what is known as a confounding, or lurking, variable. A confounding variable is an extraneous variable that should have been controlled but has been left out. This can lead to the false conclusion that the dependent variable can be explained by the independent variable. The confounding variable in these StatArb funds was that of leverage.

Leverage is something that can significantly magnify both gains and losses. The average investor in a cash account or even a retail margin account could most likely never profitably engage in statistical arbitrage. Going back to the coin flip example - very rarely is there ever a sequence of 1000 flips that results in 900 heads and 100 tails - just as there are rarely blatantly obvious statistical arbitrage opportunities. In both cases, if a reality like that existed it would be more likely that the coin was not fair or that the relationship was no longer valid. StatArb Funds, therefore bet on spreads that are more akin to 550 heads to 450 tails and smaller. The leverage enables them to realize the returns that buy them their houses in the Hamptons. As this strategy gained popularity, and more funds entered the space, more money chasing the same statistical anomalies caused the best they were making bets to be closer to 525 heads and 475 tails and then 510 heads and 490 tails, therefore more leverage was needed to maintain the widespread success (as Derbyshire points out above). This has had the effect of situations like the 900/100 example above masquerading like 600/400 situations - where are much more likely to be a statistical anomaly than a different reality - a reality that was realized this week.

The models themselves, as predictive in isolation as they may have been, once put into practice by others becomes more and more useless. The effect of increasing leverage acts to magnify what may be diminishing expected gain until of course it becomes a loss, which then is magnified quickly - convergence is finite, but divergence infinite in theory.

StatArb fund managers and the investors who have their money with them should have learned this week, that the success has not been due to the models or the high priced "quants" who developed them, but to the prime brokers who continued to give the funds leverage - squeezing more and more juice from a lemon until the lemon imploded into a black hole - something one would think the quants, if anyone, should have predicted.

Quants have been hurting lately, they are starting to get a bad reputation...but then again almost nobody claims to be a straight quant shop anymore they all have active touch points/controls along the way.

R

Posted by: Hedge Fund Consultant - Richard Wilson | December 20, 2007 at 12:08 AM

My favorite megaupload files search engine is http://megauploadfiles.com

it’s the most powerful and easy to use.

megaupload files

provides relevant search results.

Posted by: turbopidar | May 27, 2008 at 12:06 PM