A Review of "The Quants" by Scott Patterson

The word "quant" is short for quantitative analyst and refers to people who use mathematical models in finance to predict the time course of the price of assets and, on their basis, devise trading strategies. Hedge funds rely heavily on quants.

The book combines a narrative of the lives of several quants with an attempt to explain what quantitative trading means and how it affects the markets and how it contribute to the 2007-8 financial crisis. The author does not seem to know much about mathematics and as a result, his explanations are weak. However, he succeeds in conveying the main points and the interlacing with the personal stories livens up the reading. I have no background in finance but I have some background in probability theory and statistics and I found the book worth reading, although often I had to use my own understanding of statistics to decipher what was going on.

Patterson traces the history of quantitative analysis to the book "Beat the Dealer" by Ed Thorp that describes how to win in blackjack. A few years later Thorp co-authored the book "Beat the Market" and the race was on. The author correctly highlights the casino gambling origins of the quant strategies. A big step towards the spread of quant strategies was the Black-Scholes option pricing formula that is discussed repeatedly in the book. (A personal aside: A few years ago I did some consulting for a small company and, because they were short on cash they offer to pay in options using the Black-Scholes formula to convert the dollar amount of my bill into options. A couple of years later I noticed a rise in the price of the company's stock and I cashed in my options receiving almost three times the amount of my original bill. It also happened that the rise in the price of the stock was only temporary. Even though things turned out in my favor I lost respect for the formula. )

One of the favorite strategies of the quants has been arbitrage, taking advantage of the fact that prices for the same commodity are different in difference places (or in different "packages" of the commodity). Discovering such discrepancies through mathematical analysis and taking advantage of them resulted in billions of dollars in profits, for a while. The trouble was that, as more and more people knew about the discrepancies the discrepancies tended to shrink. (Arbitrage relies on imperfect information.) In order to maintain high profits the quants relied increasingly on borrowed money (leverage) a strategy that magnifies both the profits and the losses.

In other words, institutions took the mathematical models of finance too seriously and, by assuming that they were infallible, they engaged in risky investment strategies. As long as the models held profits were high. But when the models failed the losses were huge and government bailouts were needed to ensure the survival of the financial system. On p. 99 Patterson quotes Soros on the occasion of the collapse of the LTCM hedge fund: "The increasing skill in measuring risk and modeling risk led to the neglect of uncertainty at LTCM, and the result is you could use a lot more leverage than you should if you recognize uncertainty."

I did not expect to find from the book the precise technical reasons why the models failed. That knowledge should be worth a lot of money and I did not think anyone would it away in a book. (Interestingly, the hedge funds that have done best in the latest crisis are also the most secretive according to the book.) Patterson points out a major weakness, that the statistical models under estimated the probability of rare but catastrophic events. Why this was so has different explanations, the most popular being that it is hard to model human behavior that plays a big role in the markets. The importance of human factors has been the subject of other books, for example Animal Spirits by Akerlof and Shiller. (See the postscript below for another type of reasons.)

The book is also marred by several minor errors, for example senator Harry Reid is identified as representing Arizona (rather than Nevada) and there is a reference to a non-existing Long Island Rail Road station (apparently the author guessed, incorrectly, the name of the station closest to Renaissance Technologies).

Certainly, not a great book but interesting and fun to read. So I was surprised to see some very negative reviews of the book on Amazon. Some of the critics seemed to expect a technical analysis of the reasons failures of the models, a naive expectation (see the comments two paragraphs earlier). Another claimed that the chapter on Dark Pools (the latest "advance" in trading) is wrong. My search on the web on the subject of Dark Pools confirmed Patterson's description to be accurate. I can only speculate on the reasons for such extreme negative criticism.


I can add another potential reason for failure of quantitative analysis based on the mathematics of complex systems (and the global stock and derivative exchanges are certainly that). Such systems often behave in chaotic fashion: tiny differences in a variable are enormously magnified as time goes on. Sometimes such behavior can be seen in simple systems such as the one described by the equation

xn+1 = 4*xn*(1-xn)

The table below shows three scenarios on the evolution of values of x. The leftmost column is the value of n and the next three are the values of x with 5 decimals for starting values that differ only by 0.001. The fifth to seventh columns show the values of x with only 2 decimals. If one observed only the latter values for a few iterations only, he/she might assume that each was a repetition of the other. It is only after n equal to 6 that big changes appear.

 0 	0.40100,	0.40000,	0.39900		0.40, 0.40, 0.40
 1 	0.96080,	0.96000,	0.95920		0.96, 0.96, 0.96
 2 	0.15067,	0.15360,	0.15656		0.15, 0.15, 0.16
 3 	0.51187,	0.52003,	0.52819		0.51, 0.52, 0.53
 4 	0.99944,	0.99840,	0.99682		1.00, 1.00, 1.00
 5 	0.00225,	0.00641,	0.01267		0.00, 0.01, 0.01
 6 	0.00899,	0.02547,	0.05004		0.01, 0.02, 0.05
 7 	0.03564,	0.09927,	0.19014		0.04, 0.10, 0.19
 8 	0.13748,	0.35767,	0.61594		0.14, 0.36, 0.62
 9 	0.47431,	0.91897,	0.94623		0.47, 0.92, 0.95
10 	0.99736,	0.29786,	0.20352		1.00, 0.30, 0.20
Think now of the fifth column as a measure of the value of a financial asset over some past period and the sixth (or seventh) column as a similar measure over another time period. For a while one might think that he/she observers a repetition of the previous run and thus make incorrect predictions. This is only a toy example of a chaotic system but it illustrates the pitfalls of empirical models of complex systems.