A Mathematician Plays The Stock Market

In A Mathematician Plays the Stock Market best-selling author John Allen Paulos demonstrates what the tools of mathematics can tell us about the vagaries of the stock market. Employing his trademark stories, vignettes, paradoxes, and puzzles (and even a film treatment), Paulos addresses every thinking reader's curiosity about the market: Is it efficient? Is it rational? Is there anything to technical analysis, fundamental analysis, and other supposedly time-tested methods of picking stocks? How can one quantify risk? What are the most common scams? What light do fractals, network theory, and common psychological foibles shed on investor behavior? Are there any approaches to investing that truly outperform the major indexes? Can a deeper knowledge of mathematics help beat the odds?

All of these questions are explored with the engaging erudition that made Paulos's A Mathematician Reads the Newspaper and Innumeracy favorites with both armchair mathematicians and readers who want to think like them. Paulos also shares the cautionary tale of his own long and disastrous love affair with WorldCom. In the tradition of Burton Malkiel's A Random Walk Down Wall Street and Jeremy Siegel's Stocks for the Long Run, this wry and illuminating book is for anyone, investor or not, who follows the markets-or knows someone who does.

What makes the book delightful is his self-effacing sense of humor. I cannot remember reading another book in which a writer is as candid and funny about his own failings as an investor. Only Andy Tobias comes anywhere close. The book's running joke is the professor's disastrous obsession with buying WorldCom stock using borrowed money before it became apparent that the company's reported earnings had more to do with wishful thinking than reality. It is this example that makes the book also insightful for the reader because it shows how easily our emotions and instincts can lead us astray, even when we understand as much about the stock market as Professor Paulos does.

I have read dozens of stock market books that have attempted to explain the "numbers" aspect of stock-market investing. None of them covered as much ground or did so as succinctly as this book does. I was very impressed by the depth of reading that this book reflects. Although it is not an academic book, the rigor is impressive.

The basic point is that the stock market is a lot more complicated than anyone can hope to understand, and likely to be more volatile than almost anyone will be comfortable with. Professor Paulos provides potential remedies for both (index investing, diversifying active portfolios, and using derivatives as insurance against large risks).

One of the many brilliant math examples shows how some games cannot be won with "success" strategies, but if you can combine a certain two "failure" strategies you will be a guaranteed success. With that wonderful point, the idea of being a contrarian was better expressed than in anything else I have read on the subject.

By inserting himself in the book through the WorldCom example, Professor Paulos powerfully introduces the element of individual and market psychology. Although he is neither a psychiatrist nor a psychologist, the book abounds with material about the psychology of how the market works and why investors make mistakes. To me, the ultimate lesson here was that one's stock market approach has to be one that fits emotionally well . . . or you will never execute it successfully.

Ultimately, successful active investing requires you to correctly pick what everyone else will find irresistible not too long before that compulsion hits them. I came away, once again, delighted that index fund investing is available as a sure-fired way to outperform more than 90 percent of all professional portfolio managers while sleeping soundly at night.

After you finish enjoying the book, I suggest that you also think about where else you commit your financial resources in large measure more due to your emotions than to your sense of how to calculate an advantage. How could you change your approach in that other area to be more emotionally and financially rewarding?

Donald Mitchell
Co-author of The 2,000 Percent Solution, The Irresistible Growth Enterprise and The Ultimate Competitive Advantage


For each concept a tale   June 13, 2003
S. Park (Bay Area, CA)
12 out of 14 found this review helpful

Each chapter of this book corresponds to a concept in investment theory (for e.g. the efficient market hypothesis, options, risk, volatility -- see the table of contents). The concepts covered easily encompass those dealt in introductory college-level investment theory text books (for e.g. Bodie, Zane, and Marcus' "Essentials of Investments") and a bit more (for e.g. chaos theory applied to finance). As can be deduced by inspecting the length of the book (a mere 224 pages), the author's exposition is succinct and exacting. This is not to say in any sense the book is demanding or dry; quite to the contrary it is leisurely and enjoyable. Every investment concept is furnished with a story, a logical puzzle, and/or a paradox. With the ability to perform rudimentary arithmetic you will be able to understand the underlying concepts and question the "conventional wisdoms" regarding them. Paulos' wit, as with all his previous publications, shines throughout the book.

(Side note. Other things I _personally_ enjoyed about the book: 1) forward references -- I like books that direct readers to jump to a certain paragraph or section should the reader not be interested in certain parts. Inclusion of such directions not only presents convenience, but also implies that the author really thought out what he/she'd write. 2) Subject index -- needless to say it is easier to return to the part you wish to read again!)


Funny, self-effacing, and just a terrific read   March 10, 2004
Dennis Littrell (SoCal)
26 out of 33 found this review helpful

Since Professor Paulos delights in paradoxes it is appropriate that a paradox lies at the heart of this very fine book. He does indeed play the stock market, but how well and using what kind of strategy? Ironically Paulos's personal tale is one of obsession and foolhardiness, of buying WCOM at 37 (yes, WCOM), of averaging down again and again and buying calls until in near final desperation our good professor finds himself contemplating with a kind of hopeless hope his WCOM calls at $20 as the stock trades at $1.13! (p. 197)

Interestingly enough, most of what mathematician Paulos writes about here is the psychology of the market and what he learned about himself psychologically as he rode the stallion down, down deep into the valley of despair. Yes, there is some interesting and instructive math included, but how refreshing it is to read a professional academic chronicle his experience while being up-front and personal about the emotional, random, and psychological traps that often guided his decisions. It takes a certain amount of confidence to write a book like this, and it helps a lot to be able to laugh at yourself.

My experience during the period beginning early in 2000 when the market began to tank was similar to Paulos's (which is one reason I found his account so riveting) except (thanking my lucky stars) I did NOT average down as he did, and I certainly did not buy calls. Instead gradually (too gradually of course) I began to take money out of the market. For those of you who lived through those days of shock and despair, Paulos's witty self-examination will be a pleasure to read.

On another level this is a book about market theory. Paulos does not believe in the Efficient Market Hypothesis (EMH), which states that prices in the market accurately reflect the value of the market and that any subsequent deviation (without new information) from those prices is a random walk. His argument (a very persuasive one) is that the market is a self-referential system that depends on how the players view the market. Paradoxically, if they believe in an efficient market they will NOT try to figure out ways to take advantage of anomalies and the market will be inefficient! Conversely, if the players believe that the market is inefficient, that there is some surplus value to be gained, they will indeed look for ways to take advantage of differentials and anomalies, and presto! the market becomes efficient.

Consequently, Paulos' theory is a refinement of the EMH. He sees the market as constantly existing in a dynamic state poised between maximum efficiency and something less than that. He sees the market as a complex system subject to the laws of complexity theory, and like the weather only more so, impossible to predict much in advance.

As for technical versus fundamental analysis, Paulos appropriately hedges. Yes, the trend is your friend, but (e.g.) the full blown Elliot wave theory is "murky" while the fundamentalists suffer from possibly cooked numbers and from the information already being factored into the stock's price. One gets the sense that Paulos is once bitten, twice shy! However, I think he has gotten this exactly right, namely that only a small edge can be had through a lot of work using both approaches.

There are some interesting mathematical paradoxes presented here and some scams. Those of you who have read Paulos's previous books (e.g., Innumeracy: Mathematical Illiteracy and its Consequences, 1988; A Mathematician Reads the Newspaper, 1995, etc.) know he has a gift for making the obtuse and opaque clear, or at least intelligible, and that he can be laugh out loud funny. I thought that he was even funnier here than usual, perhaps because there is a taint of gallows humor infused throughout. For example, in reference to his love affair with WCOM, Paulos writes, "Investing in it had originally seemed like a no-brainer. The realization that doing so had indeed been a no-brainer was glacially slow in arriving." (p. 199)

One paradox is the familiar "All Cretans are liars" upon which Paulos plays a few variations to demonstrate the self-referential aspect which is at the heart of the paradox. Included is this illumination: "The Prosecutor booms, 'You must answer Yes or No. Will your next word be No?'" (p. 187)

One scam is the familiar Ponzi scheme. Paulos thinks of a stock market bubble (as we experienced in the nineties) as a Ponzi scheme in which dot com buyers are hoping to sell to stupider dot com buyers, etc. In another context, Paulos notes perspicaciously, "Even ravaging of the environment may be seen as a kind of global Ponzi scheme, the early 'investors' doing well, later ones less well, until a catastrophe wipes out all gains." (p. 94)

I must warn the reader to beware of many atrocious puns. In one of the "worst," Paulos is explaining the emotional differences between risk adverse people and their opposite and how a stock's beta may be personalized. "A zero beta person would have to be unconscious, perhaps from ingesting too many beta-blockers." (p. 162)

Ouch!


A Refreshing New Style For A Book On The Stock Market   May 17, 2003
Frank Rudin (Bellevue, WA USA)
11 out of 13 found this review helpful

The style of this book is refreshingly different from the typical book on investing. So, I thought I'd give this book to my dad for Father's Day, but I took a peek and found myself reading through it in two nights. The book's very informative, funny, and at times even touching. Not your usual boring stock book. There are unique perspectives on insider trading, psychology, and the efficient market hypothesis. The math is pretty easy and it's illustrated with stories and anecdotes, some at Paulos' own expense. The book is kind of a road map of the market with lots of surprising examples and little nuggets of insight on chaos, power laws, scams, etc. Now I need to buy another copy for my dad.


Common sense analysis of the stock market   June 18, 2006
sanantondan (San Antonio, TX USA)
3 out of 3 found this review helpful

Paulos offers a highly readable, comprehensive analysis of the stock market and ramifications for investors and traders. He combines his personal experience investing in WorldCom with understandable mathematics to look at market theories and technical and fundamental approaches. A short read packed with useful information presented in a witty style.