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A Mathematician Plays the Stock Market

A Mathematician Plays the Stock Market

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Rating: 5 stars
Summary: Funny, self-effacing, and just a terrific read
Review: 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!

Rating: 5 stars
Summary: A Refreshing New Style For A Book On The Stock Market
Review: 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.

Rating: 4 stars
Summary: Not a trading manual, but a good read nonetheless
Review: This book could very easily be used as a text book for most standard Security Analysis courses, and do a better job of teaching the subject matter The author takes a bit of a survey approach in discussing the various ways and methods used in forecasting and/or valuing stocks. It presents a very objective, and often lighted-hearted, review of both modern and classical financial theory, explaining them in a sufficiently technical way as to meet the needs of the topic, but not in such a manner as to make the discussions boring or opaque for those being introduced to the concepts.

This is not a manual on trading. While the author's personal story of major losses in WorldCom stock do provide the means to learn a few lessons, he is not providing a do this, do that sort of strategy for making money in the markets. That said, however, some of the research and studies he quotes are worth reviewing.

Even for an experienced stock trader or investor, this is a book worth reading. Paulos presents some things that have been overlooked, and oftentimes turns a different kind of light on the market than one generally uses.

Rating: 5 stars
Summary: Excellent and realistic investment book.
Review: This is an excellent book on investment theory. It reviews fundamental analysis, technical analysis, option theory and many other topics. The author explains exceptionally well the Efficient Market Hypothesis and the debate surrounding it. He also introduces basic concepts of behavioral finance.
Abstract.

As a mathematician having studied the stock market, he believes the stock market is pretty efficient; and that both technical analysis and fundamental analysis do not have much predictive value.

Technical analysis according to him should be renamed trend analysis, as it consists in graphing and extrapolating current stock price trends. He covers the major strategies technical analysts use such as buying stocks when their current price breaks through its moving average, and selling them when they fall under this same moving average.

He covers fundamental analysis and their associated metrics in good details. Reading this section, you will become familiar with all the usual metrics, including P/E, PEG, P/Book value, P/Sales.

Mr. Paulos makes a case that the stock market captures the aggregate of all our psychological foibles, and goes on giving a good introduction in behavioral finance. He illustrates the common psychological flaws associated with investor behavior, including: the confirmation bias, anchoring effect, status quo bias, endowment effect, and Richard Thaler's mental accounts. He also illustrates flaws we incur when doing investment research, such as: data mining back testing, and the survivor bias. But, in aggregate these human errors partly cancel themselves out rendering the stock market pretty efficient.

The book's gem is the debate on the Efficient Market Hypothesis (EMH). The fewer the investors believe in EMH, the more they will engage in technical and fundamental analysis to extract excess return above the index. These "active" investors will render the market increasingly efficient, and negate their opportunities to earn excess return. The opposite is also true. If investors believe in EMH, they will become "passive" and just buy the stock index through a Vanguard fund or an ETF. As a result, the market will not be so efficient, and the EMH will not hold up in such a situation. So if you believe in EMH, it is false. But, if you don't believe in it, it is valid.

Paulos argues that enough active investors do not believe in the EMH to render it valid. This argument is convincing when you think of the thousands of mutual funds, hedge funds, and private managers on Wall Street. Thus, there are plenty of professional active investors to render the market very efficient. But, Paulos does not deny that certain markets at certain times, temporarily ignored by Wall Street, may be less than efficient. Thus, for him the EMH debate is not just a true or false question, it is a matter of degree.

Active investors play a crucial role in making the market efficient. Paulos makes an interesting distinction between the technical analyst and fundamental analyst. He states that technical analysts are momentum investors. Thus, they cause market volatility to increase. When stock prices increase, these guys buy even more. When stock prices decrease, they sell. Thus, they accentuate the swings in stock movements. Notice that they break the rule of Buy Low Sell High. The fundamental analysts are really value investors or contrarians. They do just the opposite of the technical analysts, and cause stock price movements to moderate. Thus, the two types of analysts/investors play a different role. But, together their active analysis make the stock market very efficient. The EMH states that all information is disseminated and absorbed immediately within the investment community, and thus is fully reflected within stock prices. But, somebody has to process this information. And, that is what the technical and fundamental analysts do.

One of Paulos other big concept concerns the statistical distribution of stock price movements. According to the EMH, stock price movements are random. And, this is true as confirmed by the autocorrelation on any time series of stock prices that is typically very close to zero. If stock prices move randomly, they should assume a normal distribution. But, Paulos indicates it is not always the case. In other words, extreme events (stock crashes or booms) happen more frequently than in a normal distribution. He adds that at the tails, the price movement of stocks is better captured by the power laws. Check page 178 for a detailed explanation on power laws. This is fascinating, and it may represent an upgrade to the EMH that relies solely on the normal distribution.


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