A Mathematician Plays The Market (John Allens Paulos) 5 comments

John Allen Paulos is a professor of mathematics in the US and this book which was written in 2003 has an interesting approach: it dissects the subject of investing from the mathematician's/logician's perspective.

Using his disastrous investing experience with Worldcom as a backdrop for the book, the author discusses a number of key themes in investing/trading. These include the psychological aspects of investing, technical analysis, fundamental analysis, the Efficient Market Hypothesis, diversification, options and derivatives, and general market strategies. But readers will find his arguments quite unique, because it is unlike the common sense and experience-based advice typically dispensed in other such books; Professor Paulos analyses these issues using mathematical concepts and logic and presents his views as a conclusion of such analysis.

Don't be alarmed. Firstly, the mathematical concepts he uses for discussion are familiar to most of us with general training in maths: elementary statistics, probability, logic, arithmetic (eg. discounting of future returns), with a bit of game theory and chaos theory thrown in at the end. Secondly, he throws in a lot of analogies and mathematical anecdotes to illustrate his point and generally employs qualitative discussions while limiting use of quantitative calculations.

I think for those who like to think about the market and the logic of it all this is an excellent book to read. Of course Professor Paulos is no Buffett and does not have the backing of success; indeed his bad experience with Worldcom is the only one he discusses in the book; however his mathematical logic about various investing issues is impeccable. He employs information transfer analogies (probably from some kind of network theory) to explain why stock prices can suddenly collapse without any apparent immediate cause, and examines the frequent irrationality of people's investing decisions as a result of their inability to perceive the inherent probabilities. As expected, he sees more value in fundamental investing rather than technical analysis, the latter of which he admits he has problems understanding why for example, a stock might collapse or rally after a certain number of "waves" or whatever. What is the scale in question, he asks; one can perceive waves over an intra-day period or over multiple days. He, however, sees the logic of in simpler technical tools like moving average. I believe the professor also prefers fundamental investing because it tends to stabilise the market eg. bargain hunting arresting a stock's price fall, while technical players tend to be momentum followers chasing up prices.

It seems that a pet topic of academicians in the investing topic is the Efficient Market Hypothesis; it is a key theme of this book as well. Professor Paulos has some interesting ideas about it to contribute: his belief is that the EMH is true only if a majority believe it to be false. And vice versa. Why is this so? If everyone believes the market is efficient, they would not see any market inefficiencies to exploit or arbitrage out, even if there were; resulting in inefficient pricing. Conversely, if people believe certain stocks are undervalued (and hence inefficient) and buy in, they are effectively eradicating these pricing inefficiencies and justifying the EMH. As of now, he feels the EMH is approximately true, given the number of fund managers and traders believing they can outperform the market.

Another key theme he explores is the random nature of stock prices ie. the Random Walk theory. He is more interested in the nature of the price trends per se, rather than engaging in discussions on whether prices are truly random. Delving into statistics, he finds that the normal distribution does not describe stock price distributions well, because the latter tends to have fat tail ends ie. high frequency of very extreme (high or low) prices, while the normal distribution tends to decay rapidly at the ends; he suggests a power law distribution instead (not that it is of much use to you or me). He then discusses, in the last chapter, why it will be quite impossible to model price movements (and hence predict the future trends) given a random market: according to complexity theory, "a sequence cannot generate another sequence of greater complexity than itself"; put simply, a person has to be more complex than the market to predict its gyrations, and the professor's point is that a "random" sequence is the most complex of all, probably beyond our complexity horizons. Nevertheless, he ends by saying such market randomness is under the assumption of an efficient market; in periods when the market is less than efficient the complexity might decrease and it might be possible to model price trends (of course, again the problem arises as to how do we tell when the market is inefficient?)

Never mind if you don't understand my last one or two paragraphs. It was mainly for my personal documentation and future reference, for I found these sections quite interesting. Overall, the book is very readable but sometimes I skip over some of the numerical examples which are a bit dry. This book constitutes the professor's take on the stock market but after reading it you might be interested to find some of his earlier books, which explore the interesting role of mathematics in other aspects of everyday life. You can check them out under Amazon.