A Mathematician Plays the Stock Market Book

What's really interesting about other people's reviews of this book is that they seem to expect a book on the stock market from a mathematician to be somehow be based in finance.

There are plenty of books on the stock market out there... that do so from a finance point of view.

This book is pretty brilliant although at first glance, it appears to be pretty straight forward... you think a mathematician would use his knowledge about math to somehow find some brilliant trick about the stock market. But that's not how this plays out.

Math is a game of numbers. It's a field of study that looks at patterns. But ultimately the numbers are a measurement, some kind of metric. What's faulty about using the stock market from a pure numbers point of view is that the numbers in stock prices need to measure the a consistent value for any math relation to work. What I mean is simply that stock prices are based on what people do in terms of trading volume of a stock. Abstract all you like, but the immediate particular reason why anyone does what they do with stock is anyone's guess.

We can assume that a change in stock prices has to do with an anecdote on the news about a company, or something happening somewhere related to a company. But that's not always true. Sometimes things happen for seemingly no reason. Much of this, Paulos tries to explain has as much to do with how people perceive the market as much as it has to do with actual values. The later chapters are particularly brilliant on this account. The earlier chapters which seemed to promise this or that mathematical model, or this or that economic model... don't pan out because as Paulos convincingly tells us, any model that we use to predict the stock market can be outdated unless the model itself anticipates how others will use it, made predictions and how those predictions will affect the market. In other words, any stock market model needs to also be self reflexive in how it's applied -- not just when it's applied.

Paulo makes some pretty complex abstractions to do this; for instance, applying how the "Efficient Market Hypothesis" is either always correct (when people believe it to be wrong, thus playing the stock market off of information in the news, or about a company's state) or it is always incorrect (when other people believe the information on the news is invalid as the stock prices already reflect the current value of the stock)... that is to say that particular hypothesis doesn't work as it should because it takes for its model an absolute system of values based on how other people act. People don't do things as mechanisms do; people evaluate based off of what they believe others will do as well.

This twist of self reflexivity makes it particularly difficult to formulate any theory that is both consistent (non-contradictory) and complete... in essence, we need to formulate a model that can predict how its predictions are taken into account and then provide us with "a few steps ahead" so that profit can be captured. That would be a pretty sophisticated theory; and in fact be impossible because that theory could only work in the case of the one individual who has it. By definition the same theory could not with all the other individuals who also have it, otherwise there would be no profit!

So a quick conclusion is that the market can at times reflect real values, but often it doesn't because there's too much white noise as meanings, theories, trends and news all impact the same metric. So how can we make any consistent model on the stock market if all this information flies under the same metric as the very metric a stock price is supposed to represent?

This is all of course, extracted from the book. What I found really interesting, if one read between the lines from the get go, was that one can always take the meaning of a stock's movement anyway one likes. That is to say, we have an abundance of narratives that can fit the model of "what really happens". We simply pick the one we like the best, and go forth as if that were true. As Paulo points out, even through random chance a few individuals are bound to hit it big. And once people notice that, they will follow that person's movements, ensuring that they will always be right.

Thus, the modeling of stocks, properly considered, must also model how we think as well. But that's nothing new. Paulo is of course, writing this book as a lament of his own failed investments...and in the process of doing so, he's also somewhat justifying the bubble bursting was inevitable, a kind of normal market behavior. But he's correct; the uncertainty in the stock market is not just an uncertainty as to what the price means, but similarly that its certainty is also a reflection of what we all would also believe it to mean.

All in all, I found the book to be really entertaining and interesting. I would have liked a little more direction midway through the book... with each theory or direction Paulo brought up, he quickly shot it down at the end of the chapter. Of course, he was setting this bed of failed theories for the self reflexive analysises... but I didn't see it coming. So it felt much like wandering, and that's not a good way to treat your reader as it throws your reader out of the process of reading.