The Stock Market Does Not Have a Probability Distribution!

It’s well known that the US economy crashed in part because of faulty financial models. What is not as well known is that India narrowly escaped a similar crash because they lacked sophisticated financial models, as Somik Raha wrote in the Business Standard. With all this criticism of financial models, scholars have claimed probability distributions on market price had tails that were too narrow.  The prevailing thought is that if we fix our models with distributions having fatter tails, everything will be fine again.  Nassim Taleb, author of the wonderful best-selling book, The Black Swan, which warns us about the dangers of low probability events, joined this bandwagon and published a paper entitled “The Future has Thicker Tails….”  In his technical work, like the other analysts, he assumes stock prices are formed by some “probability generating process” which we need to understand better.  The problem with such an assumption is that the “probability generating process” is entirely a figment of my imagination, and not recognizing it will send me on a wild goose chase in the world outside to find the glass that sits on my nose.

A far more practical approach is to engage with what people actually know and use that information to encode probabilities.If I ask you “What is the probability that your phone will ring in the next ten minutes?,” you can think through your experience with calls at this time of day, day of the week, etc. and then add in special information that a friend is likely to return your call soon.  Based on this information, you can then describe this information quantitatively in terms of a single probability assessment that your phone will ring in the next ten minutes.  If I have little information about your phone calls, I would probably accept your distribution as my own; say if I had an opportunity to make a bet on this event.  However, I could have different information; for example, I might know of a test of an emergency dialing system that is in progress and assign a different probability to the same event.  Each of us has our own probability assessment, which we may or may not agree upon.  The event itself does not have a probability.The startling conclusion from this approach is: there is no market distribution! There is your probability distribution, and mine, and distributions of other individuals.  These distributions represent our individual ignorance and knowledge.  We do not all have the same information and beliefs in things like “market perfection.” We may also have different information about financial frauds, such as mortgage schemes, bad regulations, insider trading, public debts, wars, etc. Naturally, our probabilities can differ.  This is not a problem, but a great opportunity to discover where information gaps lie if we are on the same team, and where trading opportunities lie if we are not. Moreover, taking such a perspective immediately reminds us of the need to check the quality of our data ourselves instead of relying on “expert” distributions.

Instead of taking an approach like the one we have described that is grounded in reality, conventional models make theoretical assumptions on “market distributions” and brush important conversations about what we know under the carpet. These models confuse us with technical jargon making any practical conversation on risk impossible. Gigantic models based on such assumptions quickly become castles that are built on sand. For example, most housing loan models made an assumption that property prices would forever increase and did not factor in a crash in housing prices, even after the crash had actually happened! Imagine a kindergarten risk analysis which required an important value factor like housing price to be uncertain, and pushed bankers to think of good and bad scenarios. Such an exercise would be far more valuable in generating insights than a financial model that priced the loan using complex ideas borrowed from theoretical physcis.

The financial community worships and sells these faulty models, which in some form or another assume that the future is a stable continuation of the past, to be determined statistically from past data, what I sometimes call driving by looking into the rear view mirror.  Try it slowly on a deserted road – it works – until you come to the unexpected T intersection and drive straight into the ditch.  Wall Street denizens have built beautiful rear view mirrors.  I would rather have even a small forward-facing windshield.

It is time we stopped getting diverted by fancy models and did the hard work to tackle the question: how should we capture the best probability assessments we can, from ourselves or experts, when we need them to make good decisions?