Bayesian Prediction for Investors

Friday, Nov 23 2012 by
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Bayesian Prediction for Investors

Most economic theories make an assumption that humans are rational, but this definition is a peculiarly drawn one as it assumes that we all operate on the basis of Bayes’ Theorem, an idea which is freely bandied about but which very few people can actually describe.  There’s a good reason for this – it’s profoundly unintuitive, which makes you wonder if we do think the way the theorem suggests we ought to.

Unintuitive or not every investor should have a working appreciation of the ideas behind Bayesian reasoning, because it’s another one of those mental models we can use to assess the usefulness, or otherwise, of our ideas.  And oddly enough, it may be even more fundamental than we think.

The original paper on Bayes Theorem was entitled An Essay towards Solving a Problem in the Doctrine of Chances and dates from 1763.  It wasn't even published by the eponymous Reverend Baynes but by his friend Richard Price, who discovered it in his papers after his death.  As we’d expect under Stigler's Law of Eponymy it’s quite likely that Bayes didn’t even originate Bayes’ Theorem:

“It seems to be a law of the sociology of science that no discovery or invention is named after its first discoverer”.

Anyway, this Bayes Theorem thing seems to be quite important because it keeps popping up in all sorts of different places.  The question is, what is it?  Well, here it is in the words of the late and possibly great Reverend Bayes’ friend:

“To find out a method by which we might judge concerning the probability that an event has to happen, in given circumstances, upon supposition that we know nothing concerning if but that, under the same circumstances, it has happened a certain number of times and failed a certain other number of times.  He adds, that he soon perceived that it be very difficult to do this, provided some rule could be found according for which we ought to eliminate the chance that the probability for the happening of an event perfectly unknown, should lie between any two named degrees of probability, antecedently to any experiment made about it; and that it appeared to him that the rule must be to suppose the chance the same that it should lie between any two equidifferent degrees; which, if it were allowed, all the rest might be easily calculated…

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2 Comments on this Article show/hide all

David Hellens 24th Nov '12 1 of 2
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First possible objection: surely all attempts at predictive theory have to account for and overcome the implications of Chaos mathematics? Even in a fully understood system, small variations etc.
Second possible objection: Kurt Godel's Incompleteness theorems... Bayes no more 'fundamental' than any other set of mathematical ideas.
Third possible objection: the psychology of rationality implies a uniformity not found empirically in observed behaviour (Margolis and many others).

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Mark Carter 10th Jul '14 2 of 2
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An interesting subject, because I've been boning up on Bayes' Theorem recently. My conclusion so far is that it's interesting, but it is going to be difficult to apply.

One problem is that Taleb seems to be doing his best to undermine the use of statistics in finance. His basic argument is that the presence of fat tails can lead to his famous "black swan events" which can swamp out a seemingly smooth process.

Another problem is the choice of a prior distribution. How do you choose it? You could a uniform distribution.

My conception is like this: suppose I have a "strategy", like buying low PBV stocks. I need a prior distribution. I "could" use a uniform one, but I think that would be a bad choice. After all, evidence suggests that the strategy works well, so I wouldn't expect the prior to be uniform. Just how I might assume the priors to be distributed seems very much an open question. And besides, why would I follow a strategy if I believed it doesn't work?

The next step (the way I see it, anyway - I may be completely off base) is that I then implement the strategy. I.e. I go out and buy some low PBV stocks, and record my successes and failures. I'll have to define success, and failure, of course. But that's the easy bit. As I succeed or fail, I can update the prior to obtain a revised distribution.

I can then ask questions to see how effective my strategy is.

For fun, I decided to see how good my track record was. I concluded, using Bayesian analysis and a uniform prior distribution, that I had about a 97% chance of beating the market more than 50% of the time. I suspect that it's at this point that people's heads begins to swim. It's "nice", because you can quantify things, but I suspect that a more naive question "does it seem to be working?" will serve one nearly as well.

So, long story short, the secrets of the investing universe are probably not tucked away somewhere, awaiting the light of Bayes to reveal them.

I must add the cavaet that I have only just begun with Bayesian analysis, and others might find my grasp of the subject to be laughable.

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About timarr

Timarr

I'm a UK based technologist (career) and psychologist (academic) with a long-term interest in financial markets, with a particular emphasis (and skill) in how to not make money out of them. When I'm not working or blogging I'm to be found childminding, walking the dog or hiding in the garden shed with a good book :) more »



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