## Keynes, probability, asset pricing and the great clusterfuck

*by* Migeru
*Tue Jul 17th, 2012 at 07:01:15 PM EST*

A long time ago, in a galaxy far away, Drew gave me his copy of Keynes' *Treatise on Probability*, which he had acquired at some point thinking it would be relevant to his economist education but which might be more profitable to me, who had an academic interest in probability theory and had read a number of classic works already. The book languished on my shelf (and travelled in a box, and was stacked on another shelf where it languished, and so on through three separate moves) until one day last week I decided to finally read it (in fact encouraged by a conversation I had with another participant in the Minsky Seminar last month). I think it was worth it, but then again I have weird tastes in reading material.

To Keynes, probability is a branch of logic: the theory of * rational thought under uncertainty*. Ordinary logic is just the subset of rational thought dealing with certain (or certainly false) propositions. I think this is a really interesting approach. Probability to Keynes is relative but not subjective. That is, probability is

*always*relative to some data (or hypotheses), and so it is in a way subjective since each of us has different data/knowledge/experience, even different mental acuity. However, Keynes' probability is not subjective in the sense that a correctly formed probabilistic reasoning, being enunciated relative to explicit hypotheses, should be valid independently. Keynes writes at length about the problem of induction (reasoning from particular, though possibly numerous, observations to general statements) and he stresses that, contrary to what has been asserted by philosophers in the past, the fact that an inductive conclusion turns out to be false does not invalidate the inductive reasoning

*relative to the information available at the time the conclusion was formulated*.

Anyway, back in 2009 in the context of a discussion of a journalistic piece about David Li's killer formula (the gaussian copula approach to CDS pricing) I said I should probably write a diary about the arbitrage pricing theory that underlies a lot of the ongoing Global Clusterfuck. At the time I was probably thinking that I might use the preface of a popular book on derivative pricing, *Financial Calculus* by Baxter and Rennie. They begin their book with a *parable of the bookmakers* intended to disabuse the reader from the get-go that market prices are expected future values. That's right: market prices are *not* average values as normally understood. However, after having read Keynes on Probability I don't have to infringe Baxter and Rennie's copyright or even retype their text from my hardcopy of the derivatives book, because I can simply lift a section from the Project Gutenberg version of Keynes...

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