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Bayesian Updating on News

Prices in this market are probabilities, so trading it well is applied Bayesian reasoning: hold a prior, weigh evidence, update, and compare the result to the price. Traders lose here in two symmetric ways, updating too little on real information and too much on noise.

The machinery

Bayes' theorem, in the odds form that suits binary markets:

Bayes in odds form
P(A∣E)P(Aˉ∣E)=P(A)P(Aˉ)×P(E∣A)P(E∣Aˉ)\frac{P(A \mid E)}{P(\bar{A} \mid E)} = \frac{P(A)}{P(\bar{A})} \times \frac{P(E \mid A)}{P(E \mid \bar{A})}

Posterior odds are prior odds times the likelihood ratio of the evidence.

The likelihood ratio is the whole game: how much more probable is this evidence if the event is going to happen than if it is not? Evidence with a likelihood ratio near 1 is noise however dramatic it sounds; evidence with a ratio of 3 or 5 moves prices for real.

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