Bayesians in Finance

At the EconLog blog, Bryan Caplan asks why academic economists are not Bayesians. Caplan was talking about a Bayesian approach to the validity of economic theories. Stephen Gordon responded with a post about why economists do not use enough of Bayesian econometrics. Both questions are valid and should cause some introspection.

The issue is probably even more important in finance where key parameters are estimated with such large confidence intervals that the prior does not get washed out by the sample. In fact, I think that one of the defining characteristics of finance as a discipline is that first moments (for example, mean returns) are estimated very poorly even with extremely large samples while second moments (variances) are somewhat better estimated.

For example, Aswath Damodaran has an interesting paper last month discussing the difficulties of estimating the Equity Risk Premium reliably. Damodaran states bluntly that:

At the risk of sounding harsh, the risk premiums in academic surveys indicate how far removed most academics are from the real world of valuation and corporate finance and how much of their own thinking is framed by the historical risk premiums they were exposed to back when they were graduate students.

What Damodaran is really saying is that despite being exposed to recent academic research using centuries of global stock market data, the posterior distributions of most academics are still strongly influenced by the prior distributions formed during their student days. In such a situation, there is merit in making the prior distribution quite explicit rather than leaving it implicit.

Classical statistics also involves priors; the tragedy is that in that framework, there are only two kinds of priors:

1. Dogmatic priors which totally ignore what the data says, and arbitrarily set some parameters to zero or some other special value.
2. Diffuse (or improper) priors which impose no priors beliefs at all and leave everything to the data.

Bayesians can however use the more interesting priors which reflect non trivial prior beliefs that can be overruled by the data.

At a different level, I think it is also essential to incorporate Bayesian learning into theoretical models. Rational expectations models are richer when they recognize that even with large samples, posterior distributions could have large error variances.

Posted at 2:02 pm IST on Tue, 17 Nov 2009         permanent link

Categories: Bayesian probability, CAPM, post crisis finance, statistics

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