Why be normal

Robert Waldmann

is commenting on a comment at Mark Thoma’s blog. The comment
NotMarkT ha detto…

One of the difficulties with model selection for assessing tail probabilities is that the empirical data often can’t distinguish among light (e.g., normal) or heavy tailed (e.g., pareto) distributions. The model selection problem then becomes a question of optimism or pessimism in the face of uncertainty. By convention, optimism has won.

(note that firefox speaks to me in Italian.)

My reply after the jump.

I think you are absolutely right. However, the victory of optimism is odd, and, I think, impossible to reconcile with Bayesian rationality.

First. If we don’t know if distributions have thin or thick tails and the undeniably relevant data aren’t very informative (because we are talking about tails of distributions) then we should have a diffuse posterior. Yet people repeatedly assume that they know for sure that a distribution is normal and the only uncertainty concerns means variances and covariances. Acting as if you know something for sure, just because the data can’t prove you are wrong is not rational at all.

Note the key word “undeniably” in the paragraph above. Since well before Gauss, firms and people have suffered because they assumed thin tails. Financiers know this. They all convince themselves that they stress test. Then they all convince themselves that this time its different. The lack of sufficient relevant data is based on the assumption that a whole lot of data is irrelevant.

I think that lack of sufficient undeniably relevant data is important, but it can’t be the whole explanation. I think there are three other factors at work.

First there are agency problems. Traders who are allowed to cash out short horizon mark to market returns are rationally risk loving and can snow the top managers who are supposed to keep them from running too much risk.

Second there is self selection of the subjectively over confident. If rational people know that they don’t know much of anything, then only irrational people will take massive positions and trade actively. This means that the people who most affect asset prices underestimate variances of their forecast errors, but it also especially means that the people who matter over-estimate the probability that their preferred parametric specification is very close to reality.

Third there is selection of the people who take on lots of tail risk. Some will get burned by tail risk and be fired. The others will have high sample average returns with low sample variance and get promoted. Promotion can mean a tenfold increase in their allowed gross long position. This is irrational. The top managers mistake luck for skill. Obviously, their self esteem is based on assuming that what matters is skill not luck.

Finally, last but not least, as you note, optimism is more fun and people don’t like to listen to Cassandras.