Copulas as scapegoats?!

As pointed out by Revolutions, Wired magazine published last week a paper on the “formula that killed Wall Street“. The formula actually is a two-dimensional Gaussian copula with sole parameter a correlation factor γ but it is supposed to have led by itself to the financial disaster of last September!!! To use the paper’s own words, it was “instrumental in causing the unfathomable losses that brought the world financial system to its knees“. This is typical journalistic outrance: pick one single person, David Li in this case, plus one simple enough factor, namely the use of copulas in finance, and make them appear as the single cause of everything wrong with the financial system. Reading the many mistakes in the paper made me wish journalists would be a bit more subtle in their analysis of facts (and way more careful in their interpretation of maths!). Just try to make sense of the “correlation parameter reduces correlation to a single constant—something that should be highly improbable, if not impossible” or of “If there’s a 1 percent chance of default but investors get an extra two percentage points in interest, they’re ahead of the game overall”.

One valid point made in the paper is however about the irresistible attractivity of copulas in modelling because they only depend on a single correlation factor γ to represent a joint distribution. A posteriori, the short-sightedness of the approach is obvious too: Gaussian variates are inappropriate for financial data and more importantly the correlation factor cannot capture the conditional distribution (this is also the perspective defended in The Black Swan, discussed earlier) , not to mention the heterogeneity of the connection between both variables in time. But sentences like “they can model just a few years’ worth of data and come up with probabilities for things that may happen only once every 10,000 years” (similar to some found in The Black Swan) shows how far from a correct understanding of statistical models this paper stands: when the underlying model is correct, predicting very rare events is possible without waiting for those events to first occur!

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