What’s so special about zero?
March 31st, 2008Mark Thoma asks what went wrong with the risk models during the most recent crisis. He has a good discussion of structural vs. reduced form models. In practice, people use the later models because the former are pretty bad. We don’t know, in general, the causal mechanism between any two variables.
With reduced form models, measuring the correlation between two variables allows us to predict how changes in one variable will change the other variable. Because we know gold prices are inversely correlated with GDP, we can predict that in a recession gold prices will go up.
The problem with reduced form models is that we don’t understand what’s causing the correlation and that causal relationship might change over time. Maybe, in the past, gold prices happen to go up because demand for gold tooth fillings goes up in recessions as people switch their diets to cheaper, sugary foods. But in this recession corn prices, and thus corn syrup, has become much more expensive, sugary foods aren’t cheaper and thus gold prices don’t go up. (WARNING: I completely made up this example.)
In any case, you see my point. Correlation’s not causation and all that.
But that’s not I want to talk about. What I want to question is why do we think the risk models failed? The risk models don’t guarantee against negative shocks, they make them less likely. We happened to hit a state of the economy where lots of returns where zero. This doesn’t mean the models didn’t anticipate zero returns. Because it was an unlikely, but not impossible, event, its likely the models had this set of events priced in.
Would we ask this question if returns were unusually low, but not zero? Probably not. What’s so special about zero returns that realizing them means our models are broken?
I almost titled this post, “Life has a measure zero.”
March 31st, 2008 at 11:39 pm
Topology references will lead to measure 0 visitors.
April 1st, 2008 at 12:17 am
Well, ok. At least you have congratulate me for not making it the title of the post…