Paul Kedrosky on 50 standard deviation shocks — memorize the last paragraph:
I was scanning some Morgan Stanley bond data this morning, specifically its 6.625% issue maturing in 2018. Its recent behavior is instructive in thinking about what happened last week, how unusual it was in historical terms, and why models broke down as badly as they did.
Morgan Stanley is seen as a stable issuer, and this bond has traded accordingly. It has sat more or less flat between $94 and $96 over the last three months, hardly moving at all through the various waves of the credit crisis.
And then last week struck. In the space of two days the bond price fell from $94 to as low as $60, only to recover again to $84 by yesterday afternoon.
Think about what what means in statistical terms. The mean price for this bond most of the early part of this year was around $94, and the standard deviation on a daily basis was approximately $0.45. Assuming normality (which is a species of the assumption made my many default risk modelers), and noticing that we saw a $34 price decline, we witnessed a 50-plus standard deviation event, the sort of thing that shouldn’t happen without dinosaurs reappearing too.
In short, to a first approximation, at least from a modeling point of view, last week didn’t happen. And hence the problem with frequentist risk models, which is, in part, why we are in the trouble we are in. These models work wonderfully, until something exogenous changes, and then they don’t work at all anymore.
And when that happens correlations converge.
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