I’m shocked – shocked! – that daily stock returns don’t follow a normal distribution. And so is Bjarne Graven Larsen, chief investment officer of Denmark’s biggest pension fund, ATP.
Short story: Larsen’s crew looked at daily investment returns since 1/1/06 and found two trading days with nasty dropoffs – 7% and 8.7%. According to the distribution ATP was using, you should see the former once every 1,500 years and the latter once every 450,000 years. Having both occur in a four- or five-year span means its time for a new model.
I’ve reproduced his chart below. The normal curve is the blue line – the model. The orange bars are the empirical distribution – what actually happened. When the orange bars extend above the line, it means the result occurred more often than the model predicted it would. And the zoomed-in shot shows how the model missed predicting those bad boys on the left.
Their model also underestimated how often the market is boring – moving only a sliver up or down. You can see that in the middle of the chart. And he doesn’t mention it, but if you look to the right, the model also underestimated favorable days.
Larsen’s point: All market hedges are underpriced, because nobody’s model anticipated how likely such extreme movements are.
All a bit of a chuckle for casualty actuaries, who long ago stopped using normal distributions to model losses, preferring the fat tail of the lognormal (or even fatter tails, if we can get away with it).
Larsen, therefore, is sanguine about the extra capital Solvency II’s standard model would require. S-II’s model would require you to hold capital for a one-in-200-year blowout, but its curve likely has the same problem that ATP’s had. That would imply that S-II underestimates how much capital a company should hold, though Larsen doesn’t go so far as to say that. He does say this:
It turns out our risk model is far more conservative. But if a firm were to rely solely on the standard [Solvency II] formula they might run into some problems.
This all comes via risk.net.