Chris Dillow speaks:
Stumbling and Mumbling: Chebyshev and chickens: Mr Viniar can't be that stupid. He knows financial returns are not normally distributed, but have fat tails; extreme events are more likely than a bell curve suggests. More likely, he's thinking of Chebyshev's inequality. It says that in any data sample, no more than 1/k2 of the values are more than k standard deviations away from the mean. On this view, a 25 standard deviation event is a one in 625 probability.
Does this make Mr Viniar look less stupid? No, however we cut it, [Goldman Sachs's] Mr Viniar is talking wibble. He just under-estimated risk.
There's one very stupid way of doing this. Imagine you're a chicken. Every day, the farmer feeds you. After a while, you figure: "My returns from the farmer are pretty stable, as I seem to get roughly the same amount of corn every day. Being a chicken is a low-risk business." The following day, the farmer breaks your neck.
Any hedge fund who took default risk (say by holding CDOs) and boasted about its Sharpe ratio based on post-2003 returns would have done much the same as this; you can't measure default risk by looking at past returns. I had assumed that no-one was stupid enough to fall for this trick; one reason why I was underwhelmed by Taleb's The Black Swan - which laboured similar points - was that I thought he was just stating the bleedin' obvious. But perhaps I was wrong.
Not only were they massively exposed to subprime risk, but they didn't know that they were massively exposed to subprime risk, and they don't seem now to be able to coherently explain why they didn't know that they were massively exposed to suboprime risk.