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August 14, 2007

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I recall reading that price movements tend to be normally distributed near the mean and power-law distributed at the tails. Do the "hedge funds" (that aren't actually hedged) ignore this solely out of mathematical convenience? 25 standard deviations? Do they really believe that? Is this an arbitrage opportunity or does the correct math show that leveraged strategies are bound to fail?

Brad DeLong:

"25-Standard Deviation Moves, Several Days in a Row"

Think carefully of what Brad is telling us about statistics and about justifications for inherently flawed investment models. Brad is making a most important point.

Extreme value theorem? Fat tails? Long tails? Give me a break! My models are right, and reality is wrong.

Brad DeLong:

"25-Standard Deviation Moves, Several Days in a Row"

Think carefully of what Brad is telling us about statistics and about justifications for inherently flawed investment models. Brad is making a most important point.

Extreme value theorem? Fat tails? Long tails? Give me a break! My models are right, and reality is wrong.

Wow, that quote from Goldman will be the signature quote for this mess.

Our models are good. It's not our fault. We're just unlucky. REALLY unlucky. Even if ever atom in the universe were a hedge fund, making one trade per second for the last four billion years, we'd still be the unluckiest one of them all. We're sorry, but hey (shrug), s*** happens!

Ah crap. Here I go an do some snarky commentary on The Black Swan by Nassim Nicholas Taleb:

http://unintentional-irony.blogspot.com/2007/06/central-limit.html

and about how decent statisticians and scientists don't make the mistake of thinking that a gaussian distribution is about the tails of the distribution (they start arguing about whether the distribution is "really" lognormal, or Weibull, or whatever), when this guy Viniar comes along and demonstrates that there are plenty of people who are even stupider than Taleb says, and they control vast amounts of money.

Judas Maude, Viniar should be horsewhipped for a remark like that. Anyone with half a brain would take their money as far away from Viniar as they could get it.

Think mixture distribution. You have one model for the overwhelming majority of activity. The trick is that the extreme highs and lows are out there, and you need huge quantities of data in an 'ergodic' market market to accurately measure the tails. In fact, you might need a huge quantity of data to spot the extremes.

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