Are We Facing an Exponential Rate of Decay?

It never ceases to amaze me how tiny technical details can have massive implications. Here’s perhaps the biggest example I’ve ever seen.

In a recent post I cited the 1987 Long-Term Capital Management hedge-fund fiasco, which occurred because they were assuming a normal distribution bell curve for financial events. “A one-in-five-hundred-year event on a normal bell curve was a one-in-five-year event in the actual distribution of market movements.”

Now the New York Times (from Reuters) reports that even 20 years after the 1987 LTCM meltdown, Wall Street risk mangers were still using that la-la land distribution. August, 2007:

“We were seeing things that were 25 standard deviation moves, several days in a row.”
–David Viniar, chief financial officer, Goldman Sachs

25 standard deviations means about one chance “in the lifetime of a billion universes.” Think it might be time to take another look at that model?

And even today, after the 08/09 catastrophe — at least according to this article — many still use the “normal” or “Gaussian” distribution — what you get if you throw a bunch of pennies on the ground, measure all their distances from the center, and plot those distances on a histogram.

Why do they assume that the penny distribution is the same as the distribution of financial events encompassing hundreds of trillions of dollars and millions of (presumably, sort of) intelligent agents? No reason that I can discern. And I can’t find anyone who has attempted to plot the actual distribution of market events. (Pointers to the contrary from my gentle readers much appreciated.)

The closest, cited in the article, was the mathematician Benoit Mandelbrot (of fractal fame, among others). In 1962 he looked at a hundred years of cotton prices, and plotted a bell-curve for that actual emprical data.

So here’s the tiny detail: the shape of a bell curve is determined by a single simple number — the exponential rate of decay. The normal, gaussian distribution has an ERD of 2. Flatter bell curves with fatter tails — more unusual events — have lower numbers. Mandelbrot came up with 1.7 for the distribution of cotton-market events. According to Reuters, with some exceptions the normal, gaussian distribution is still “the one that is actually used.”

I recommend giving it a read for more details. It’s quite short.