When Genius Failed
I'm re-reading Roger Lowenstein's When Genius Failed, and I'm finding it a remarkable book. Again. It's about the Long-Term Capital Management debacle of 1998, but it could easily be about the financial meltdown of 2007-2009. On pages 71 - 77, Lowenstein discusses "fat tails" in the distribution of returns to financial assets, beginning with this quotation from Eugene Fama's dissertation, about daily volatility of stock prices:
"If the population of price changes is strictly normal, on the average for any stock...an observation more than five standard deviations from the mean should be observed about once every 7,000 years. In fact such observations seem to occur about once every three to four years."
Such large, discontinuous, and "unexpected" events (based on a normal distribution happen fairly frequently. Only seven years before LTCM was founded, prices on the NYSE fell by 23% in one day, an event that Lowenstein characterizes as follows: "In fact, had the life of the Universe been repeated one billion times, such a crash would still have been theoretically 'unlikely.' But it happened anyway." "Theoretically unlikely" means "almost impossible, if the distribution of price changes is normal." But the non-normality of returns was well known...
Lowenstein attributes this, in part, to the (high) probability that returns on Day i and on Day i+1 are not independent of each other (which is an assumption of random walks and normal distributions). While that may be sufficient, it is not necessary. The distribution of returns can be non-normal (e.g., have fat tails), but still display independence of observations.
What remains amazing is how short the memory of people engaging in financial speculation can be. After the Great Crash of 1929 - 1933, it took nearly 40 years for people to begin to forget. But the lessons of 1987 seem to have evaporated by 1994, and the lessons of 1998 (the LTCM crash) seem to have dissipated by 2002 or 2003. Oddly enough, the new lesson was not that returns to investments in housing would follow a normally-distributed random walk, but that they were non-normal in a specific way--highly, extremely positively skewed.
The events that resulted in these crashes may have been low-probability events (even if they were not as low-probability as people thought). But they were probable enough to result in financial crises.
Keynes pointed out, 70 or 80 years ago, that even low-probability events, even events that we might attribute to "irrational" movements in market prices of financial assets could be devastating: "Markets can remain irrational for longer than you can remain solvent."
I wonder how long we'll remember this lesson this time.