Thin Tails... relative to the hype

A lot of people think that this last recession was caused by fat tails in the market. When they think of the market, they are generally thinking about a stock market like the Dow Jones Industrial Average or the S&P 500.  Fat tails refers to a distribution of returns with more extreme points than suggested by a simplistic approach that only looks at the standard deviation and assumes a normal distribution.  The below chart shows the kurtosis (The higher the kurtosis, the fatter the tail) and volatility of the S&P 500 market over the past 80 years. Click on the chart to enlarge.

Source: Palantir Finance

It is interesting to note that the returns of the S&P 500 during the downturn didn’t have fatter tails than past market meltdowns. While it is true that deleveraging and liquidity events caused some positions popular with leveraged quantitative funds to all move in the same direction and models with uncorrelated and always rising house prices banks used to asses their risk were quite unrealistic, the popular myth that quants just didn’t understand that general market returns are not normally distributed is not true on many different levels.

2 responses
This is surprising to me. Especially during the crisis when daily moves of the S&P were frequently >5%, you'd expect the tails to be fatter. What's the look-back on your estimation of kurtosis? Perhaps the issue is that the distribution was still normal, but the SD was just higher. In this way, relative to the 'norm' the kurtosis would be quite high, but relative to the recent norm, nothing special.
250 day look back for both kurtosis and historic volatility. The large moves in the market were captured by higher volatility instead of much fatter tails. The calculation divides the 4th moment about the mean by the standard deviation raised to the 4th power, so a higher standard deviation would serve to lower the measured kurtosis by quite a bit.