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Market Statistics

8-Sigma Shock

A nearly 8-sigma event rattled U.S. stock market on March 9, 2020, due to selling stampede.  Charts with interesting statistics are included below.

This is a histogram of S&P 500 daily returns from August 1940 to March 9, 2020:

This is a highly leptokurtic distribution with kurtosis at 22.01. There is also negative skew of -0.6489. The mean daily return is 0.03% and the standard deviation of the sample is 0.958. There are 19999 daily returns with maximum at 11.58% (2008)  and minimum at -20.47% (1987 crash.)

The index fell -7.5% yesterday or about -7.9 standard deviations.

Market participants should understand what they are dealing with when the return distribution is highly leptokurtic as above: there is large tail risk. When one is caught betting against the tails, left or right, there is potential for large losses. However, passive investors profit longer-term because the mean return is positive although that comes at a relatively high standard deviation.

Some  in social media have complained they do not understand histograms. This is understandable because  of the frequency domain. Below is the histogram in the time domain most are accustomed with.

There have been seven returns lower than -7% since August 1940, as shown in chart above. However, there have been only four returns greater than 7%,  two during the 2008 downtrend , one at the bottom of that downtrend and the other one after the 1987 crash.

Just a reminder, I avoid predictions, especially long-term  but this one was sort of expected in the short-term


Charting and backtesting program: Amibroker

Data provider: Norgate Data

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