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Market Abnormality

Life teaches us to deal with uncertainty, but it's usually a predictable type of uncertainty. For example, you probably feel like you see "all kinds" of people every day, but if you saw somebody who was seven feet tall you'd really notice (and if you were uncool you might even ask him how the weather was up there, with a low probability that he'd think you were funny).

Statisticians can easily explain why you react that way: like almost everything else in life, the heights of U.S. adult males form a normal distribution or "bell curve", in this case one with an average value of 69 inches and a standard deviation of 3 inches (according to the CDC, a government agency that secretly measured you while you were asleep). That means that 7-foot guy is 5 standard deviations from average, and in bell curves "5 SD events" are incredibly rare:

 

Show   Guys   Gals
with heights from average
Results

But market volatility can be scary because it definitely isn't normal: far too much keeps happening too far away from the average. The quick way to see that is to count the "big SD events" for short time frequencies like Daily or Monthly returns; they happen many orders of magnitude more often than what you get in a bell curve like the heights example:

Date range: through  
Frequency:
Detail: events


 
Results
Total US Stock Market Data: Ken French
For yearly, note that "average" is not the same as annualized.

 

The details are even worse than you would think from the summary:

 

Frequency:
 
Worst Returns

(Update: On Monday September 29 2008, the S&P 500 dropped 8.78%. We're living in interesting times.)

October 19, 1987 was the worst day in stock market history, with a drop of 19 standard deviations (that's for the Total Stock Market; the Dow dropped even more). In real life bell-curve world, something like that would be virtually impossible: it would be like seeing a science-fiction giant, or else a weird little hyper-midget who had to look up to see down.

The Moral So Far...

The stock market is never appropriate as a short-term investment. It's "abnormally" volatile in ways that real life and statistics classes can't help you deal with.

 

Article Contents
Market Abnormality
Significant Outliers
Ups and Downs
Long Term Risk
Momentum & Reversion
Crashes & Recoveries
Retirement Planning
MPT, VaR
Skill vs. Luck
Books & Links

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