Skip to main content
Message Font: Serif | Sans-Serif
 
No. of Recommendations: 1
You know you're working with data that are approximately normal if they have a classic bell-curve shape that's fairly symmetrical about the middle.

That's where I was mistaken. I thought a bell curve had to be perfectly symmetrical.

I posted something on the Berkshire board awhile back about there being more stock market crashes than buying panics and Peter L. Bernstein's conclusion, in his book Against the Gods: The Remarkable Story of Risk, that this means "At the extremes, the market is not a random walk." http://boards.fool.com/Message.asp?mid=16273617

But it's almost impossible to have enough data to accurately understand what's happening out in the tails. Two sigma events only occur about 1 time out of 19, so to observe 200 of them we need to sample 3,700 independent events. To witness that many 3-sigma events, we need to sample 45,000 independent events. For 4-sigma, we'd need 1.5 million events, and for 5-sigma, we'd need 135 million. There simply aren't enough independent data, on anything, to understand what's happening way out in the tails. That word "independent" is critically important too. Stock market data are notoriously autocorrelated,

The Wall Street Journal had a Stock Market Quarterly Review Section in its April 1st edition. It showed the twenty biggest one day percentage gains and twenty biggest one day percentage losses of all time for the Dow Jones Industrial Average. 1929 had four of the biggest declines but they clearly were not independent of each other. They took place on Oct. 28, Oct. 29, Nov. 6 and Nov. 11. There were two drops back to back in 1933, on July 20 and 21. The last pair was the Oct. 19 and Oct. 26 declines of 1987.

The other twelve big declines are not near each other.

An interesting fact about the twenty biggest gains is that fifteen of them, or 75%, took place in the three year span 1931-1933.

jkm929

Print the post  

Announcements

What was Your Dumbest Investment?
Share it with us -- and learn from others' stories of flubs.
When Life Gives You Lemons
We all have had hardships and made poor decisions. The important thing is how we respond and grow. Read the story of a Fool who started from nothing, and looks to gain everything.
Contact Us
Contact Customer Service and other Fool departments here.
Work for Fools?
Winner of the Washingtonian great places to work, and Glassdoor #1 Company to Work For 2015! Have access to all of TMF's online and email products for FREE, and be paid for your contributions to TMF! Click the link and start your Fool career.