Oct

17

What would a weekend be without my noting that Mr. Dow crosses back and forth over magic 10000 gravitational level six times on Friday, as was guaranteed to happen.

Allan Millhone comments:

I note a different Isaac Newton effect as pump prices rise in the last ten days. I read in morning's paper an inside trader hedgie arrested. I feel as a sheer novice it is scoundrels like him who moved the Market to ten thousand and not a solid economy; as to foreclosures we have yet to see the true picture. This coming Winter will be a very cold one and demands will be made on natural gas and ole Reddy Kilowatt. People will use their cash for food and fuel and home utilities and holiday retailers will suffer.

Alston Mabry takes out pencil and paper:

The Dow first crossed 10,000 on 12 March, 1999. The first open above 10,000 was 19 March, and the first close above was 29 March.

Looking at all Dow days from 29 March, 1999, to present and calculating how far in points each close is to its nearest round thousand, produces the following stats:

Total days: 2657

Mean distance in Dow points from nearest round thousand: 265.46

Histogram (using 25 point bins):

bin//frequency//%totaldays

0-25 112 4.22%
50 122 4.59%
75 104 3.91%
100 119 4.48%
125 132 4.97%
150 135 5.08%
175 105 3.95%
200 124 4.67%
225 144 5.42%
250 115 4.33%
275 126 4.74%
300 135 5.08%
325 140 5.27%
350 116 4.37%
375 131 4.93%
400 156 5.87%
425 168 6.32%
450 156 5.87%
475 157 5.91%
500 160 6.02%

Looking again at this histogram, one can total the bin %'s in different ways:

distfromround / %totaldays

.   0-250 45.6%
250-500 54.4%

.   0-125  22.2%
125-250  23.4%
250-375  24.4%
375-500  30.0%

We are honored to receive this communication from Prof. Charles Pennington:

Benford's Law gives expectation frequencies for the first digit of a numerical quantity that's thought to be uniformly distributed logorithmically over several orders of magnitude. The Dow has varied by about 2 orders of magnitude since 1928. Here's its distribution along with the Benford's Law prediction:

columns:
first digit / frequency of occurrence in daily Dow 30 prices /
expected frequency from Benford's Law

1 35.0% 30.1%
2 12.5% 17.6%
3 6.3% 12.5%
4 4.7% 9.7%
5 3.7% 7.9%
6 5.5% 6.7%
7 6.1% 5.8%
8 14.2% 5.1%
9 11.9% 4.6%

(There were 20,352 observations.)

So there are "too many" 1s, 8s, and 9s, and not enough 2s, 3s, 4s, and 5s. Because of the serial correlation in the daily prices, it's not obvious (to me) whether this is statistically significant, but over history the Dow has spent some extra time hanging around near the powers of 10.

Victor Niederhoffer bypasses Benford's Law in his evaluation:

Yes, it seems significant. There were 45% within 250 points and the standard error expectation was 25. So the deficiency of 130 is five standard errors from expectation.

Alston Mabry follows up:

I broke the Dow into non-overlapping 250-day segments and counted the number of times within each segment that the Dow had an 8- or 9- handle. Chart of the results (click on All Sizes [magnifying glass] to see large version).

Conclusion: the big skew is there from the mid 1960s into the early 1980s.


Comments

Name

Email

Website

Speak your mind

Archives

Resources & Links

Search