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):


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:

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.





Speak your mind

5 Comments so far

  1. anton johnson on October 18, 2009 12:45 pm

    Below is an update of an earlier study I conducted to determine if Dow adheres to Benford’s Law. I used a starting date of 11-24-1982, when the index first closed above 1000. This eliminates distortion caused by using a start year of 1928, when the index was at ~240, that has absent significant data from a theoretical initial index level of 1 through the ~240 level that occurred in 1928.

    First column is first digit of Dow index value.

    Second column is frequency occurrence of first digit in Dow daily close, from 11/24/1982-10/16/2009.

    Third column is frequency occurrence of first digit in Dow daily close, from 02/30/1981 the date of first close >= 1000 through 4/05/1999, the date of first close >= 10,000. I consider this is the most reliable distribution used here.

    Forth column is Benford’s distribution.

    1 42.04% 26.25% 30.10%
    2 15.04% 23.80% 17.60%
    3 12.02% 19.02% 12.50%
    4 2.55% 4.04% 9.70%
    5 3.16% 4.99% 7.90%
    6 1.88% 2.87% 6.70%
    7 4.03% 4.78% 5.80%
    8 10.41% 8.71% 5.10%
    9 8.87% 5.53% 4.60%

    Although possibly containing an insufficient number of data points to determine the validity of gravitational attraction, it seems historic Dow 1000-10000 fairly follows Benford’s predictions, at least as accurately as most other real-life examples cited.

    More fun facts to come.

  2. Mr. Quibble on October 18, 2009 6:25 pm

    Anton, didn’t the Dow first close above 1000 on Nov. 14, 1972, rather than Nov. 24, 1982?

  3. Steve Leslie on October 19, 2009 3:13 am

    with respect to my fellow buckeye,You bring fresh ideas and unique observations due in part to your amateur standing and the fact that you reside outside the warm environs of Wall Street (pun intended) You are not jaded by group think inside the "Manhattan crowd".

    I have heard of conspiracy theories in price manipulation for 30 years in all types of traded markets. I do not know whether a "grassy knoll theory" has ever been confirmed. Perhaps this occurred during the Vanderbilt and Kennedy eras and the latest attempts were in the Hunt's forays across the Rubicon to corner the silver market. Other than those examples I think experts in general will confirm that the markets are way too complex to manipulate these days. Remember the Hunts eventual demise was due to re writing of the rules by the SEC and others as the Chair has described brilliantly in his book.

    That said your points as to a difficult winter amidst rising oil prices is duly noted and should be observed. Maslow's hierachy of needs will suggest that food water shelter clothing will be sought first. Then other less essentials. Should this impact retail sales from Thanksgiving to Christmas will determine the path of the averages into 2010.

    Other big and I mean big variables will be Health Care and unemployment. Should the Congress employ the nuclear option as suggested by Pelosi, Reid and other buffoons, the consequences could be disastrous for equities and the dollar. The second variable is much more problematic and will not be resolved by superfiicial speeches by the Commander-in-Chief of ballyhooism.

  4. anton johnson on October 19, 2009 7:45 am

    Mr Quibble, thanks for pointing out my errata. Corrected data closely correspond to second column figures.

  5. Steve Leslie on October 20, 2009 8:15 am

    The ceiling has now become the floor This week the Dow will probably break 10100 the SP 1100 and the NAZ 2200. All this through the very unpredictable October that I cautioned about several months ago. Looks as though the shorts are leaving the scene of the accident.

    The old adage is A Bull Market climbs a wall of worry. Is this a bull a Bear Market Rally? March Low of 6900 just 7 months ago pretty remarkable and only rarely been accomplished with such magnitude in such a short time.

    Positives Fed continues to pump money into the system. Liquidity is still job one. Rick Santelli likened this liquidity theme to holding a balloon underneath a faucet and filling it with water. How much will it sustain. Banks are healing real estate sales are stablilizing and improving.

    Worries. B of A announces earnings problems based on credit card problems. Congress fighting mightily to coordinate a health care bill. Pelosi and Reid becoming desperate trying to put a 60 person consensus in the Senate. Snowe indicates a favorable leaning toward approving something. Unemployment still 10 percent nationwide and much higher in some states. Administration unable to budge this number down. Oil up and the dollar is down ( the people ride in a hole in the ground.) Christmas season starts in 30 + days.


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