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Strategies & Market Trends : Graham and Doddsville -- Value Investing In The New Era -- Ignore unavailable to you. Want to Upgrade?

To: Ed Brynes who wrote (598)	8/7/1998 11:46:00 AM
From: porcupine --''''>	Read Replies (2) \| Respond to of 1722

<< ...if these prices were translated into German marks (about 2 to the dollar), most of the initial 1's would be changed into 2's, and then Benford's law would fail. I don't see how the probabilities can be "scale invariant" as Dr. Hill says. >> But, for example, if all of the prices from 50 to just under 100 were doubled, then the first digit of the new figures would be 1. I checked the Frankfurt exchange listing, which is presented in marks in the WSJ. 19 out of the 38 that were published had a price beginning with the digit 1. << At any rate, before we get too confident about the DJI reaching 10,000, let's consider that according to Benford's law, it would be just as likely to drop to 1,000. >> I didn't mean to seriously suggest that Benford's law "pulls" prices, in either direction. The law underscores a consequence of logarithms -- for example: that the Dow was likely to spend more time between 1000 and 1999 than any other 1,000-point spread. As it turns out, that is what happened. However, I am suspicious of the requirement that the number have at least 4 digits. This seems arbitrary, since the consequences of logarithms are the same for 3 or fewer digits. By a happy coincidence for this arbitrary rule, the vast majority of the dates in record books are from the 20th century, and therefore begin with 1. All dates between 999BCE and 999CE are excluded for having fewer than 4 digits. And, there are relatively few "milestone" dates before then. Come the new millenium, dates for the next 7,999 years will not begin with 1. It will be interesting to see if this skews the data in the centuries ahead.