# Chances of a down market, four years in a row?

From: John Conover <john@email.johncon.com>
Subject: Chances of a down market, four years in a row?
Date: 3 Jan 2003 23:44:33 -0000

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So far, in the last week, (CNBC, etc.,) I've heard that the last time
we had four down years in row in the major US indices was the early
Thirties in the Great Depression-implying that its almost a certainty
that this year, (2003,) will finish up.

What's the chances?

The market indices increase at a little less than 10% per year, (over
the Twentieth Century,) so, we would expect a four year gain of about
1.1^4 = 1.46.

But about a 2% deviation per day in index values, (for the Nasdaq-a
little less for the S&P and DJIA,) would be about e^(0.02 * sqrt
(1012)) = 1.89 at four years, or 1.89 / 1.46 = 1.3 standard
deviations, which has a chance of 0.0968, or about 0.1 = 10%, or about
one chance in ten.

So, the chances of the market indices finishing down at the end of
2003 is about one chance in 10-and a 90% chance of finishing up.

John

BTW, sanity check: If this year finishes down, then there will have
been two times in 70 years-for a total of at least 8 years-or 8 / 70 =
11% that the possible combinations of years finished down in
succession-approximately. Or, about 10%-which is reasonable.

--

John Conover, john@email.johncon.com, http://www.johncon.com/

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