Daily Speculations 

The Chairman
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11/14/2005
Predicting the Dow, by Victor Niederhoffer
An analysis of sweeping moves in the Dow reveals a practical example of why analysis of ratios is very confusing, especially when the analyst is a chronic bear. Take for example the numerous studies that show that the average P/E of the Dow over the last five years is somewhat negatively correlated with future returns and moves in the Dow. (The studies of course are biased in the sense that they assume earnings were available as of yearend, and they tend to throw out the negative earnings. But put that aside for a moment.) If such a negative correlation exists (and the correlation between a ratio consisting of a 0 correlated bottom and a 0.30 correlated top with the variance of the bottom say five times the variance of the bottom is indeed problematic), the question is, what causes the correlation? The top or the bottom of the ratio?
It turns out that the correlation between the last five years' change in the Dow and the change the next year is 0.25. A good regression equation for the forward oneyear Dow return is 11%  1/10 x previous fiveyear Dow return, with an rsquared of about 0.08.
Thus, if the return on the Dow is 20% over the previous five years, the predicted return for the Dow next year is:
11%  1/10 x 20% = 13%
The current Dow of 10,686 is about 1% below where it was five years ago, so a good regression prediction for the Dow one year later is 11%.
A good way to study regressions is to divide the independent variable into classes and note the mean of the dependent variable in each class. The slope of this relation between the means of the dependent is how the greats originally calculated and motivated the regression line. Until the last 30 years, when computer calculation made statistical work an exercise in the use of cans, this was still the way most investigators looked at linear relations.
Such an analysis shows the following:
Returns of DJI Number of Average return prev 5 years obs next year 100%  50% 4 20% 50%  0% 22 18% 0  50% 40 06% 50%  100% 18 06% 100%  150% 10 04% 150% and up 01 20%
Note that the Dow on average is up 7.5% a year. The current fiveyear change of 0 is quite low on a relative basis  in the bottom quartile. The prediction one year ahead is not encouraging to the chronic bears. But this is just when they are the most vociferous. Of course, this is ideal in the sense that they make the greatest contribution to the market and have the greatest capital and mojo at their disposal at such a time.
Note also how the numerator of the ratio under consideration is the key variable that truly is negatively correlated with the future and how hard the chronic bears and their supporters in the recyclingofinformation business must work to obfuscate the true source.
Year DJIA 12/31/1980 963.98 12/31/1981 875.00 12/31/1982 1046.55 12/30/1983 1258.64 12/31/1984 1211.56 12/31/1985 1546.67 12/31/1986 1895.95 12/31/1987 1938.80 12/30/1988 2168.60 12/29/1989 2753.20 12/31/1990 2633.66 12/31/1991 3168.83 12/31/1992 3301.11 12/31/1993 3754.09 12/30/1994 3834.44 12/29/1995 5117.12 12/31/1996 6448.27 12/31/1997 7908.25 12/31/1998 9181.43 12/31/1999 11497.12 12/29/2000 10786.85 12/31/2001 10021.50 12/31/2002 8341.63 12/31/2003 10453.92 12/31/2004 10783.01 11/14/2005 10683.48Thanks to the Minister of NonPredictive Studies for his calculations and regression.