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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 year-end, 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 one-year Dow return is 11% - 1/10 x previous five-year Dow return, with an r-squared 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 five-year 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 recycling-of-information 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 10683.48```
Thanks to the Minister of Non-Predictive Studies for his calculations and regression.

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