# Testing a Market Prediction, from Kim Zussman

December 21, 2007 |

Vitaliy N. Katsenelson, CFA wrote: "Over last two hundred years every secular bull market was followed by a range-bound market.". Test this and discuss your results.

There are a number of ways to test this, but here is a first look:

SP500 1950-present (monthly) was used to calculate Dec-Dec returns (w/o dividends), as well as check for intra-month high and low. The intra-month high and low for Jan-Dec were used to find annual high and low, and the annual range was defined as [(max monthly high)/(min monthly low)]-1

Annual range for the series ranged from 0.10 (1993) to 0.66 (1974); 2007 is 0.16

First, what effect do last year's range and return have on this year's return?

Regression Analysis: nxt yr rt versus yr ret, yr range

The regression equation is nxt yr rt = 0.0537 - 0.069 yr ret + 0.151 yr range

`Predictor    Coef   SE Coef      T      P  VIF`
`Constant   0.0536   0.0551    0.97  0.335`
`yr ret    -0.0691   0.1361   -0.51  0.614  1.0`
`yr range   0.1510   0.1782    0.85  0.400  1.0`

S = 0.165498 R-Sq = 1.8% R-Sq(adj) = 0.0%

Durbin-Watson statistic = 1.92818

Both annual return and range have insignificant effect on the following calendar year's return (though there is positive correlation with range and negative with return).

Second. What is the effect of last year's return on this year's range? Here is regression of this year's range vs last year's return (ie, does last year's return predict whether this year has big or small range?):

Regression Analysis: this range versus last yr rt

The regression equation is this range = 0.303 - 0.292 last yr rt

`Predictor     Coef  SE Coef    T      P`
`Constant    0.3030  0.0179  16.87  0.000`
`last yr rt -0.2921  0.0959  -3.04  0.004`

S = 0.116678 R-Sq = 14.9% R-Sq(adj) = 13.3%

Sure seems to be predictive and in the hypothesized direction, but is the correlation due to prior years which are down or up? Ran another regression: Dependent var = this year's range, IV's are last year's return if up (otherwise zero), and last year's return if down (otherwise zero):

Regression Analysis: this range versus last up, last dn

The regression equation is this range = 0.241 + 0.023 last up - 0.982 last dn

`Predictor   Coef  SE Coef      T      P  VIF`
`Constant  0.2411   0.0281   8.57  0.000`
`last up   0.0229   0.1457   0.16  0.876  1.4`
`last dn  -0.9822   0.2659  -3.69  0.001  1.4`

S = 0.110013 R-Sq = 25.7% R-Sq(adj) = 22.9%

Durbin-Watson statistic = 1.88298

The effect stems from prior years which were down. So you can't say that this year will be range-bound if last year was up big, but you can say that if this year was down - the bigger the decline the larger next year's range will be. (Actually you can say whatever you want because Putin is not running here).

Conclusion. Since declines and high volatility tend to come together, and volatility clusters, it makes sense that big down years are followed by large range years. A more correct restatement of the original hypothesis would be: large secular bear markets are followed by wide ranging markets.

## Vitaliy Katsenelson writes in:

Kim took the following phrase and tested it: Vitaliy N. Katsenelson, CFA wrote: "Over last 200 years every secular bull market was followed by a range-bound market."

I understand the desire to test things, but it is also important to test the RIGHT things. My book is written about secular markets, not minute, hourly, weekly, monthly, or even yearly (if you choose to look from a single time perspective) markets. Kim tested something that has no relevance to my book.

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