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5/13/2005
Victor Niederhoffer: A Little Table

A little table comes my way via a tennis buddy who runs a research and investment firm. It divides the stock market into periods of bull and bear moves as follows:

StageBeginEndStartFinish
Rally6/26/19622/9/196652.394.1
Decline2/9/196610/7/196694.173.2
Rally10/7/196611/29/196873.2108.4
Decline11/29/19685/26/1970108.469.3
Rally5/26/19701/11/197369.3120.2
Decline1/11/197310/3/1974120.262.3
Rally10/3/197411/28/198062.3140.5
Decline11/28/19808/12/1982140.5102.4
Rally8/12/19828/25/1987102.4336.8
Decline8/25/198712/4/1987336.8223.9
Rally12/4/19877/16/1990223.9368.9
Decline7/16/199010/11/1990368.9295.4
Rally10/11/19907/17/1998295.41186.8
Decline7/17/19988/31/19981186.8957.5
Rally8/31/19983/24/2000957.51527.4

Several questions arise. Are the swings consistent with randomness? Are comparable swings in individual stocks consistent with same? Are there any predictive merits to such a typology? Can other typologies be developed which are predictive? Is such a descriptive typology useful or educatory? How could other rules be developed which are more useful? Is there any relation between local maxima and minima in markets? How could such a table be best extended forward or backward?

For many years, I have had a guest meeting with my tennis buddy's summer students and presumably this will continue in the future. This year, I will ask my summer people to answer some of these queries and share them with him. Perhaps our readers will wish to make their own contributions to these and related queries.

Professor Bud Conrad responds:

I put Vic's data into a spreadsheet, and added a few entries to interpret the latest five years.

The rallies were over 100% and the declines around 30%. The annualized rally and decline were about the same at around 30%. The average duration of the rallies was almost four years and the declines less than a year.

I added a decline to Oct 2002 and a rise to yesterday. As an alternative, I also added a line for considering the whole five years as a single decline. One of the biggest problems of this form of analysis, is that we never know if the last data point is potentially a turning point until way after the turn is taken. In my attempt to decide if we are in a long five year decline, or a decline to October 2002 and a rise since, I see the decision is arbitrary. As an additional example of the difficulty, I see that we are off highs now, that could mean we are in a third leg of decline, but we won't know until much later.

Duration% ChangeAnnualized
StageBeginEndStartFinishRalliesDeclinesRalliesDeclinesRalliesDeclines
Rally6/26/19622/9/196652.394.13.60.80.22
Decline2/9/196610/7/196694.173.20.7-0.22-0.34
Rally10/7/196611/29/196873.2108.42.20.480.22
Decline11/29/19685/26/1970108.469.31.5-0.36-0.24
Rally5/26/19701/11/197369.3120.22.60.730.28
Decline1/11/197310/3/1974120.262.31.7-0.48-0.28
Rally10/3/197411/28/198062.3140.56.21.260.2
Decline11/28/19808/12/1982140.5102.41.7-0.27-0.16
Rally8/12/19828/25/1987102.4336.852.290.45
Decline8/25/198712/4/1987336.8223.90.3-0.34-1.21
Rally12/4/19877/16/1990223.9368.92.60.650.25
Decline7/16/199010/11/1990368.9295.40.2-0.2-0.84
Rally10/11/19907/17/1998295.41186.87.83.020.39
Decline7/17/19988/31/19981186.8957.50.1-0.19-1.57
Rally8/31/19983/24/2000957.51527.41.60.60.38
Average3.90.91.23-0.30.31-0.33
Decline3/24/200010/9/20021527.4776.82.6-0.49-0.19
Rally10/9/20025/13/2005776.811602.60.490.19
Decline3/24/20005/13/20051527.411605.1-0.24

Aaron Koral replies:

Based on a cursory review of the rally/declines table, I noticed three things:

From the standpoint of randomness, where the same event happens with some probability distribution, I would say there is a low degree of randomness with the declines.

One could, for example, extrapolate forward what is the probability of declines lasting more than one year over the next 20 years from 2003 to 2023, based on the data given in the table.

Here is something to think about: since 1987, Alan Greenspan has been at the Fed as Chairman. Is there be a possibility that, during his tenure, monetary policy and low inflation contributed to the decrease in time for market declines to end?

As for the rallies, there is a degree of randomness. The length of time varies but generally rallies last approximately two years on average.

One way to extrapolate this rally theory backward would be to look at market movements from the Great Depression onward to 1962 and determine whether rallies during that period of time had the same "legs" as during the period of time given in the table.

If so, this could mean that there is some correlation with the length of time in declines and the length of time when rallies start to finish.

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