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10/24/2005
Dow Moves, by Victor Niederhoffer

A Spec writes that the market has a natural four-year cycle to bear markets, plus or minus seven years or so, as believed and doubtless charted by his Australian market guru. This is the type of thing that we don't accept on face value around here. Indeed, the idea that there are such things as bear and bull markets, except retrospectively vis-a-vis the retrospective performance of the market in the last x months, is antithetical to the facts.

A famed analyst had a similar take on this question, showing turning points in the market over the last 20 years, with hypothetical buy and sell points a few months or years apart that made a similar tabular case. We tested it, found that the turning points were completely consistent with randomness, and extended it by looking at the future distribution of changes that occurs in the DJIA, conditional on the extent of the decline in the previous x months. As we wrote in our analysis:

To test it, the Professor, his student Chris Hammond, the master simulator Tom Downing and I looked at all those months in the last 100 years when the closing price was below the year end four years earlier. For example the Dow price at October month end 1907 was 57.7. This was lower than the price at the end of 1902, which was 64. That's four years and 10 months without a profit.
During the period from 1900 to date [May 2005] there were 1,264 months examined. Two hundred seventy, or 22%, of them showed such a loss( the dry years). The average one-month price appreciation the next month was 0.8% -- a standard deviation of 7%. This compares to a return of 0.5% a month with a standard deviation of 5% on all other months. Such a difference is merely a 1-in-10 shot to have arisen if indeed there was no difference between the months. In the usual terms, the difference was not significant. The question arises if the price appreciation over bigger periods was more significant. For example, in the year following the dry months, the average price appreciation was 14%, versus 5% in the bountiful months.
Because of the clustering of dry months, without a gain, it was necessary to do some relatively sophisticated simulation to determine the likelihood of such differences arising by chance. We chose to do it by assuming that the distribution of intervals between dry months was our total sample. We chose a random price from the full 105 years, and then classified it as to whether it was a dry or bountiful year. Then we chose the next 12 months, skipping an appropriate number of months based on the distribution of intervals between consecutive months of dryness in the sample. The results show that the difference is about 1 in 40 to have arisen by chance. Thus, there is some support for the idea that dollar averaging works and the idea that buying is best when the doomsday scenarists are gloating the most.

We found the most significant result that when the market is down over the last three to five years, then its expectation is considerably higher than when it's up. That, and the Fed model, are by far the best ways we have come up with, and indeed the only scientific methods that we have ever found, of making a long-range prediction in the market that seems of relevance today.

 Note that the DJIA is currently in an current position relative to these results. Here are some relevant prices:

Date              DJIA Price
10/23/1998        8452.29
10/23/1999        10470.20
10/23/2000        10271.72
10/23/2001        9340.08 
10/23/2002        8494.27
10/23/2003        9613.13
10/23/2004        9757.81
10/23/2005        10215.22

Thus, the average is up over the comparisons with prices one, two, three and four years ago, but down relative to where it was five and six years ago. It would seem to be most similar to where it was in the early 1980s or the mid-1930s. Such comparisons would tend to be interesting but certainly not scientific.

Kim Zussman adds:

Just as a review of history, checked Dow annual returns (Yahoo data adjusted for splits and dividends) Dec-04/Dec-28.  The mean annual return was 6.02% with SD 18.69%.  In other words, though Dow was up significantly over the past 76 years, it achieved this through great variability (presumably that's why it gains).

Here are % annual returns ranked from worst to best.

Also, If last year's return <1 (ie, negative), next year's return:

avg = 1.074 (+7.4%),  stdev = 0.26

If cumulative return of past 5-years <1 (derived as product of each year's return over overlapping 5-year periods), next year's return:

avg = 1.129 (+12.9%),  stdev = 0.22

This last group overlaps since stepping forward by single years includes all contained 5-year down periods.  In other words the five-year priors overlap. I will see if I can fix it but for now we are out the door for some family activities!

The Minister of Non-Predictive Studies adds:

Starting in year 1933...

One year Dow returns following 5-year declines: avg 10.7%; stdev 18.6%; count 14; t-score 2.2

One year Dow returns following 5-year increases: avg 7.2%; stdev 15.8%; count 57; t-score 3.4

A table showing trailing 5 year and 1 year returns

Also, here are the gains/losses that one would have had if he had bought on the first year-end when the 5-year return became negative and then held until the next year end for which the 5-year return was positive:

Buy year-end 1934, sell year-end 1937; gain 72%
Buy year-end 1941; sell year-end 1942; gain 1%
Buy year-end 1944; sell year-end 1945; gain 11%
Buy year-end 1970; sell year-end 1972; gain 21%
Buy year-end 1974; sell year-end 1976; gain 14%
Buy year-end 1978; sell year-end 1980; gain 14%
Buy year-end 1981; sell year-end 1983; gain 13%

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