We have selected the Dow Jones Industrial Average (DJIA) for analysis because data is available since before 1900. In the table below are shown all the primary bear markets of the past 107 plus years, based on closing prices (daily). All primary market tops and all primary bottoms are identified since 1900. There have been 32 primary bull markets and 33 primary bear markets in this time period. The bottom of the latest primary bear market has yet to be defined. Although it is possible that it has been reached, it can not be defined and confirmed until a closing daily high is reached that is at least 20% above the lowest low since the last primary top. This lowest low is then defined and confirmed as the bear market bottom.

Some of the primary tops and bottoms qualify as secular tops and bottoms. These secular tops and bottoms are identified in Table 1 with ** bold italic blue** entries. Primary bull markets have been discussed in the previous part of this series (Part 2). Entire primary cycles will be discussed in Part 4. Secular market cycles will be discussed in a future part of this series (Part 5). The market top of 10/9/2007 has qualified as a primary top. It remains to be seen if it is a secular top or not. The most recent market low in Table 1 is the low of 10/10/2008. It remains to be seen if this is a primary market bottom. It took only one trading day to confirm that 10/10/2008 defined a secondary market bottom. Secondary market cycles will be discussed later in this series.

Following Table 1, there is a statistical analysis of the 33 primary bear markets. We look at what can be said, meaningfully, about the average loss for a primary bear market, as well as the average length (average duration). We also look at what the relationship is between duration and total loss for the primary bear markets.

## Table 1. Primary Bear Markets (Part 1)

## Table 1. Primary Bear Markets (Part 2)

It may be useful to analyze the sizes and durations of these primary market moves. For bear markets, the variation in both gains and durations is very large. An attempt to apply simple statistics runs into some difficulty as discussed below.

In Table 2 there are simple statistics results for primary bear market durations. When all 33 samples are analyzed, we see that the standard deviation (191 days) is a large percentage of the average value (242 days). This indicates that one must view the average with suspicion because it may represent more than one distinct normal distribution (or may contain no normal distributions at all). If we partition the 33 samples into four sub-groups, the resulting statistics are much more satisfying for two of the groups, with standard deviations much smaller than the average values. The results are less satisfying for the very short duration (<120 days) group. If the 21 day duration is eliminated as an outlier, the remaining eleven samples have excellent “tightness”. The longest duration group has two diverse sub-groups: two samples (728 and 761 days) and a second group of four ranging from 416 to 481 days. There is no reason to analyze these two sub-groups individually, since such small groups may not accurately represent larger populations. Simply recognize that the spread in data for that data set (last row in Table 2) is much wider than for the other groups and it is possible that this group might be divided into two groups many years from now when more data is available. Our definitions of quality of distribution “tightness” are shown in Table 3.

## Table 2. Primary Bear Market Durations

## Table 3. Rating Distribution “Tightness”

In Table 4 are shown the statistics for returns of primary bear markets since 1900.

## Table 4. Primary Bear Market Losses

Although the distribution tightness is excellent for all primary bear markets as a group of 33, exceptionally tight distributions result when they are divided into three sub-groups. There is much less dispersion of results for primary bear markets than was the case for primary bull markets (Part 2 of this series).

The distribution of primary bear markets over time are shown in Table 5. Part 1 shows analysis by duration and Part 2 is for distribution of losses over time. These can be compared to similar tables for bull markets in Part 2 of this series.

## Table 5. Primary Bear Market Occurrences Over Time.

*Part 1. Analysis by Duration*

## Table 5. Primary Bear Market Occurrences Over Time.

*Part 2. Analysis by Magnitude of Loss*

Note that 40% of the primary bear markets during the 1930’s fell into the larger loss (>40% loss) category. Compare this to the fact that only 18% of the bulls fell into the larger gain (>100% gain) category. The duration distributions were very similar for bears and bulls with respect to short and very short durations during the 1930’s. For bulls 91%, and for bears 90% had durations <200 days during the time period.

Only a small number of primary bear markets (18%) fall into the medium loss category. The distribution of losses is barbell shaped, with 82% on the ends of the bar.

Larger losses have been quite rare since 1940; only 17% have occurred in the last 68 years (63% of the time span.

The distribution of durations over time is rather uniform with a few exceptions. Among these exceptions: (1) No short duration primary bears occurred between 1940 and 1990; (2) There were no moderate duration bears between 1900 and 1930; (3) The 1930’s saw 30% of all primary bear markets in the 108 year period; and (4) No very long duration bulls (>400 days) have occurred since the 1970’s.

In the graph below we plot % loss vs. bear market duration.

Unlike this plot for primary bull markets (Part 2 of this series), there is no linear relationship between the gain (loss) and the duration of bear markets, indicated by R-squared near zero. Attempts to fit other functions, such as quadratics, other polynomials, logarithmic functions and exponentials all produced very small R-squared values. The variation of gain (loss) as related to bear market duration is strictly random scatter.

Some summary observations are:

- The average primary bear market has lasted for 242 days (approximately 1 year).
- The average primary bear has lost 34%.
- Because there is no relationship between the amount lost in a primary bear market with its duration, one should not make assumptions about
the current bear market will end (reach a bottom) based on amount lost and duration to date.*when* - In contrast to the difficulty (based on history) of projecting the duration for this (or any) primary bear market, it is reasonable to make projections about the extent of the loss. There is a probability somewhere around 67% that we have reached the bottom
of this bear market, based on occurrences of the past 107+ years.*value* - Continuing the speculation from 4. (above), there is only a 6% probability that the current bear market will ultimately have a bottom below DJIA 7082 (50% loss). That leaves a 27% probability that the bottom for the current bear will be below the current low of 8175.77 (10/27/2008) and above 7082.
- Larger bear market losses (>40%) have been very rare in the past 68 years. We are in such a bear market right now and another ended 12/6/1974. The other ten (83% of the total) occurred before 1940.
- The total time spent in primary bear markets was 31% of the past 107+ years. Obviously, then, more than twice as much time was spent in primary bull markets than contending with the bears.
- Since 1940, 16.67 years have been spent in primary bear markets. This is 24% of the elapsed time, much less than the 41% of the time spent with the primary bears from 1900 to 1940.

Comments()