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December 31) are looking at an astronomically based cycle.

CMT Research Article: Does a Lunar Cycle
Affect Market Averages?
© Bill Meridian, 2. Methodology
Abu Dhabi, United Arab Emirates The lunar cycle is defined by astronomers by the period beginning and ending with
the conjunction of the sun and the moon. The two bodies are conjunct when they are
zero degrees apart. The faster moon then races ahead of the sun, makes a 360-
1. Introduction degree arc, and then conjoins the sun again, completing a cycle. This process takes
This is an abridged version of a study that was conducted in 1994. The purpose of a mean time of 29 days, 12 hours, 44 minutes, and 2.78 seconds. This period may
this paper is to derive a cycle relating the lunar cycle to an equity average. This cycle vary by as much as 13 hours.
will then be evaluated for its profitability versus a buy-and-hold strategy. The results
may be of interest to short-term traders with an interest in cyclic analysis.

Those who seek a causative link might consider the following. Serotonin is the
substance in the brain of a homing pigeon that sensitizes the bird to the earth's
magnetic field, allowing the pigeon to 'home in.' The field itself has been shown to
fluctuate with lunar and solar influences. Nelson's work demonstrates a relationship
between all of the planets and solar activity. Serotonin exists in the human body. The
substance was neglected until biotechnology companies recently took an interest.
Perhaps this is the link.

The Link to Markets

In John Murphy's text, Technical Analysis of the Futures Markets, he writes, "There is
another important short-term cycle that tends to influence most commodity markets-
the 28-day trading cycle. In other words, most markets have a tendency to form a
trading low every 4 weeks. One possible explanation for this strong cyclic tendency
throughout all commodity markets is the lunar cycle. Burton Pugh studied the 28-day
cycle in the wheat market in the 1930s and concluded that the moon had some
influence on market turning points. His theory was that wheat should be bought on a
full moon and sold on a new moon. Pugh acknowledged, however, that the lunar
effects were mild and could be overriden by the effects of longer cycles or important
news events."

John McGinley, writing in Technical Trends, once mentioned that Arthur Merrill
conducted a study of market behavior around full and new moons and found no
strong correlation. More recently, the February 27,1994 issue of Mark Liebovit's The 29-day lunar cycle was related to the DJIA on a day-by-day basis. This
Volume Reversal Survey stated that he had noted a correlation between the lunar calculation was performed by PC as any other cycle computation would. The
cycle and Federal Reserve actions. Chris Carolan, noted for his work with the Spiral difference between this cycle and any other, such as the annual or 1-year cycle, is
Calendar, has achieved some success with a lunar-based forecasting system. the method of choice of starting date. The starting date was the day of the new moon.
Indeed, many older societies utilize a lunar calendar. Our own calendar year is based The ending date is the date of the next new moon. Indeed, there may be no causal
upon the movement of the earth around the sun. Those technicians who rely upon relation between the moon and prices, but the time series that will be utilized to
the annual cycle (the average percentage change in the DJIA from January 1 to define the cycle will be determined by lunar motion, just as the annual cycle is
determined by our calendar which is derived from the solar cycle. 5. Fourier least squares approximation was utilized to determine the equation of the
line of this cycle. This cycle line can be projected backward or forward. The result is
The cycle study is conducted through a series of steps: graph 1.

1. A list of dates of all lunar cycles from 1915 through 1994 was calculated. See table 6. This cycle line was tested versus a buy-and-hold strategy from 1960 through 1993
1 as an example. to determine its predictive value.

3. Discussion of the Results

Graph 1 summarizes the results. The horizontal axis represents the 29-day cycle.
The gradations denoted by the dashed vertical lines are 10% of the cycle, or 2.9
days. The vertical axis represents the average percentage price change in the DJIA.
For example, the DJIA has risen an average of 0.1% from the new moon to the cycle
peak about 7 days later. The DJIA has then dropped 0.22% from this cycle peak to
the cycle trough.

2. This database of dates is then instructed to access a daily DJIA quotes from the
price database. The program then selected the DJIA price on the day of the first new
moon in 1915. In the next cell, the DJIA for the following day was inserted, and so on,
through to the day of the next new moon. The PC used the Friday close when it
encountered a weekend. The result was a row of prices. This process was repeated
for each year, 1915 through 1994. There are about 13 such cycles per year. The
sample size was over 1,000 cycles.

3. The resultant array of prices was smoothed.

4. Individual cycles were then combined to obtain a composite cycle through vector
addition. This depicts the average percent change in the DJIA from new moon to new
moon from 1915 through 1994.
Graph 1 reveals that the DJIA has, on average, risen from the new moon for about 7
days. The DJIA then has bottomed about 4 days before the next new moon. The
price slide seems to accelerate after the occurrence of the full moon. (This would
explain why Arthur Merrill did not find turning points near the actual lunations; the top
and bottom of the cycle tend top fall between the two phenomena.)

Graphs 2 through 9 depict the same relationship broken into time segments. Graph 3
shows the same relationship from 1915 to 1920 only. Graph 4 represents the cycle
for the decade 1920 to 1930 only. Graphs 5 through 9 depict the cycle by decade
through 1990. The period 1920-1930 (graph 3) shows the greatest difference from
the average in graph 1. The 1960 decade in graph 7 is similar to the average, but
shows a higher peak 1 to 2 days after the full moon. In the 1970s (graph 8) the cycle
bottom occurred much earlier then in the average cycle in graph 1. In the remaining
decades, the relationship was fairly consistent with the average overall cycle. The
cycle in the 1980s was consistent with average.
Graph 10 is the same study applied to the S&P 500 from 1950 through 1994. The
shape of the curve is roughly the same. This study was added to demonstrate that
there was little variation in the effect of the cycle in relationship to these two popular
averages.
 Table 2 summarizes the results for 1993.

Buy and Sell Test Versus a Buy and Hold Strategy

The cycle was tested as a short-term timing aid. The program was instructed to buy
the DJIA at every cycle bottom and to sell (move to cash) at every cycle high. The
program bought at every "long" arrow (marked by 'lo' on the graph).
The test began in 1960 and concluded with 1993. The yearly results depicted in table
2 are summarized in annual form in table 3.

1. The signals derived from the cycle turned an initial $1,000 into $2,138. A buy-and-
hold strategy returned $5,526.
2. Of the 421 buy signals, 228 or 54% were profitable. July 29-Sept. 5
Sept. 30-Oct. 5
3. Trading by the cycle exceeded the buy-and-hold in 11 of the 34 years tested. Oct. 26-Nov. 6
Nov.24- Dec.3
4. Cycle trading yielded the best returns in 1987 (21% versus 2.9%) and 1988 (15.4% Dec.18- Jan.11
versus 11.9%).

5. Cycle trading returns were poorest in 1973 (23% loss versus a 16.6% loss).

Three Attempts to Improve the Results

Attempts were made to improve the batting average of the cycle by confirming the
buy signals with a 14-day oscillator such as an RSI or a stochastic. These tests did
not significantly improve the results.

1. This strategy underperformed both the first strategy and the buy-and-hold strategy.
It returned only $1,416.

2. Of the 420 buy signals, 239 or 57% were profitable.

3. Trading by the cycle exceeded the buy-and-hold in 11 of the 34 years tested.

4. Cycle trading yielded the best return in 1975 (19%), but underperformed a buy-
and-hold (38.3%).

5. Cycle trading returns were poorest in 1990 (18% loss versus a 4.5% loss).

One more attempt was made to improve the results. The buy-sell test was repeated
as in the first test. That is, the cycle lows were bought and the cycle highs were sold. So a lunar cycle buy signal was accepted if it fell in one of these time periods. These
However, this time the buy signals were accepted only if the annual cycle pointed up. were times when both the lunar and the annual cycle pointed up. Buy signals that fell
1 day before any of the above time periods were accepted. I felt that the annual cycle
The annual change in the DJIA was computed on a daily basis. (The annual cycle is upturn only 1 day later would be sufficient reason to initiate a long position. Buy
based upon the calendar, which is derived from the relationship of the earth and the signals that occurred 1 day before the end of any of these time periods were rejected.
sun. So, a solar cycle was calculated. The methodology for the determination of the This was done because the shorter lunar cycle would have to 'swim upstream' versus
annual cycle was the same as that for the lunar cycle.) The relationship is shown as the stronger annual cycle which was only 1 day away from topping. One possible
graph 11, and will likely be familiar to any technician who employs the seasonal criticism is that the annual cycle may have had a different shape in the 1960s or the
cycle. This cycle rises, on average, in the following time periods every year: 1970s. This would then change the time periods above. But seasonality appears to
be consistent enough, especially in the post-WW2 years, that the analysis was
Jan. 26-Feb. 9 conducted.
Feb. 23-March 12
April 1-18 The results did not enhance the trading record. The number of trades dropped from
May 28-June 12 420 to 182. The number of profitable trades was 102, or 56% of the total. The
June 24-July 15 theoretical portfolio of $1,000 increased to only $1,875.
DJIA Highs and Lows in Relation to the Cycle The results reveal a somewhat higher probability for 10% highs in the crescent and
Another test was devised in order to determine if there is any consistency to the gibbous phases (2 of the 3 phases around the cycle top) and a lower probability of
cycle. A list of highs was generated utilizing a 10% filter rule from Arthur Merrill's highs in the cycle bottom, or 3rd quarter phase.
books, Behavior of Prices on Wall Street and Filtered Waves. That is, all moves of
less than 10% were filtered out of the DJIA from 1885 through 1994. This produced a This process was repeated for 10% lows (see graph 13). Few lows (16.8%) fell in the
list of 249 highs and lows. These dates were then sorted to determine where they 2 phases around the projected cycle high. Most of the lows (29.6%) fell in the last 2
occurred in the 29-day cycle. For these purposes, the cycle was divided into its 8 phases, near the projected cycle low.
astronomic phases as in chart 1. These 8 divisions are marked on the cycle graph as
8 vertical solid lines in graph 12. The name of the phase appears at the bottom of the
graph. The percentages represent the percent of 10% filter highs that fell in that
phase historically. For example, 8.9% of all highs determined by the 10% filter
method from 1885 to 1994 fell in the new moon phase.

The same test was conducted for a 5% filter set of highs and lows from 1885 to 1994.
This produced 851 turning points. This was done because the 29-day cycle is a short
one, and the use of a 10% filter produced an average of only 2.5 turning points per
year. Graph 14 depicts the distribution of 5% highs. There has been a greater
percentage of highs in the second, third, and fourth (crescent, 1st quarter, gibbous)
If the highs were evenly distributed, one would expect an average of 12.5% of the phases, the high phases of the cycle line. Graph 15 demonstrates the same graph for
highs to fall in any one phase. If the cycle is indeed operative, then the highs would the 5% lows. This gave a less definitive picture of than did that for the highs. The
tend to cluster around the cycle high, the crescent, 1st quarter, and gibbous phases. lows tended to be somewhat more evenly distributed than the highs. There tended to
Fewer cycle highs would be anticipated at the cycle bottom, the 3rd quarter phase. be more lows in the crescent and the balsamic phases, the latter phase being the
bottom in the cycle line.

Big One-Day Rises and Declines in Relation to the Cycle

A list of the 100 largest one-day rises and the 100 largest declines (in terms of DJIA
points and in terms of percentage change) was obtained from Delafield, Harvey, and
Tabell. The list was updated before this study, so the total numbers 102 in each case.
As with the highs and the lows in the previous test, the lunar phase in which these
changes occurred was determined. The results are plotted in graphs 16 and 17 at the
bottom of the graph, in the same fashion as that for the highs and lows in graphs 14
and 15.
The greatest percentage of rises occurred in the crescent and full moon phases. The
cycle is rising in the crescent phase, so the large number of increases here is in
agreement with the cycle. The large number in the full moon phase differs from the
cycle, which is declining in that phase. Perhaps this reflects the "blow off" nature of
tops.

The distribution of 1-day declines was more closely in agreement with the cycle line.
Most of the drops (35.3%) fell in the disseminating and 3rd quarter phase, at the
bottom of the cycle. Perhaps this reflects the occurrence of selling climaxes at lows.

This analysis was repeated utilizing the 100 biggest up and down days in terms of
percentage change, rather than points. This method yields many days in the 1930s.
The points method yields many days in the 1980s and the 1990s. The results are
plotted in graphs 15 and 16 at the top of each graph.

The percentage method reveals many more big up days in the first 3 phases, more in
line with the cycle graph. The biggest difference was in the full moon phase where
the percent of big 1-day moves fell from 20.6% to 9.0%.

In terms of the percentage of 1-day declines, the major difference was, again, in the
full moon phase where the percentage almost doubled.

Support from a Previous Study

Frank Guarino conducted a study entitled Relationship of the Stock Market to the
Lunar Cycle as a requirement for an MBA at Pace University in the late 1970s.
Guarino tested the rate of change in the DJIA between lunar phases from 1950
through 1973.

He also computed the number of price increases and decreases and the averages of
these changes between phases. The actual rates of change were also compared to
the average rates of change. The ranges and the average deviations were also
calculated. The average deviation was the arithmetic mean of the absolute values of
the deviations of the rates of change from the arithmetic mean.

The findings were:

1. The period from the balsamic (last) phase to the new moon (first) phase showed
the largest average rate of increase and the smallest average rate of decrease. The
period from the full moon to the balsamic (last) phase had the largest average rate of
decrease and the smallest average rate of increase. apples-for-apples basis, but the scant excess of the cycle-generated trades over 52%
does not seem encouraging. Methods designed to enhance the returns did not
2. The highest average rates of change occurred in the 2 phases around the new succeed. The addition of technical oscillators as a confirming mechanism did not
moon. improve the results, nor did selling cycle highs or confirming buys with the annual
cycle. Traders who are tempted by the sale of such trading systems are advised to
3. DJIA increases (in terms of the number of increases) were more prevalent think twice before purchasing any system based upon this one cycle. These findings
between the new moon phase and the 1st quarter phase. should not discourage further attempts to link price series cycles to phenomena
outside of the marketplace.
4. Analysis of the ranges revealed that the period between the 1st quarter and the full
moon had the widest limits. This period also had the largest average deviation. The OEX traders with short-term time horizons who rely upon cycles may wish to take
period from the 3rd quarter to the new moon had the most narrow range and the note of certain findings. By itself, the lunar cycle does not outperform. But the DJIA
smallest average deviation. does demonstrate more upside volatility from the phase prior to the new moon to the
phase immediately after. There also is a slight tendency for the DJIA to show more
Guarino concluded that the period from the full to the balsamic phase (from the 50 downside volatilty after the cycle peak. This may be useful knowledge to shorter-term
gradation through the 100 gradation on graphs of the cycle) were the least favorable players who employ leverage.
for the trader who is long. The period beginning with the balsamic and new moon
phases (90 and 0 gradations on the graphs) is the most favorable for the bull.

This study, conducted along different lines and for a much shorter time period,
supports the relationship that has been demonstrated in Graph 1. Note that the
highest average rates of change and the largest number of price increases fell in the
phases at the bottom of the derived cycle. Also, prices tended to have the smallest
deviation around the cycle bottom and the highest around the cycle top. In other
words, price action at cycle bottoms was more descriptive of a bottoming or basing
process. The Guarino numbers show that prices fluctuate more around the projected
cycle top. Volatility is known to increase around market tops.

4. Summary of Findings
The study indicates that there is, on average, an upmove in the DJIA commencing in
the days prior to the new moon and ending about 6 to 7 days afterward. The
breakdown of the cycle by decade demonstrates this as does the Guarino study. In
addition, the buy-and-sell tests show that buying the lows outpeforms buying the
highs. Whereas the 'batting average' of profitable trades did not decrease when the
highs were used as buy points, the magnitude of the profits shrank while the
magnitude of the losses grew.

This cycle is too weak to be relied upon solely as a trading timer. The buy-and-sell
study shows that such a strategy does not keep pace with a simple buy-and-hold
strategy. Only 54% of the purchases timed by the cycle were profitable. This
percentage is approximately in line with the percentage of rising days (52%) in the
DJIA as calculated by Arthur Merrill. The two percentages are not comparable on an