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Tuesday, July 21, 2009

The U.S. Stock Market Correlated with the Phases of the Moon Research Paper

As we approach a new moon phase tomorrow July 22, 2009 (local time July 21, 2009), I decided I would share this today. A while back for an econometrics class, I conducted a study to see if the U.S. stock market was at all correlated with the moon phases. The findings are certainly interesting, and some statistically significant, however this is not a basis for any investment strategy!

My original research paper is embedded below. View, print, or download my paper from the Scribd box below.


The U.S. Financial Markets are Correlated with Specific Moon Phases Accurate or Complete “Lunacy”? Marco Hickey April 2009 Statistically significant correlation exists between the U.S. financial markets and certain lunar phases. Regressions were performed on data from 1988-2008 for five U.S. stock market indices and the ten year Treasury bond, juxtaposed to the phases of the moon. Since ancient times entire civilizations have associated the lunar phases with specific human behaviors. Extensive research has been conducted over the years to see if there are any significant changes in human behavior during specific lunar phases. As written by Paracelsus in the 16th century “mania has the following symptoms: frantic behaviour, unreasonableness, constant restlessness and mischievousness. Some patients suffer from it depending on the phases of the moon” (1). More recently Lieber and Sherin reported homicides over 15 years in from 1956-1970 given the lunar phase, and found it to be statistically significant peaking at times of a full moon and a secondary peak at periods just after the new moon phase (2). If the lunar phases do affect human behavior, can it be said that they also affect the United States financial markets? If investors do react based on the lunar phases, it would be a complete violation of the Efficient Market Hypothesis, which states that all financial instruments reflect perfect information when being bought and sold. This study has been performed based on a psychological hypothesis. A similar study was conducted in 1985 by Ivan Kelly and James Rotton, investigating a relationship between the moon phases the Dow Jones Industrial Average, but nothing was proved to be significant. The goal of this research is aimed at finding any significant correlation between the U.S. financial markets, using data from five major indices and the ten year bond, and the moon phases, using data from four lunar phases. Data from the United States Naval Observatory website was obtained. The data includes information on four moon phases which are: new moon, first quarter, full moon, and last quarter. This data also included information on total lunar eclipses, and total solar eclipses. Data was obtained for 21 years from years 1988-2008. Data from Merrill Lynch was also obtained. The data includes information for the 10 year Treasury bond note, and five major U.S. stock indices which are: Dow Jones Industrial Average, NASDAQ, New York Stock Exchange, Russell 2000, and S&P 500, for the same 21 year period. The data was organized in a spreadsheet for each index. In the first column was the date, in the next column was the index closing price corresponding to each date, and in the next six columns were: new moon, first quarter, full moon, last quarter, total solar eclipse, and total lunar eclipse, respectively. The moon data was filled in the spreadsheet where a one indicated an occurrence for each specific lunar event, and a zero indicated no occurrence, corresponding to each date. Similar research papers include a time window, where as many as 2-7 days before and after the moon phase occurrence are marked. Note that research conducted for this study only included the date of the lunar occurrence. Four dummy variables were created for the regression, to indicate an occurrence of a specific lunar event. The dummy variables are: d1 , d 2 , d 3 , and d 4 . The econometric model used for the regression was yt = β 0 + β 1d1 + β 1d 2 + β 1d 2 + β 3d3 + β 4d 4 + yt −1 + ε t where yt = index closing price, d1 = 1 if new moon event, = 0 otherwise, d 2 = 1 if full moon event, 0 otherwise, d 3 = 1 if total solar eclipse event, = 0 otherwise, d 4 = 1 if total lunar eclipse event, = 0 otherwise, and yt −1 = index closing price in the previous period. Six regressions from Stata were performed; five of which were U.S. financial indices, and one for the 10 year Treasury bond note. For the S&P 500 index there was a significant Original Research by Marco Hickey OptionMaestro.com relationship between the close price and the occurrence of a new moon phase. The table below is the Stata regression. As one can see the only significant statistic besides the previous day’s index closing price (lag close) is d1 which is the occurrence of a new moon. This regression suggests that The S&P 500 index is higher by 6.41 points on average, with the occurrence of a new moon relative to a normal day. For the Dow Jones Industrial Average index the findings were similar. Again the Stata regression is below. The data from the Dow Jones Industrial Average demonstrates the only significant statistic besides the previous day’s close is dummy variable 1 again. The regression suggests that the Dow Jones Industrial Average index is higher by 56.18 points on average, with the occurrence of a new moon relative to a normal day. For the NASDAQ index again the findings were similar as seen in the table below. Original Research by Marco Hickey OptionMaestro.com For the NASDAQ the only significant statistic besides the previous day’s index close is the dummy variable for new moon again. This regression shows that NASDAQ index is higher by 10.50 points on average, with the occurrence of a new moon phase relative to a normal day. This data may just be a coincidence because these are the major averages which seem to move together. However, the next three regressions include two indices much less covered in the media, and the 10 year Treasury bond note. The first is the New York Stock Exchange Composite Index which covers all of the common stocks listed on the New York Stock Exchange, including foreign listings, Real Estate Investment Trusts (REITs), American Depository Receipts (ADRs), and even tracking stocks. Below is the Stata regression. Again the results are similar as the previous three. The only significant statistic besides the previous day’s index closing price is d1 or the occurrence of a new moon. This regression shows that NYSE composite index is higher by 37.19 points on average, with the occurrence of a new moon phase relative to a normal day. The next index is the Russell 2000 index or a combination of 2000 small cap stocks. Small cap stocks historically have much less interest than the large cap stocks or typical household name stocks. However small caps are largely institutionally owned, meaning there are fewer shares to be purchased, making them more volatile and less attractive to the average investor. The question here is with fewer shares available to be bought or sold directly by humans and less human interest in these types of assets, could the new moon correlate with these small cap securities the same as the securities in previous four indices? The results from the regression are in the table below. Original Research by Marco Hickey OptionMaestro.com Once again the results are identical to that of the previous four. The d1 variable being an occurrence of the new moon is significantly correlated to the Russell 2000 index. As the results show with each occurrence of a new moon relative to a normal day, the Russell 2000 index trades higher by an average of 2.86 points. The final observation is that of the 10 year Treasury bond note. To test the old saying “when bonds fly, stocks die” and vice versa the regression on a bond needed to be ran. The assumption is that when the bond yield begins to rise, equities suffer because there is less risk involved with the Treasury bond(s), therefore investors take less of a stake in equities and invest in bonds getting a “guaranteed” return for less of a risk. Buying a bond causes the bond yield to move lower. Similarly when bond yields rise, it means there is selling pressure on the bond. Therefore the assumption with the last five regressions would be that the bond yield will increase with each occurrence of a new moon. The regression results can be seen in the table below. Note that the price measured is actually the rate of the bond yield. Sure enough the assumption is correct. The d1 variable is significantly correlated to the 10 year Treasury bond note. As the results show with each occurrence of a new moon relative to a normal day, the yield on the 10 year Treasury bond note is higher by an average .02 percentage points or two basis points. In conclusion, there seems to be correlations between the U.S. financial markets, using data for the five major indices and the ten year bond, juxtaposed to the phases of the moon by analyzing the data from four lunar phases. Not taken into account in this research paper are matters of political actions, natural disasters, and technological developments which have Original Research by Marco Hickey OptionMaestro.com affected the markets for generations. In every regression, equities (inverse for the 10 year bond) gained value on average with the occurrence of a new moon. Speaking of animal spirits, when humans (consumers) are confident, the economy is much healthier. When the economy is healthy the stock market performs well; this results from a number of factors, two being lower unemployment and higher levels of job security. When more people have jobs and there are higher levels of job security, it results in individuals taking greater risks, all of which attribute to stock market growth. Could the new moon phase have a psychological effect on humans, where it creates confidence and makes the stock market increase in value? The regressions from this research certainly suggest it could. In a simple syllogism: If a new moon phase affects humans to be more confident, and confident humans take more risk attributing to stock market growth, then a new moon phase will result in the stock market doing well. Original Research by Marco Hickey OptionMaestro.com REFERENCES (1) CMA Media Inc. Bad Moon Rising: the persistent belief in lunar connections to madness [LINK] (2) Lieber Arnold L, Sherin Carolyn R. Homicides and the lunar cycle: Toward a theory of lunar influence on human emotional disturbance. [LINK] Original Research by Marco Hickey OptionMaestro.com


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3 comments:

Anonymous said...

Lunar phase can be correlated with financial activity, but this does not allow accurate forecasting. Alas the real situation is a lot more complicated than just using lunar phase. Numerous other factors have to be considered - the lunar nodes, apogee, ecliptical positions of the Moon and Sun, etc etc. Numerous correlates can be produced to support the Moon Sun hypothesis using small sample sizes.

www.davidmcminn.com

The answer to accurate market forecasting lies in Moon Sun cycles, but the mathematics involved is very complex and beyond me personally.

David McMin

Buy Research Paper said...

Many institutions limit access to their online information. Making this information available will be an asset to all.

Lachoneus said...

This paper is a great example of time series analysis without time series tools.

First of all--why was the modeling choice of New Moons done as a dummy? Why not the day before or after? Why should a naturally smooth event be discretely modeled?

Second why haven't you accounted for serial correlation in the standard errors by either estimating autocorrelation robust standard errors and/or an ARIMA model?

Third, by including a Lagged Close variable, you have ignored what is known as a "unit root" in time series econometrics. When data follows a random walk (like the stock market), it impacts the estimates of standard errors. You should probably be first differencing the closing price to properly account for this.

Fourth, why have you not accounted for any other omitted variables such as seasonality.

While I believe that the hypothesis itself has merit--I was driving down the road a few days ago and saw the full moon and wondered if it reduced accidents by providing additional light on roadways making animals and pedestrians more visible or if it distracted drivers by its beauty (it was certainly distracting me at the time with this thought). However, as stock prices are actually an aggregation of information, a correlation with stock prices that shows a significant correlation with the moon just shows that perhaps somebody is trading on that information, not that it necessarily truly correlates with returns, dividends, etc. Yet, regardless, it could mean that there is an arbitrage opportunity available that should be traded on.

I like the hypothesis, but a deeper econometric analysis will likely undo the result as most of the issues I have described typically will boost standard errors--and lower your t-statistic and significance.

BTW, do you have the data? It could be a great exercise for a time series econometrics course to explore different estimators.

Thanks!

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