Average Return on Various Days of the Week 0.10% 0.08% 0.06% 0.04% 0.02% 0.00% -0.02% -0.04% -0.06% -0.08% Monday Tuesday Wednesday Thursday Friday

Ruminations on Calendar Effects on Stock Returns

In general we believe in semi-strong form market efficiency, which is a technical way of saying that due to many investors attempting to find attractive investments, those investments tend to be priced correctly. If they weren’t, the proverbial “free lunch” would be available. There do appear to be some exceptions to the general rule however. The most familiar (and best documented) ones are the value premium (value stocks beat growth stocks), the size premium (small company stocks outperform large company stocks), and momentum (a good or bad daily return tends to be followed by the opposite on the next day, while a good or bad quarter or year is followed by additional movement in the same direction).

There are also a number of calendar effects that have been documented. Those are the ones we are going to explore here, taking them in order from the shortest time period to the longest.

Day of the week effect. There is no reason investors should receive higher returns on some days and lower returns on other days. And, since most stock markets are open five days a week and thus no trades over the weekend, the return (as measured from Friday’s close to Monday’s close) should be three times the “normal” return on Mondays. That isn’t what we find at all. Here is the average return of the S&P 500 by day of the week from 1950 through 2010 inclusive:

Average Return on Various Days of the Week 0.10% 0.08% 0.06% 0.04% 0.02% 0.00% -0.02% -0.04% -0.06% -0.08% Monday Tuesday Wednesday Thursday Friday

As you can see, not only do Mondays not have three times the return of the other days, but are actually negative. The differences from average are sizable for Mondays, Wednesdays, and Fridays, but Mondays have a further distinction. Since much of the time extreme news is released over the weekend, Monday might also have an abnormally large range of returns. Here is a graph of the best and worst days over our 61 year period by day of the week:

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Day of the Week Range of Returns 15%

10%

-5%

-10%

-15%

-20%

-25% Monday Tuesday Wednesday Thursday Friday

As you can see, Monday seems much more volatile, but that is entirely due to October 19th, 1987. Without that data point, Monday’s downside would be just slightly less than Wednesday’s though its standard deviation remains slightly higher than the other days:

Standard Deviation of Returns 1.20%

1.00%

0.80%

0.60%

0.40%

0.20%

0.00% Monday Tuesday Wednesday Thursday Friday

While the abnormal returns on Mondays, Wednesdays, and Fridays are interesting (and statistically significant at the 95% level) the picture changes if we look at the effect decade by decade. Over the last 20 years the effect has disappeared and over the past 10 years the Wednesday and Friday outperformance has turned into underperformance.

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Day of the Week Effect by Decade 0.30%

0.20%

0.10%

0.00%

-0.10%

-0.20%

-0.30%

-0.40% 1950's 1960's 1970's 1980's 1990's 2000's

Monday Tuesday Wednesday Thursday Friday

Day of the month effect. Similar to the previous anomaly, there appear to be abnormal returns near the turn of the month. This graph uses the same S&P 500 data as earlier:

Average Return on Various Days of the Month 0.20%

0.15%

0.10%

0.05%

0.00%

-0.05%

-0.10%

-0.15%

-0.20% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Average Trimmed Average

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The average is the mean, while the trimmed average has both the best and worst days removed (to show outliers didn’t significantly affect the results). While the 31st, 1st, and 2nd have excellent returns, some other days are notable as well. A day with an absolute value greater than about 0.085% (it varies slightly due to differing numbers of observations) is significant at the 95% level.

Here is the same graph with the data by decade:

Day of the Month Average Return by Decade 0.80%

0.60%

0.40%

0.20%

0.00%

-0.20%

-0.40%

-0.60% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1950's 1960's 1970's 1980's 1990's 2000's

As you can see, there doesn’t appear to be nearly as large an effect when viewed this way.

January and September effects. The conventional wisdom has long held that summer has particularly low returns. October is also considered risky, and this belief is attributed to the 1929 and 1987 plunges (and validated perhaps in 2008). It is interesting that October apparently had a bad reputation well before 1929 though. In 1894 Mark Twain observed, “October: This is one of the peculiarly dangerous months to speculate in stocks. The others are July, January, September, April, November, May, March, June, December, August and February.”

The best-known monthly anomaly is the January effect. Here is average return by month from 1926 through 2010 inclusive (CRSP 1-5 is large U.S. companies, while CRSP 6-10 is smaller companies):

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Average Monthly Returns 6% 5% 4% 3% 2% 1% 0% -1% -2%

CRSP 1-5 CRSP 6-10

As you can see, the January effect has been concentrated in those smaller companies, but the effect may have worn off over the past decade. Here is how investing in those smaller companies during January would have worked out each year:

CRSP 6-10 Returns in January 40% 35% 30% 25% 20% 15% 10% 5% 0% -5% -10%

-15%

2001 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2006 1926

The astute reader may also have noticed the abnormally low returns in September, but the effect is concentrated around 1931 and there has been no net negative return (compounded) over the past 20 years. Here is the September performance year by year:

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CRSP 1-5 Returns in September 20% 15% 10% 5% 0% -5% -10% -15% -20% -25% -30%

-35%

1991 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1996 2001 2006 1926

“Sell in May and go away.” The specific origins of this saying are murky, but the original version was "Sell in May and go away, stay away till St. Leger Day.” St. Leger Day was the horse race of the season in Great Britain. Today the ending event is Halloween, but it doesn’t rhyme as nicely so the saying has been truncated. The adage seems disproved by the monthly return graphs already shown.

Election cycle effect. We have one more calendar anomaly to examine, the third year of the presidential election cycle. This is a graph of the average return (CRSP 1-10, i.e. the entire U.S. stock market, from 1926 through 2010 inclusive) where year four is the election year and year one is the inauguration year:

Average Return by Election Cycle Year 25%

20%

15%

10%

0% 1 2 3 4

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Though not quite rising to the level of statistical significance, the third year does appear to be propitious for investors. Here it is year by year:

Returns in the Third Year of the Election Cycle 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% -10.00% -20.00% -30.00% -40.00%

-50.00%

1931 1999 1935 1939 1943 1947 1951 1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 2003 2007 1927

While there are no guarantees and currently the political landscape doesn’t appear favorable for additional stimulus, based on history investors may be pleased with the growth of their portfolios in 2011.

Conclusion. While calendar effects are interesting historical anomalies, it appears that their publicity may have caused them to cease to exist. This is exactly what we would expect in an efficient market. As Milton Friedman was fond of saying, “There’s No Such Thing as a Free Lunch.”

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Notes:

Mr. Hultstrom is the president of Financial Architects, LLC, a financial planning and wealth management firm. Questions or comments are welcome, and he may be reached at [email protected] or (770) 517-8160.

Reasonable care has been taken to assure the accuracy of the data contained herein and comments are objectively stated and are based on facts gathered in good faith. We disclaim responsibility, financial or otherwise, for the accuracy or completeness of this report. Opinions expressed in these reports may change without prior notice and we are under no obligation to update the information to reflect changes after the publication date. Nothing contained in this material is intended to constitute legal, tax, securities, or investment advice, nor an opinion regarding the appropriateness of any investment, nor a solicitation of any type. The general information contained in this publication should not be acted upon without obtaining specific legal, tax, and investment advice from a licensed professional. Past performance is no guarantee of future results. This is not an offer, solicitation, or recommendation to purchase any security or the services of any organization. The foregoing represents the thoughts and opinions of Financial Architects, LLC, a registered investment advisor. Your mileage may vary.

This report was originally written in February, 2011 and was last reviewed/updated in April, 2013.

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