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Alternative U.S. Stock Market Calendar Visualizations

Posted in Calendar Effects

The Trading Calendar presents cumulative return visualizations for the S&P 500 Index across the calendar year and across each calendar month. Here are three alternative visualizations of U.S. stock market performance by calendar month: (1) percentage of positive returns; (2) ratio of average return to standard deviation of returns; and, (3) distribution of returns. Using monthly returns for the S&P 500 Index during January 1950 through April 2017 (67-68 observations per month), we find that:

The following chart shows the percentage of S&P 500 Index returns that are positive and reward-to-risk ratio (average S&P 500 Index return divided by standard deviation of returns) by calendar month over the available sample period. Results suggest that September (December) is the worst (best) month for U.S. stock market investors.

The next chart shows the distributions of S&P 500 Index returns for all 12 calendar months, each ordered from lowest (most negative) to highest (most positive). The horizontal axis is simply a cumulative count of observations (67-68 total for each month). The overlay of months obscures features of individual months, but October stands out as having strong tails.

For better visibility, we extract just the last four months of the year.

The next chart shows the distributions of S&P 500 Index returns for September, October, November and December, each ordered from lowest to highest. September stands out as having a large number of negative returns. October again stands out as having large tails. December stands out as having a relatively high number of positive returns and a small negative tail.

For reference, the following table summarizes average monthly return, standard deviation of monthly returns, ratio of average to standard deviation, skewness of monthly returns and kurtosis of monthly returns for the S&P 500 Index by calendar month over the sample period. Notable points are:

  • March, April, November and December are especially attractive from a reward-to-risk perspective.
  • Skewness is negative (long negative tails) for all months except January and December.
  • Kurtosis is especially high for October (fat tails).

In summary, evidence suggests, from a variety of perspectives, that September (December) tends to be the worst (best) month for the U.S. stock market.

Cautions regarding findings include:

  • The S&P 500 Index does not include dividends (thereby understating returns). Nor does it account for any costs of creating a tradable asset from a changing membership of stocks (thereby overstating returns).
  • The above analyses are in-sample. An investor operating in real time may generate different findings at different points during the sample period. The sample is not long enough for reliable out-of-sample testing.
  • The above analyses test no trading strategies, which would involve trading frictions, thereby inhibiting exploitation of any anomalies.

See “Basic Equity Return Statistics” for statistics by decade rather than by calendar month.

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