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In our blog entry of 10-23-07, we identify the worst and best calendar days of the year on average for the U.S. stock market. In this entry, we take a different perspective to envision average daily returns and average daily close-to-close volatility across the calendar year. Using daily closes for the S&P 500 index during 1/3/50-10/19/07, we find that...
The following chart shows the average daily returns for U.S. stocks by calendar date (excluding February 29) since 1950 and since 1990. On the possibility that the calendar influences investor behavior in a complex way, the chart includes sixth-order polynomial fits for both series. In general, results for the entire sample show less variation because more data increases the likelihood that extremes will cancel. The best-fit polynomial curves indicate strength at the beginning of the year, in the second quarter and in the fourth quarter and weakness in the third quarter. These results generally confirm the cumulative return picture shown in the Trading Calendar.
Next we zoom in for a close-up on average daily returns.
The next chart truncates the scale of the vertical axis in the preceding chart and mutes the colors of the average daily results to facilitate observation of the best-fit polynomials for average daily returns by calendar date since 1950 (dark blue) and since 1990 (dark red). The modeled curves for the total sample and the recent subsample are similar, but they suggest that the attitude toward the end of the year has changed recently.
Note that these modeled daily returns are small in magnitude compared to year-to-year variations of actual returns.
Would a similar approach work for average daily close-to-close volatilities?
The next chart shows the average daily return volatilities (standard deviations) for U.S. stocks by calendar date (excluding February 29) since 1950 and since 1990. On the possibility that the calendar influences investor behavior in a complex way, the chart again includes sixth-order polynomial fits for both series. Results show somewhat higher daily volatilities for most of the year in the recent subsample. 4/14 is, of course, the day before the income tax filing deadline in the U.S. Stock market gyrations from 1987 drive the 10/19 peak. The best-fit polynomial curves indicate volatility peaks at the beginning of the year and in the transitions from the first to second and third to fourth quarters.
Next we zoom in for a close-up on average daily volatilities.
The next chart truncates the scale of the vertical axis in the preceding chart and mutes the colors of the average daily results to facilitate observation of the best-fit polynomials for average daily return volatilities by calendar date since 1950 (dark blue) and since 1990 (dark red). The modeled curves for the total sample and the recent subsample are generally alike, with a hint that the one for the recent subsample is shifted a little to the left compared to that for the total sample.
Excluding 10/19 flattens the blue (total sample) curve slightly but does not greatly affect its shape.
In summary, these models of daily U.S. stock returns and volatilities by calendar date offer another perspective on baseline expectations for different times of the year.
Note that sample sizes are modest and, in general, randomness dominates actual short-term stock market movements.
For related research, see Blog Synthesis: Calendar Effects.
