A behavior of a financial instrument is also studied ‘within the month’, by splitting of the month in multiple parts and measuring the returns in each one. A possible explanation of this anomaly (and not only) is the irregularity of capital inflows in a market which affect asset returns.

A month can be divided in multiple parts:

2 parts
The month is divided in 2 parts:

  • the 1st part goes from the 1st day of month to the 15th.
  • the 2nd goes from the 16th day to the end of the month.

The Ariel's 1987 study covers the period from 1963 to 1981 of Dow Jones Industrial Average and consists of dividing the months into two parts: the results showed that in the second half of the month returns were negative, and all monthly profit was derived from the first 15 days. He noticed that returns of the Dow Jones Industrial Average of the first half of the month were, on average, nine times higher than the returns produced in the second half of the month.

3 parts
The month is divided in 3 parts:

  • the 1st part goes from the 1st day of month to the 10th.
  • the 2nd goes from the 11th day to the 20th.
  • the 3rd goes from the 21th day to the end of the month.

In the paper by M.Qadan et.al “Seasonal patterns and calendar anomalies in the commodity market for natural resources”, they present studies on the commodity markets and interesting results:

“…dividing the whole month into 3 parts results in abnormal returns in the first part, but a decreasing trend in the second, and in third part returns are either very low or negative. Results demonstrating that the time-of-the-month effect does exist mainly in copper, gold, silver, zinc and oil. According to these findings, the coefficients of the returns in the second half of each month are positive and significant mainly for the period after 2004.”

4 parts or Weeks of the Month
In this case the month is divided in 4 parts:

  • the 1st part goes from 1st day of the month to the 7th,
  • the 2nd goes from 8th to 15th day,
  • the 3rd from 16thto 23rd,
  • and finally, the 4th from 24th day to the end of the month.

30 parts (DOM) and 23 parts (TDOM)
The month can be divided in units, according to calendar days (DOM), or trading days (TDOM).

Such anomalies seem to be explained, at least partially, with the irregularity of private capital inflows on the stock market.

WTM returns of S&P 500 and Treasury Note future

In the following table there are the returns in the different monthly parts of the S&P 500 (from 1928 to 2020) and Treasury Note future (from 1982 to 2020).

WTM returns of S&P 500 (1928-2020) and TNote future (1982-2020)

About S&P 500 returns, they have been a way better in the 1st half of the month: 0.49% vs 0.14% of the second half, but the most significant indication can be noticed by dividing the month in 4 parts: more than two third of the monthly return is concentrated in the 1st quarter of the month: 0.44% vs a mean quarter return of 0.15%.

While, about TNote returns, the average return of the 2nd half of the month has been the double (0.24%) than the one of the 1st half (0.12%); and the best quarters of TNote have been the 2nd (0.14%) and the 4th (0.18%), in which returns have been more than four times greater than the quarters n° 1 and 3.

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