# Equity returns by day of the month

There is well documented evidence that equity returns vary based on the day of the month. In particular, returns at the “turn” of the month (the first few and last few days) are higher than returns through the rest of the month.

#### Prior work

There’s quite a bit of prior work on this topic that goes in much more depth than I’ll look at here.

- This 2014 paper confirms the existence of the turn of the month effect in 19 of 20 countries studied using a Periodic GARCH model.
- This 2008 paper shows the strength and persistence of the turn of the month effect over cross sections of time, countries, market capitalizations, and months of the year. A freely available draft can be downloaded here.
- This paper, written in 2010, explores different calendar anomalies and finds that the turn of the month effect is one of the two strongest.

#### Full sample

While some papers look at returns from all the way back to 1926, we are more interested in recent years. We’ll look at S&P 500 data from 1988 and we are interested in finding whether any specific days of the month are more profitable in equity returns than other months.

Using month end as point 0, we look at days from month end. So, for example, if return on March 1 is 0.3%, then we credit that to day +1 from the end of the month.

The chart above shows that returns centered around the end of the month (from 3 days before to three days after) are quite attractive. Additionally, returns around the middle of the month are also attractive, though not as much.

The table above shows the average return given a certain window around month end. For example, the boxed -3, 3 window is three days before month end to three days after. While this represents seven calendar days, it actually is on average only 4.9 trading days.

The average return per day during this period is 0.13%, giving a total return per month end of 0.62%. Over 12 months, this is a 7.40% per year, and 31.9% annualized given the investment is only seven days of the month.

Note that many studies annualize returns by investing in the risk free rate for the remainder of the month. However, I look at this strategy as one of many strategies in a portfolio, and since it only consumes investment on certain days, it makes sense, in this context, to annualize these returns.

#### Quarter ends

Some studies have pointed out that most excess returns come around quarter ends. However, a quick analysis of the months that contribute the returns shows otherwise. In the table below, the months refer to the return of the prior month end. So 1 is the December month end.

Quarter ends and non quarter ends yield almost identical results. Quarter end returns are driven by high year end returns (month 1).

#### Returns over time

Returns from the month end strategy have declined markedly over time, though, and the strategy has not performed nearly as well in recent history.

Though total returns have only been around 5% since 2010, annualized, this represents a healthy 20%.

#### Transaction costs

All numbers above are before transaction costs. Since we only have been looking at the S&P, transaction costs should be minimal. SPY is usually quoted a penny wide on around $200, or 0.5 bps. This will not really impact returns.

*Sources: *Bloomberg, Yahoo! Finance