Don't fear Friday the 13th, but investors should watch for these days

* The 16th day of the month has uniquely high returns.
* Experts suggest this is from semimonthly paychecks and automatic retirement plan purchases.

There's no evidence traders are superstitious about Friday the 13th, and there's no reason they should be, because returns on that day are perfectly normal. But one particular day of the month does actually stand out from the rest — in a positive way.

The 16th of the month has the distinction of being the best performing day for stocks, going back decades. And the first is a consistent outperformer, over time, as well.

Analysts and researchers have documented all kinds of "calendar effects," looking at the breakdown of days, weeks, months, seasons, years, presidential cycles and on and on. It is often hard to distinguish statistically between a true effect and a random blip. And even when an effect has been proven to exist, future traders in a more efficient market can eliminate the expected gains over time.

The Big Crunch looked at S&P 500 median daily returns in a given month since 1980, and found evidence for consistent outperformance on the first and 16th of the month. The median return for all trading days is about 3 basis points, or 0.03 percent. But look at the chart above, and median returns for the first and 16th of a month are almost 0.25 percent per day. (And because those are median returns, they are not skewed by large individual outliers). The data suggest consistent outperformance on those two days, month after month.

The "turn of the month" effect was first publicized in a 1988 paper, which found that the first four days of the month accounted for all of the positive return in the Dow from 1897 to 1986. Another paper found a similar effect from 1926 to 2005. Our data suggest a similar effect from 1980 through 2017. Even when we focused on the more recent time period since 2008, we saw similar gains.

The cause of the effect isn't clear, but in the 2008 paper, the researchers found the early-month gains exist in other sets of trading data. It wasn't limited to small cap or cheap stocks, it wasn't caused by higher volatility at month-end, and it occurs in most countries. The effect also doesn't seem to be caused by higher trading volume or mutual fund flows.

Paycheck and 401(k) effects

The middle of the month effect propping up the 16th appears to be relatively new. Median daily returns from 1950 to 1979 did not show any bias to mid-month outperfomance. But since 1980, the 16th of the month has been the biggest buying day. It's often attributed to a "payday effect" because of the invention of 401(k) plans in the late 1970s, when millions of Americans began pouring their earnings into the stock market at the same time each month.

"The growth of 401(k) accounts and automatic deductions at payday is certainly a factor at play," said Paul Hickey, co-founder of Bespoke Investment Group. "And it has actually become more pronounced since the 1980s when 401(k) plans really started to become more mainstream."

In the Stock Trader's Almanac, Editor-in-Chief Jeffrey Hirsch has also documented the effect. He references the growth of 401(k) plans, IRAs, and other retirement plans with twice-monthly salary payments as being responsible for the bump.

For our more statistics-focused readers, note that we considered many other starting dates in addition to 1980, such as 1990, 2000, etc. In all of our tests, we saw the same basic effect: Median returns on the first and 16th day of the month are generally higher than the rest. And when we calculated mean (instead of median) returns, we found statistical significance: There was less than a 1 percent chance these patterns could have happened by random chance. In this regard, the 16th of the month was often better than the first of the month, especially more recently.