# Do the number of days in a month affect monthly return? (seasonality)

When I see data like monthly return on news or tv, I always find the concept a bit strange, because obviously if you calculate monthly return for February and March, all things being equal, the monthly return of March would be slightly larger than February due to the fact March has more days than February. Is this the case in real life?

• Sometimes places will report monthy data corrected for the number of days, sometimes for the number of business days. In practice, as @FooBar says, it doesn't really matter. – Jamzy Jun 16 '15 at 0:00

It usually does not matter, at least in practical applications, because to compute monthly we usually take end of month closes. See the MSFT case:

           MSFT.Adjusted        Return
2014-12-31      45.82396              NA
2015-01-31      39.85550     -0.13024755
2015-02-28      43.56686      0.09312032
2015-03-31      40.39746     -0.07274798
2015-04-30      48.32593      0.19626168
2015-05-31      46.86000     -0.03033425


$R_{Jan}=\frac{39.85550}{45.82396}-1$

$R_{Feb}=\frac{43.56686}{39.85550}-1$

Let's make a fake example.

Compound interest of 0.1% over 30 days gives

$$1.001^{30} = 1.030439088$$

Compound interest of 0.1% over 31 days is

$$1.001^{31} = 1.031469527$$

And the percentage change is 1.000970497. That is, you would over estimate the growth rate of a stock by 0.009% if you would compare 30days and 31days without adjusting for it.