# Fama-French Data from daily to monthly returns

Ken French on his website publishes daily, monthly and yearly returns for the Fama-French 3 Factors model which are excess market (Rm-Rf), small-minus-big (SMB) and high-minus-low (HML) returns.

I don't understand how he converts daily to monthly returns. For example for the last month the daily returns are

           Mkt-RF     SMB     HML      RF
20150501    1.01   -0.33   -0.60   0.000
20150504    0.32    0.06    0.16   0.000
20150505   -1.19   -0.10    0.34   0.000
20150506   -0.31    0.62   -0.20   0.000
20150507    0.39    0.03   -0.43   0.000
20150508    1.21   -0.54   -0.21   0.000
20150511   -0.39    0.67   -0.11   0.000
20150512   -0.27    0.00    0.11   0.000
20150513    0.01    0.02   -0.06   0.000
20150514    1.01   -0.10   -0.36   0.000
20150515    0.05   -0.26   -0.01   0.000
20150518    0.44    0.72   -0.09   0.000
20150519   -0.09   -0.08    0.03   0.000
20150520   -0.05    0.21   -0.09   0.000
20150521    0.23   -0.31    0.09   0.000
20150522   -0.22   -0.11   -0.14   0.000
20150526   -1.01   -0.04   -0.02   0.000
20150527    0.93    0.33   -0.39   0.000
20150528   -0.11    0.11    0.07   0.000
20150529   -0.58    0.02    0.05   0.000


And the monthly returns are

        Mkt-RF     SMB     HML      RF
201505    1.36    0.92   -1.89    0.00


For example to convert the daily Mkt-RF return to a monthly returns I use the following formula

$$\text{ret}_\text{monthly} = \left(\prod_{i\in\text{day}} \left(\frac{\text{Mkt-RF}_i}{100} + 1\right) - 1 \right)*100$$

which is

$$\text{ret}_\text{monthly} = \left[\left( \left(\frac{1.01}{100} + 1\right)\times \left(\frac{0.32}{100} + 1\right)\times\cdots\times \left(\frac{(-0.58}{100} + 1\right) \right) - 1\right]\times100$$

So I find the following monthly returns

               CUSTOM CALCULATIONS
Mkt-RF     SMB     HML      RF
201505    1.35    0.91   -1.85    0.00


I don't understand why I get these differences. What am I doing wrong?

• Couldn't this be due to rounding error as there are only two decimal places? Jul 10 '15 at 2:16
• I think it might be due to regression differences vs rounding errors. I think what happens is that they regress daily data using daily factors & also regress monthly data with monthly factors. @conighion
– Rime
Jul 10 '15 at 11:21
• @Rime that is correct as well. Jul 10 '15 at 11:25
• @Rime They don't do any regression to get Fama-French factors.
– John
Apr 17 '17 at 16:10