Saturday, December 29, 2018

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?





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