# Why monthly stock returns instead of daily returns in multiple regressions?

This is probably a naïve question.

Why do many multiple regression analyses of the Fama-French 3 or 4 factor model of fund returns use monthly return data instead of daily return data? I would have thought that having more data from the daily returns would get you more accurate coefficients in the regression models. Why get a more coarse sampling of the data? Am I missing something obvious about this? Thanks.

• I would imagine, though this is a guess, that there's a lot of "random" fluctuations (note inverted commas) in daily return prices which aren't related to the variables of interest. Looking at monthly returns would be a crude way of averaging out this "noise".
– Eoin
Commented Nov 17, 2014 at 17:08

The primary benefit of using monthly returns data instead of daily return data is that with monthly data, returns are at least approximately normally distributed (or, at the very least, the simplifying assumption of normality is much less crazy for monthly returns than it is for daily returns).

As an aside, check out this quotation from Eugene Fama's book, Foundations of Finance (available here):

The usefulness of the portfolio model depends not on whether the normality assumption which underlies it is an exact description of the world (we know it is not), but on whether the model yields useful insights into the essential ingredients of a rational portfolio decision. Likewise, the usefulness of the model for securities prices depends on how well it describes observed relationships between average returns and risk. If the model does well on this score, we can live with the small observed departures from normality in monthly returns, at least until better models come along.

• Oh, good to know. I see what you mean (after looking at some indexes). Commented Nov 21, 2014 at 21:13

Moving to daily data for a large number of stocks might require switching to a database (instead of loading everything in memory). Some people might not want the hassle.

Mean-variance optimization suffers from estimation error, particularly in the mean. It's not clear that moving to daily data will sufficiently resolve this problem. It can be difficult to separate the signal from the noise.

Nevertheless, there are many situations when people look at higher frequency data. Even looking past intraday trading, it is well-established estimating risk using higher frequency data will give you better results.

Further, there are also event studies papers that will look at daily data. For instance, what the the performance of stocks N days after earnings announcements.

• I was hoping that convenience wasn't reason. It wasn't clear to me either whether daily would be better. I was thinking about when you would be smaller timespans (under 4 years). About the risk estimation with high frequency data, do you have a citation for an introductory paper you could introduce me to? Commented Nov 21, 2014 at 21:18
• Convenience isn't the only reason. When I think about estimation error, I tend think about the forecast horizon versus how much data I have. Four years of daily data might be fine if you forecast one day ahead, but maybe not one year ahead. How about: public.econ.duke.edu/~boller/Published_Papers/ier_98.pdf
– John
Commented Nov 21, 2014 at 21:47