# Returns on the Fama-French size sorted portfolios

For my thesis, I need to replicate a specific research paper in the field of empirical asset pricing, mentioning the CAPM in particular. The data mainly consists of monthly returns on portfolios formed on size and different risk characteristics, including book-to-market, momentum, investment, and profitability obtained from the website of Prof. Dr. Kenneth French.

Here's my problem: as it is common practice in asset pricing, it is key to use excess returns rather than raw returns. However, I am not sure whether the portfolio returns from Kenneth French are already defined as excess returns. The website, as far as I know, does not give much indication about that, unfortunately. Interestingly, I obtain regression results that are very similar to those reported in the paper when subtracting the risk-free rate from the portfolio returns beforehand.

Any help is much appreciated!

## 1 Answer

Ken French's homepage is surely one of the most useful resources for asset pricing on the internet! :)

Short answer: They are raw returns and you ought to subtract the risk-free rate. You're right.

Typically, we consider excess returns to account for funding cost. If Apple has a return of 5% but I need to pay 6% risk-free rate to borrow a dollar to buy a share of Apple, then I'm not making much money. In asset pricing, we often sort stocks in portfolios based on some variables and then build spread portfolios (and normally hope for high $$t$$ statistics). These spread portfolios sell one dollar of the short leg and invest that dollar in the long leg. Thus, they are also called ''zero-cost portfolios'' (or ''arbitrage portfolios'' which is a terrible name). Thus, you do not subtract the risk-free rate from the returns of such spread portfolio.

Other than breakpoints, industry portfolios etc., there are two main data sets provided by French

• Risk factors to their 3 and 5 factor model (plus a momentum factor)
• Portfolio returns for various sorts

The risk factors are returns on spread portfolios, see here. Take $$SMB$$ representing the size factor: sort stocks into six (value-weighted!) portfolio using the median of market equity as breakpoint and the 30 and 70 percentile of BE/ME. Thus, you have six time series of raw returns. Then, you take the average return of the three portfolios of small stocks and subtract the average return of the three portfolios of big stocks.

The portfolio returns are even simpler (that's the key to your question): They are just returns of a particular portfolio. Take the portfolios which are sorted based on size, see here. You take market equity of June of NYSE, AMEX and NASDAQ stocks and compute your breakpoints: bottom 30%, middle 40% and top 30%, the five quintile and the 10 deciles. Then, you take the monthly returns of the stocks in the particular portfolios and average them. French provides the (monthly and annual) returns for value and equally weighted portfolios. Thus, you are correct with subtracting the risk-free rate prior to running any regressions. Indeed, that's precisely what Fama and French (1993) do.

Also note that, of course, all returns are percentage returns (and not log-returns) and given as percentages (i.e. 12[%] instead of 0.12).

• Quite a detailed response, thanks for that!
– Ben
Apr 28, 2020 at 16:23