Aligning Portfolio Returns, Risk-Free Rates, and Fama-French Factors
Summary
The document raises a replication question about estimating a monthly factor regression for European equity portfolios, with particular interest in the intercept as abnormal risk-adjusted performance. It describes calculating monthly portfolio returns from prices, subtracting a risk-free rate, and using market, value, size, and momentum factors from a developed-markets dataset. The question is whether annualized government bond yields can be converted to a monthly rate and whether factor series should be adjusted when using a country-specific risk-free rate.
The material highlights the need for consistent return periods and definitions: portfolio returns, risk-free returns, and factor observations must refer to matching frequencies. It also notes that the market factor is presented as market return in excess of the dataset’s risk-free rate, alongside that risk-free series. However, the document contains the replication question rather than an answer or empirical comparison. It does not establish that long-term government bond yields are appropriate risk-free proxies, specify a conversion convention, or resolve how substituting a country-specific rate affects factor construction and interpretation of the regression intercept.
Key ideas
- The proposed regression explains portfolio excess returns with market, value, size, and momentum factors.
- Portfolio returns, factor returns, and risk-free rates need compatible observation frequencies.
- The market factor is reported as a return in excess of the dataset’s risk-free rate.
- The document leaves open whether long-term government yields are suitable risk-free rates and how to substitute them consistently.
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Full text
# Matching periodicity Fama-French Factors, Portfolio Return and Risk Free rate
# Matching periodicity Fama-French Factors, Portfolio Return and Risk Free rate
I am trying to replicate certain aspects of the following paper: "Does the stock market fully value intangibles? Employee satisfaction and equity prices" - Alex Edmans (2011) for three European countries (GER, FR, UK).
I am interested in replicating the following regression (1) and I am particularly interested in the $\alpha$:
$$R_{t} = \alpha + \beta _{MKT}MKT_{t} + \beta _{HML}HML_{t} + \beta _{SMB}SMB_{t} + \beta _{MOM}MOM_{t} + \varepsilon_{it}$$
- $R_{t}$: the return on Portfolio I in month t in excess of a risk-free rate
- $\alpha$: intercept that captures the abnormal risk-adjusted return
- $MKT_{t}, HML_{t}, SMB_{t},MOM_{t}$:the monthly returns on the market, value, size, and momentum factors for Europe, taken from Ken French’s Web site under the "Developed Markets Factors and Returns" section.
I am not sure whether I am comparing apples and oranges here. To calculate the individual components I have done the following:
- for $R_{t}$ I have used monthly price data and calculated the monthly returns (i.e. from one month to the next), which I have then used to calculate a monthly portfolio return.
- The paper states that I should subtract the risk-free rate from the PF returns, therefore I downloaded on a monthly frequency the 10year government bond returns from Bloomberg for Germany, France and the UK respectively. I understand that those rates are annual rates. Am I correct to assume that I would have to divide those rates by 12 in order to obtain monthly risk-free rates that I can subtract from my PF returns?
- In the Excel file from Kenneth French's website, the $MKT$ variable is reported as "Mkt-Rf", "SMB", "HML" and "Rf". Hence, my understanding is that if I wanted to use my own (country-specific) risk-free rate, I could add-up "Mkt-Rf" and "Rf" and then subtract the country-specific 10-year gov-bond rates. Here I am not sure however, how to read those Fama-French factors and whether I would need to subtract the monthly or annual risk-free rate. Do the reported Fama-French factors need to be adjusted to match the monthly portfolio returns as well?
So to sum up, is my approach of using the monthly PF returns in excess of the monthly (and hopefully correctly broken-down) risk-free rate compatible with using the Fama-French Factors (monthly or yearly?) feasible?
I hope that this makes my problem clear - however, if this is not the case I will happily provide further information.
Thank you in advance for your time and help!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.