Which proxy is the best to calculate daily risk free rate for a capital asset pricing model?

Question

I need to get daily risk free rate to measure my capital asset pricing model. However, I am still confused on which proxy to use for that (my sample comprises German stocks). Some empirical studies use 3 month treasury bills, others one month government bond rate.

Which proxy should I use for my study.

Thank you in advance.

Answer 1

There are many proxies for the risk free interest rate. For most purposes you may need a short term risk free rate, but there are in general no significant differences which one you chose.

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Treasury bill rates are commonly used for studies on the US-equity market. For European countries, many researchers use 1-month or 3-month EURIBOR rates for empirical studies in academic research. However, LIBOR rates and OIS rates are often used in practice for valuing collateralized derivatives, but you may be aware of a structural change in their spread which is described in this answer.

Let's take a look at the different EURIBOR rates (1-week in green, 3-month in blue, 1-year in red):

It is obvious, that there are no major differences on these rates. Especially if you look at the 1-month and 3-month rate (in R):

library("Quandl")
euribor1m <- Quandl("BOF/QS_D_IEUTIO3M", type = "xts")
euribor3m <- Quandl("BOE/IUDERB3", type = "xts")
difference <- euribor3m-euribor1m
plot(difference)

Since the year 2002, there is actually no difference between 1-month and 3-month EURIBOR rate. There are only 3 times, where their spread exceeds 0.5 percentage points:

summary(difference)
      Index             difference            
Min.   :1999-01-04   Min.   :-0.0540000  
1st Qu.:2004-01-06   1st Qu.: 0.0000000  
Median :2008-12-31   Median : 0.0000000  
Mean   :2009-01-02   Mean   : 0.0006019  
3rd Qu.:2014-01-01   3rd Qu.: 0.0000000  
Max.   :2019-01-11   Max.   : 1.0000000  

index(difference[which(difference>0.5)])
"2000-10-31" "2001-10-04" "2001-10-10"

However, these differences may occur due to incorrect data. Other free data providers like here do not show a spread of exactly one percentage point within 1999-01-01 to 2001-12-28:

In summary, you may use data from commonly used providers to avoid these issues, but you are in general free to use any EURIBOR, OIS, T-bill rate as a proxy for the risk free rate.