Choosing a Short-Term Euro Rate for CAPM Risk-Free Returns
Summary
The document considers which daily risk-free rate proxy to use when estimating a capital asset pricing model for German stocks. It explains that researchers commonly use short-term rates, with U.S. studies often using Treasury bills and European studies often using one-month or three-month EURIBOR. It distinguishes these empirical choices from LIBOR and OIS rates often used in practice to value collateralized derivatives, and flags that changes in their spreads can matter.
An example comparison of EURIBOR tenors reports generally small differences between the one-month and three-month series, while some unusually large historical gaps may reflect data problems. The answer recommends using a reputable data provider and concludes that several short-term EURIBOR, OIS, or Treasury bill series may serve as proxies. It does not prescribe a single rate for German equities; the suitable choice depends on the study’s conventions, currency, and data quality.
Key ideas
- CAPM studies typically use a short-term rate as the risk-free proxy.
- U.S. equity studies often use Treasury bills, while European research commonly uses short-term EURIBOR rates.
- OIS and LIBOR are also used in collateralized derivatives valuation, where spread changes can matter.
- The cited comparison finds little difference between one-month and three-month EURIBOR in most of the observed series.
- Data quality and consistency should inform proxy selection.
Tags
Full text
# Which proxy is the best to calculate daily risk free rate for a capital asset pricing model?
# Which proxy is the best to calculate daily risk free rate for a capital asset pricing model?
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 by skoestlmeier (score 5)
https://quant.stackexchange.com/a/43530
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.
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.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.