Align Return and Risk-Free Rate Series for CAPM Beta
Summary
This discussion addresses a CAPM beta calculation that fails when asset returns, market returns, and a daily risk-free-rate series are supplied as separate time series. Although the data are requested over similar date ranges, their observations do not line up. The accepted answer attributes the dimension error to incompatible series lengths and explains that the function cannot coerce them into matching observations as supplied.
The proposed remedy is to represent the inputs as indexed financial time series, merge them by timestamp, and exclude rows with missing values before passing the aligned asset, market, and risk-free observations to the beta function. The example uses European stock and market data with EONIA as the risk-free proxy. Its useful lesson is about data preparation: CAPM inputs need matching dates and a consistent observation frequency. The answer does not discuss whether EONIA is an appropriate proxy, how to convert its quoted rate to the return interval, or how missing-data removal affects the sample. Those choices should be checked for the intended analysis.
Key ideas
- CAPM beta inputs must align by observation date and frequency.
- Similar requested date ranges do not guarantee that downloaded time series have matching observations.
- Merging indexed series by timestamp makes it possible to compare returns and the risk-free rate on common dates.
- Rows with missing values can be excluded after merging, though this changes the usable sample.
- The example does not assess the suitability or rate conversion of EONIA as a risk-free proxy.
Tags
Full text
# Package ‘PerformanceAnalytics’ - Risk-free rate : Trouble using CAPM.beta() function
# Package ‘PerformanceAnalytics’ - Risk-free rate : Trouble using CAPM.beta() function
This is the first time I use the Package ‘PerformanceAnalytics’. I have a problem when it comes to use "Rf" (risk-free rate) when using the CAPM.beta. I use EONIA as a proxy for the risk free-rate. Here is my code :
```
library(zoo)
library(Quandl)
library(PerformanceAnalytics)
cac <- Quandl('YAHOO/INDEX_FCHI', start_date = '2014-01-01', end_date = '2016-01-01', type = 'zoo')
saf <- Quandl('YAHOO/PA_SAF', start_date = '2014-01-01', end_date = '2016-01-01', type = 'zoo')
eonia <-Quandl("BOF/QS_D_IEUEONIA", start_date = '2014-01-01', end_date = '2016-01-01', type = 'zoo')
safreturn <- Return.calculate(saf$Close, method = ("log"))
cacreturn <- Return.calculate(cac$Close, method = ("log"))
```
then when I try to use the CAPM.beta() function I get :
```
CAPM.beta(safreturn, cacreturn, eonia)
Error in NextMethod(.Generic) :
dims [product 523] do not match the length of object [266730]
```
I think that I understand that the problem comes from the length of `Rf = eonia`. I have noticed that even if the length of `safreturn` and `cacreturn` are not the same, if I put a random number for `Rf` I can obtain a solution, but I need to use the daily rate of EONIA.
Can someone help me ? Thanks in advance :)
## Answer by Forgottenscience (score 0, accepted)
https://quant.stackexchange.com/a/31682
The problem is that the length of the time series are different, despite you setting similar starting dates. CAPM.Beta then try to coerce the data unsuccessfully, which can be seen in the `length of object [266730]`, which is equal to 510 * 523, which in turn is the length of the eonia series and the cacreturn series, respectively.
I am not much of a zoologist, so I prefer to use the `xts` library for financial series. The following should solve the problem:
```
library(xts)
library(Quandl)
library(PerformanceAnalytics)
cac <- Quandl('YAHOO/INDEX_FCHI', start_date = '2014-01-01', end_date = '2016-01-01', type = 'xts')
saf <- Quandl('YAHOO/PA_SAF', start_date = '2014-01-01', end_date = '2016-01-01', type = 'xts')
eonia <-Quandl("BOF/QS_D_IEUEONIA", start_date = '2014-01-01', end_date = '2016-01-01', type = 'xts')
safreturn <- Return.calculate(saf$Close, method = ("log"))
cacreturn <- Return.calculate(cac$Close, method = ("log"))
retmerge <- na.exclude(merge.xts(cacreturn, safreturn, eonia)) #na.exclude removes all rows with NA values
CAPM.beta(retmerge[,1], retmerge[,2], retmerge[,3])
```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.