
Hi Benoit,
 
 
This is my opinion and I will make it short as you seemed to ask for people's opinion/experience on the topic. For the sake of information here, I am quant analyst on equity funds in a large UK asset manager
 
1. I ALWAYS use log returns instead of simple (p(t)/p(t-1) - 1) >> they handle compounding much better & are usually more conservative (google "arithmetic Vs geometric returns", that should tell you which one you want to use)
2. annualization: 
>> not needed on beta since annualizing the numerator (Cov(stock,mkt)) and denominator (Var(Mkt)) requires the same factor, i.e. *252 if you had daily returns at the start
>> For alpha, since it is simply a return itself: alpha(annual) = ([1+alpha(daily)]^252)-1, the daily alpha in decimal form of course...
With regards to risk free rate mentioned in Brian's answer below, I would definitely use a time series of the reference risk free rate (take the 3Month rate in your base ccy if doubts) and not a fixed value...If you think about it, that makes much more sense than a fixed interest rate...
 
As I mentioned, all this are my opinions...and subject to the reason why you want to compute an alpha & beta...the beta being one of the most notoriously misleading indicator out there...ask me more on this if interest.
 
 
Hope this helps
 
 
Best regards,
Julien Cuisinier
 
 
> Date: Mon, 27 Oct 2008 06:45:26 -0500> From: brian@braverock.com> To: Benoit.Schmid@unige.ch> CC: r-sig-finance@stat.math.ethz.ch> Subject: Re: [R-SIG-Finance] Returns used to compute the alpha and the beta> > You will find all of the classic CAPM functions implemented in > PerformanceAnalytics, including CAPM.alpha, CAPM.beta (and their bul/up > and bear/down market counterparts), timing.ratio, Return.excess, > CAPM.Riskpremium, and the SML and CML. We have attempted to implement > these using the definitions described in Sharpe's papers as well as > generally agreed by other authors who have covered CAPM. So all your > functions, I hope, are already written, documented, and cited.> > There is some disagreement in the literature and among practitioners > regarding different aspects of CAPM that affect your inquiry. One of > them is the risk free rate. In the original papers the risk free rate > was a single (scalar numeric) number, while many more recent sources and > practitioners prefer to use the risk free rate as a time series (for > instance of returns on Treasury bills). The function Return.excess > allows either a scalar or time series representation. > > Classic CAPM alpha will not change based on the periodicity, as it > measures the _portion_ of a set of returns that are not attributable to > the benchmark return, and should be calculated with the highest regular > periodicity available. Return.excess may calculate what you are > referring to as "alpha" if by alpha you mean returns over a benchmark > return, in which case you would first run Return.excess using the > benchmark return as the parameter 'rf' and then cumulate your daily log > returns to get a cumulative return over some other periodicity (annual > in your query).> > Returns and 'risk' may be annualized as a way to simplify comparison > over longer time periods. Although it requires a bit of estimating, > such aggregation is popular because it offers a reference point for easy > comparison. "Annualizing" the CAPM numbers and other related numbers > such as the Sharpe ratio you will find significant disagreement among > different authors. We have provided in our functions many of these > different interpretations, including 'Return.annualized', > 'sd.annualized', and 'SharpeRatio.annualized' functions.> > We have also provided many of the extensions of classic CAPM by Sharpe, > Sortino, and others that are generally grouped into "Modern Portfolio > Theory". In addition to The Sortino ration and related semivariance and > downside deviation measures, you will find active premium, information > ration, and tracking error implemented in most of their commonly > presented forms.> > Hopefully my long response helps to answer your question. If there are > other questions that this raises, please ask them, and the list will > attempt to provide a rational response.> > Regards,> > - Brian> > Benoit Schmid wrote:> > Good morning,> >> > I would like to know what people generally use when the compute> > the alpha and the beta (linear interpolation used for benchmark> > performance measure).> >> > From what I have seen, log return (log(V(i)/V(i-1))) and net return> > (V(i)/V(i-1) - 1) seems to be used.> > But, in general, what do people "prefer" to use?> > And why?> >> > I am working with daily values and I would like to provide annualized> > values.> > I have not found that many documentation on the web concerning> > that kind of annualized information.> >> >> > Intuitively the beta does not change, when it is annualized as it is a > > ratio.> >> > Concerning the alpha, it is a return therefore I should use:> > 252*alphaDaily for logr and (alphaDaily + 1)252 for netr,> >> > Am I right?> >> > Thanks in advance for your answer.> >> > _______________________________________________> > R-SIG-Finance@stat.math.ethz.ch mailing list> > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > -- Subscriber-posting only.> > -- If you want to post, subscribe first.> > _______________________________________________> R-SIG-Finance@stat.math.ethz.ch mailing list> https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only.> -- If you want to post, subscribe first.
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