The beta will change if measured over different intervals, e.g. daily,
weekly and monthly because of some serial correlation in returns in either
the stock price returns or even the index. (There are techniques used to
correct for this problem (e.g. Dimson approach).
There is even the oddity that  the beta will change depending on which day
of the month is used to measure monthly returns!  See D Acker and N
Duck, "Reference-Day
Risk and the Use of Monthly Returns Data"Journal of Accounting, Auditing &
Finance; Fall2007, Vol. 22 Issue 4, p527-557. This anomaly is quite
startling.
Therefore because the beta changes, the alpha would change too if measured
over different intervals. As far as the risk free rate is concerned, by
definition, the CAPM is a single period model so depending on the interval
of measurement, the risk-free return should yield a certain return over that
horizon so  1 month TBills in 1 monthly returns, 2 month Tbills in quarterly
returns. In the original Jensen paper (1968) on Mutual Fund performance he
used an average return as the risk free rate but it should really depend on
the period-by-period risk-free rate, i.e a time series of risk free rates as
well as a time series of stock price returns.

 Charles Ward

On Mon, Oct 27, 2008 at 7:14 AM, Benoit Schmid <Benoit.Schmid@unige.ch>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.
>
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