[R-SIG-Finance] Returns used to compute the alpha and the beta

[Benoit Schmid]

Good afternoon Charles,

Charles Ward wrote:
> 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).
I fully agree with you, but my question is much simpler.
I assume the autocorrelation of the return to be zero.
I think that I could start adding non-zero autocorrelation
only when all the basic alpha computations would be fully understood.
> 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.
I also fully agree with you and I am assuming that Rf is constant
(even uglier Rf=0) up to now,
so that my understanding of this alphas computations
would be easier to construct.

You are basically, pointing out my future questions.
You are too fast for me. :-)