Returns used to compute the alpha and the beta
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. :-)