excuse me, I noted (in a work of others) that for the computation of the beta (as in the CAPM framework), i.e. as "Covariance(asset i, market) / variance(market)", has been used a different lenght of the time series. I mean, for the numerator, if for the asset i for example only 5 years of historical data are available, the Covariance has been computed by using 5 years of historical data (both for asset i and for the market); while, if for the market instead are available 10 years of historical data, the denominator, i.e. the variance(market), has been computed by using 10 years of data.
I think this is a bit incorrect, since a common sense would suggest me to use the same lenght of (historical) data for both the numerator and denominator... but, do you know if there is some explicit reference for this? I mean, some article, paper, or even book for that?
Thanks a lot.