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

[Benoit Schmid]

Good morning Julien,

julien cuisinier wrote:
>
> >> 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...

1.  As you deal with log return why do you use this geometric aggregation
that should be used for classical net returns?

For log return, as far as I know, the annualized value is simply
252 * dailyLogReturn because the sum of logs is the log of the product.

2. You say that you always compute with log return.
But when you have to present your results, do you convert
your log returns (with exp(logR)-1) or do you let log returns
on your presentations and assumed that log returns are closed
to net returns because log(1+x) ~ x when x is small?

Thanks in advance for your answer.