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

[Benoit Schmid]

Good morning,

Just to add to my previous mail.
This is what you get by amplifying the variation by a factor of 10
in your serial time.

	Arithmetic returns	Geometric returns
arithmetic	1.9	-0.08
geometric	5.67	-0.08
"real" return	-0.08	-0.08

You clearly see that arithmetic returns give bad results, even with
geometric aggregation.

In this example we have the logr that is small (-0.08).
This is why we have logr ~ netr

See you,

julien cuisinier wrote:
> Hello,
>  
> Please look at the attached example in the spreadsheet.
>  
> The closest I got to "real return" if by using geometric annualization
>  
> The link you sent me seems to be correct in the sense that daily returns 
> can be seen as not compounding through the day, but I have harder to 
> consider non compounding of daily return...
>  
> I guess it depends what is the underlying of the returns...for a stock, 
> one can consider the return as compounding every minute - hence the use 
> of geometric annualization of geometric returns...for an other 
> investment where "return" such as interest are compounded only once a 
> year it might be wise to use arithmetic annualization of arithmetic 
> returns...
>  
> Personally, the key points is geometric annualization of an average 
> return that make the difference - using arithmetic or geometric returns 
> does not makes much differences...
>  
>  
> Hope that helps
>  
> Rgds,
> Julien
>  
>  
>  
> 
>  > Date: Wed, 29 Oct 2008 14:00:44 +0100
>  > From: Benoit.Schmid at unige.ch
>  > To: r-sig-finance at stat.math.ethz.ch
>  > Subject: Re: [R-SIG-Finance] Returns used to compute the alpha and 
> the beta
>  >
>  > Hello again,
>  >
>  > Quoting julien cuisinier <j_cuisinier at hotmail.com>:
>  >
>  > > (arithmetic & geometric) >> the closest to the real return (as
>  > > (Price(252)/Price(1)-1, so what an investor would actually get over
>  > > a year) I get is by taking geometric annualization of the log
>  > > returns...geometric annualization of arithmetic returns still yields
>  > > close approximation but arithmetic annualization got it off the
>  > > chart...
>  > >
>  >
>  > Just to be sure, let's use the following article as a base:
>  > http://www.riskglossary.com/link/return.htm
>  >
>  > For time aggregation, they use n*z for logr.
>  > What you are suggesting is to use (1+z)^n-1
>  > instead of n*z.
>  > Am I right?
>  >
>  > Thanks for your answer.
>  >
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