t-stat for Jensen's alpha and t-stat for info ratio

[ajsa]

Hi David,

It seems that t-stat for Jensen's alpha and t-stat for info ratio are same (=IR * sqrt(T))?

What about t-stat for Sharpe ratio? is it equal to Sharpe * sqrt(T)?

Thanks.

 

[David Harper CFA FRM]

Hi asja

well, i am not sure what to make of "t-stat for the information ratio;" I have difficulty interpreting that.
You may find helpful this thread with Paul:
http://forum.bionicturtle.com/viewthread/1242/
...which i think teased out an interesting relationship

Following Grinold, I'd rather say: the info ratio is an annualized t-stat (of Jensen's alpha)
It may help to be mindful that alpha is "just the intercept" in a regression (i.e., the excess return not explained by factor exposure), so the t-stat is the same old t-stat in Gujarati's regression: alpha/StdDev(alpha) = intercept coefficient / StdError (intercept coefficient)

Re: t-stat for Sharpe ratio, that probably exists but i don't know. See how that is a different idea: the t-stat of a RAPM is different that the t-stat of a regression coefficient (intercept, slope)...it sounds interesting, i just haven't used it/seen it

David

append: actually, I am thinking there is no reason to assume student's t is appropriate sign test of sharpe ratio...so, i really don't know on that..