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Hi Everyone:
In the attached, I show how Grinold's "tracking error" is consistent with that of Litterman's. Specifically, I show that their definitions of portfolio variance are equivalent. This simple proof is useful to those trying to reconcile the notations between the two authors. For example, David Harper mentioned in his 2010 video tutorial on Litterman that it is not clear how to reconcile Litterman's notation with Grinold's, which I take as a thinly-veiled challenge to those mathematically inclined. So if you are one, read on in the attached.
I also have a follow-on question regarding Grinold's definition of "information ratio," and would appreciate anyone who has new insight. But be gently warned that it is a long-running problem of inconsistency in GARP's readings, between Grinold and other authors. My aim is to understand why Grinold uses his own peculiar definition (IR = residual return/residual risk), especially since he seems to be aware of the general definition used by others (IR = active return/active risk).
In the attached, I show how Grinold's "tracking error" is consistent with that of Litterman's. Specifically, I show that their definitions of portfolio variance are equivalent. This simple proof is useful to those trying to reconcile the notations between the two authors. For example, David Harper mentioned in his 2010 video tutorial on Litterman that it is not clear how to reconcile Litterman's notation with Grinold's, which I take as a thinly-veiled challenge to those mathematically inclined. So if you are one, read on in the attached.
I also have a follow-on question regarding Grinold's definition of "information ratio," and would appreciate anyone who has new insight. But be gently warned that it is a long-running problem of inconsistency in GARP's readings, between Grinold and other authors. My aim is to understand why Grinold uses his own peculiar definition (IR = residual return/residual risk), especially since he seems to be aware of the general definition used by others (IR = active return/active risk).
