|WikiProject Finance||(Rated Start-class, Mid-importance)|
What is the beta in the formula?
Confusing phrase in the description
The description mentions a fallacy of ex post TE in a case where active returns in multiple periods do not change. The standard deviation of the active returns would be zero. This part is true.
But the second part which says "Such a series has 0 standard deviation, i.e., there is no variability or dispersion in the active returns. However, the portfolio is not truly tracking the benchmark; it is, in fact, increasingly diverging from its benchmark." is not true - it is not increasingly diverging, but diverging at a constant rate.
If a series of active returns over multiple periods is always 3% per period, there is zero standard deviation of active return, because the active return is highly consistent, not variable. This series of active returns would produce zero TE.
Zero TE by definition means there is no change in the similarity to the benchmark; instead the similarity (or dissimilarity) does not vary, it is consistent.
An investment which is increasingly dissimilar to the benchmark would not have zero TE. Instead of a pattern of active return which is like a series of 3% per period, it would have either a series like 3%, 4%, 5%, 6%, 7% active return, showing that it is increasingly diverging from its benchmark, and demonstrating an increasingly higher TE with each observation.
I cannot cite a source for the above, I am just doing the math and using logic to apply the formula. I am an investment professional who uses such formulas in practical application. — Preceding unsigned comment added by 94608Katsu (talk • contribs) 23:56, 4 August 2015 (UTC)
I am adding a citation for further reference on the subject.