[Many thanks to Matt Grayson for his help on this.]

Many investors focus on alpha when considering the returns of a particular hedge fund.  As shown below, while alpha at times is a compelling measure of risk-adjusted returns relative to a specified benchmark, investors should be aware of some of its limitations as an analytical tool.

In the examples below, I first show how a non-correlated return stream can have identically high alpha relative to two other returns streams even when one of those returns streams is definitively superior.

Consider this hypothetical returns series:

B has an Alpha of 1.3% per month over A. Indeed, B is a slightly noisy version of A with a constant added, as the plot below shows.

Series C is a slightly noisy constant, and is thus very uncorrelated to A. Its alpha over A is about 1.2% per month.

Since B is very correlated with A, it should be no surprise that C also has an Alpha of about 1.2% per month over B.

The Important point is that even though B consistently outperforms A by 1% per month, C has the identical alpha over both of A and B.

A more subtle example follows.  In the scatter plot below, we show two non-correlated return series.  Each return series has a positive mean return.  Statistically, Series D as an alpha of 0.1 per month over Series E.  Paradoxically, Series E also has an alpha of 0.1 per month over Series D.

The key point here is that alpha is a measure that explains the outperformance of one return stream against another, after adjusting for the amount of return that is explained by the other.  If the return streams are non-correlated, then the explanatory power is lost.

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