[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.