Suppose we have the following:
Risk-free rate: 1%
Market’s return: 11%
Let’s say we have a portfolio with a Beta of 0 which returned 5% and an active risk of 6%.
The information ratio of this portfolio would be: (5% - 11%)/6% = -1
However, the portfolio has an alpha of 4% because it would be expected to return 1% according to CAPM but returned 5% instead.
Am I missing something?
A portfolio with 0 beta has a benchmark that is a market with beta 1?
I believe the issue comes from speifiying an innapropriate benchmark. A beta 0 strategy would be more of a long/short equity neutral strategy and would possibly be benchmarked against a risk free rate or absolute return.
As for a more real world discussion of typical low volatility strategies, there has been a lot of discussion within the industry regarding what is an appropriate benchmark. Many managers are making the push towards more customized benchmarks, trying to distance themselves from the typical cap weighted benchmark. In such cases where the client insists on a cap weighted benchmark, it is important to educate them on how typical performance ratios will be affected. For instance, many industry participants are aware that low vol strategies produce very high tracking errors verse cap weighted indexes. As such, the information ratio usually receives less importance when picking between low vol managers. More important factors would be the realized reduction in volatility of the strategy and how its returns compare to other low vol strategies. So yes, if you have an inappropriate benchmark, the information ratio could be a poor measure of perfomance for a manager.