Friday, October 26, 2012

You can pay me (annualize) now, or you can pay (annualize) me later

One of our clients introduced me to alternative ways to calculate two commonly used risk-adjusted return measures: information ratio and Sharpe ratio. Their immediate derivation is from Zephyr, and I am attempting to identify their origin. I confirmed that Morningstar also uses them.

In both cases, they annualize and then do the math, rather than do the math and then annualize. This calls to mind the associative property of mathematics, which says the order does not matter. While in addition, this holds (2 + 4 = 4 + 2 = 6, for example), it does not in these methods, as we get different results.

This also reminded me of how some attempted to derive my favorite risk-adjusted measure, Modigliani-Modigliani (annualize first or last?).

The information ratio differences:

And, the differences with Sharpe ratio:

This raises numerous questions. For example, is one approach superior to another? My suspicion is that most firms use what I refer to as the "typical" formulas. The reference materials I've checked only show these approaches. But clearly, some favor the alternative. The CFA Institute's CIPM(R) program, as I recall, also references the "typical" approach.
We know that there are multiple ways to derive various statistics, and here are just two more cases. As I learn more, I will share it with you. In the mean time, feel free to "chime in" with your thoughts. 


  1. Hi David. Interesting post. I would definitely annualise first, then do the 'math'. In the information ratio example you've posted, it states: "To annualize, mutiply by the square root of 12" - assuming that the returns are cumulative, and the standard deviation is unannualised, merely 'annualizing' by multiplying the ratio by the square root of 12 is meaningless, because annualising returns and standard deviations are done in mathematically different ways. Hence I think it's better to annualise each component first, then calculate the ratio. It would be interesting to see if there's any industry standard on this. All the best.

  2. Thanks for your comments. This is a topic that is gaining some interest, so more to follow!


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