Information Ratio: Active Return, Tracking Error, and Variants
Summary
The document discusses two formulations of the information ratio: expected residual return relative to residual risk, and active portfolio return relative to its volatility, commonly called tracking error. It presents the latter as average portfolio excess return over a benchmark divided by the standard deviation of that excess return. This makes clear that the numerator and denominator depend on how active or residual performance is defined.
The answer cautions that this ratio can be misleading when leverage makes a manager’s returns weakly correlated with the benchmark, and notes alternatives that use Jensen’s alpha or geometric returns. It offers no data or worked calculation to compare these variants, so it leaves open which measure is appropriate for a particular evaluation. The practical lesson is to check the benchmark relationship and the precise return and risk definitions before comparing reported ratios.
Key ideas
- A common information ratio divides average active return by tracking error.
- Residual return terminology may refer to benchmark-relative performance after risk adjustment.
- Leverage can make the conventional ratio misleading when portfolio returns have weak benchmark correlation.
- Alternative formulations include using Jensen’s alpha or geometric returns.
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# How to calculate Information Ratio?
# How to calculate Information Ratio?
In the book titled "Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk" by Grinold & Kahn, the information ratio is defined as "the ratio of the expected annual residual return to the annual volatility of the residual return". The key concept is "residual return" in the definition, which is risk adjusted return, i.e. the so-called "alpha". However, in other books, articles and blogs on the Internet, the Information Ratio is always calculated as the ratio of expected annual active return to the annual volatility of the active return. I'm so confused about this.
So why are there two different definitions? Which one is more proper?
P.S., The active return is the portfolio return minus benchmark return.
## Answer by amdopt (score 2)
https://quant.stackexchange.com/a/47340
I know Information Ratio to be:
$IR = {E[R_p - R_b] \over \sqrt{var[R_p - R_b]}}$
Meaning the ratio ($IR$) is equal to the average excess return (Portfolio return - Benchmark return) divided by the standard deviation of excess returns relative to a benchmark. You could also say that this is the active return divided by the tracking error. Note that this formula can be misleading by way of producing negative numbers if/when a fund/manager uses leverage and creates excessive alpha compared to a benchmark. For this reason, you should be sure that the fund/manager is strongly correlated to the benchmark.
Variations of IR include using Jensens's Alpha as the numerator as well as the Geometric Information Ratio. Geometric IR is preferred for managers that use leverage.
References:
Informatio Ratio from Wikipedia
Jensen's Alpha
Geometric IR
Thoughts On Grinold & Kahn’s “Fundamental Law Of Active Management”Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.