Information ratio
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The Information ratio is a measure of the risk-adjusted return of a financial security (or asset or portfolio). It is defined as expected active return divided by tracking error, where active return is the difference between the return of the security and the return of a selected benchmark index, and tracking error is the standard deviation of the active return; i.e., the information ratio IR is:
![IR = \frac{E[R-R_b]}{\sigma} = \frac{\alpha}{\omega} = \frac{E[R-R_b]}{\sqrt{\mathrm{var}[R-R_b]}}](http://upload.wikimedia.org/math/3/1/7/3179d249a7a2dcffe1df3366e02a67cd.png)
,
where R is the portfolio return, Rb is the benchmark return, α = E[R − Rb] is the expected value of the active return, and ω = σ is the standard deviation of the active return, which is an alternate definition of the aforementioned tracking error.
The information ratio is often used to gauge the skill of managers of mutual funds, hedge funds, etc. In this case, it measures the expected active return of the manager's portfolio divided by the amount of risk that the manager takes relative to the benchmark. The higher the information ratio, the higher the active return of the portfolio, given the amount of risk taken, and the better the manager. Top-quartile investment managers typically achieve information ratios of about one-half.[1]
Generally, the ratio compares annualized returns of the manager's portfolio with those of benchmarks such as the yield on three-month Treasury Bills or an equity index such as the S&P 500. Since this ratio considers the annualized standard deviation of both series (as measures of risks inherent in owning either the portfolio or the benchmark), the ratio shows the risk-adjusted active return of the portfolio over the benchmark.
The information ratio is similar to the Sharpe ratio but, whereas the Sharpe ratio compares the excess return of an asset against the return of a risk free asset, the information ratio compares active return to the most relevant benchmark index. That is to say, the Sharpe ratio equals the information ratio where the benchmark is a risk-free asset (e.g. cash or government bonds).
Some hedge funds use Information ratio as a metric for calculating performance fee.
[edit] See also
- Jensen's alpha
- Modern portfolio theory
- Sortino ratio
- Calmar ratio
- Treynor ratio
- Upside potential ratio
- Sharpe ratio
- Coefficient of Variation
[edit] Notes
- ^ Richard C. Grinold and Ronald N. Kahn, Active Portfolio Management, Second Edition, page 114.
