The Information ratio is a measure of the risk-adjusted return of a financial
security. It is also known as Appraisal ratio and 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 is: where is the portfolio return, is the
benchmark return, is the expected value of the active return, and is the
standard deviation of the active return, which is an alternate definition of the
aforementioned tracking error. Note in this case, is defined as excess
return, not the risk-adjusted excess return or Jensen's alpha calculated
using regression analysis. Some analysts, however, do use Jensen's alpha
for the numerator and a regression-adjusted tracking error for
the denominator. The information ratio is often used to
gauge the skill of managers of mutual funds, hedge funds, etc. In this case,
it measures the 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 annualized information ratios of about one-half.
There are both ex ante expected and ex post observed information ratios.
Generally, the information ratio compares the returns of the manager's
portfolio with those of a benchmark such as the yield on three-month Treasury
bills or an equity index such as the S&P 500.
The information ratio is often annualized. While it is then common for
the numerator to be calculated as the arithmetic difference between the
annualized portfolio return and the annualized benchmark return, this is an
approximation because the annualization of an arithmetic difference between
terms is not the arithmetic difference of the annualized terms. Since the
denominator is here taken to be the annualized standard deviation of the
arithmetic difference of these series, which is a standard measure of
annualized risk, and since the ratio of annualized terms is the annualization of
their ratio, the annualized information ratio provides the annualized
risk-adjusted active return of the portfolio relative to the benchmark.
The information ratio is similar to the Sharpe ratio but, whereas the Sharpe
ratio is the 'excess' return of an asset over the return of a risk free asset
divided by the variability or standard deviation of returns, the information
ratio is the 'active' return to the most relevant benchmark index divided by the
standard deviation of the 'active' return or tracking error.
Some hedge funds use Information ratio as a metric for calculating a
performance fee. One of the main criticisms of the
Information Ratio is that it considers arithmetic returns and ignores leverage.
This can lead to the Information Ratio calculated for a manager being negative
when the manager produces alpha to the benchmark and vice versa. A better
measure of the alpha produced by the manager is the Geometric Information
Ratio. Characteristics of the information ratio
The main characteristics of the information ratio are as follows:
The information ratio estimates ex-post value added and relates this to ex-ante
opportunity available in the future. The residual frontier that describes the
opportunities accessible to the active manager is identified by the information
ratio. The level of aggressiveness for each
manager is decided by his/her information ratio.
Sometimes intuition can give a good clue about the information ratio and residual
risk aversion. Value added depends on the managers’
prospects and aggressiveness. See also
Jensen's alpha Modern portfolio theory
Omega ratio Sortino ratio
V2 ratio Calmar ratio
Sterling ratio Treynor ratio
Upside potential ratio Sharpe ratio
Coefficient of Variation Information coefficient
References Further reading
Bacon, "Practical Risk-adjusted Performance Measurement", Wiley, 2012.
ISBN 978-1-118-36974-6 Bacon, "Practical Portfolio Performance
Measurement & Attribution", Wiley, 2008. ISBN 978-0-470-05928-9