Information ratio
Encyclopedia
The Information ratio is a measure of the risk-adjusted return of a financial security (or asset or portfolio). 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 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.
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 just 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 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 much better measure of the alpha produced by the manager is the Geometric Information Ratio.
Tracking error
In finance, tracking error is a measure of how closely a portfolio follows the index to which it is benchmarked. The most common measure is the root-mean-square of the difference between the portfolio and index returns....
, 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 valueExpected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
of the active return, and
is the standard deviationStandard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
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 alphaJensen's alpha
In finance, Jensen's alpha is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return....
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 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.
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
S&P 500
The S&P 500 is a free-float capitalization-weighted index published since 1957 of the prices of 500 large-cap common stocks actively traded in the United States. The stocks included in the S&P 500 are those of large publicly held companies that trade on either of the two largest American stock...
.
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 just 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
Sharpe ratio
The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...
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 performance fee
Performance fee
A performance fee is a fee that an investment fund may be charged by the investment manager that manages its assets, calculated by reference to the increase in the fund's net asset value , which represents the value of the fund's investments...
.
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 much better measure of the alpha produced by the manager is the Geometric Information Ratio.
Characteristics of 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 alphaJensen's alphaIn finance, Jensen's alpha is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return....
- Modern portfolio theoryModern portfolio theoryModern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
- Sortino ratioSortino ratioThe Sortino ratio measures the risk-adjusted return of an investment asset, portfolio or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target, or required rate of return, while the Sharpe ratio penalizes both upside and downside...
- Calmar ratioCalmar RatioCalmar ratio is a performance measurement used to evaluate Commodity Trading Advisors and hedge funds. It was created by Terry W. Young and first published in 1991 in the trade journal Futures....
- Sterling ratioSterling ratioThe Sterling ratio is a measure of the risk-adjusted return of an investment portfolio.Multiple definitions of the Sterling ratio exist...
- Treynor ratioTreynor ratioThe Treynor ratio , named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk , per each unit of market risk assumed.The Treynor ratio relates...
- Upside potential ratioUpside potential ratioThe Upside-Potential Ratio is a measure of a return of an investment asset relative to the minimal acceptable return. The measurement allows a firm or individual to choose investments which have had relatively good upside performance, per unit of downside risk....
- Sharpe ratioSharpe ratioThe Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...
- Coefficient of VariationCoefficient of variationIn probability theory and statistics, the coefficient of variation is a normalized measure of dispersion of a probability distribution. It is also known as unitized risk or the variation coefficient. The absolute value of the CV is sometimes known as relative standard deviation , which is...