Information ratio 1

Information ratioThe Information ratio is a measure of the risk-adjusted return of a financial security (or asset or portfolio). It is alsoknown as Appraisal ratio and is defined as expected active return divided by tracking error, where active return isthe difference between the return of the security and the return of a selected benchmark index, and tracking error isthe standard deviation of the active return; i.e., the information ratio is:

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where is the portfolio return, is the benchmark return, is the expected value of theactive return, and is the standard deviation of the active return, which is an alternate definition of theaforementioned tracking error.Note in this case, is defined as excess return, not the risk-adjusted excess return or Jensen's alpha calculated usingregression analysis. Some analysts, however, do use Jensen's alpha for the numerator and a regression-adjustedtracking 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, itmeasures the active return of the manager's portfolio divided by the amount of risk that the manager takes relative tothe benchmark. The higher the information ratio, the higher the active return of the portfolio, given the amount ofrisk taken, and the better the manager. Top-quartile investment managers typically achieve annualized informationratios of about one-half.[1] 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 asthe 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 thearithmetic difference between the annualized portfolio return and the annualized benchmark return, this is anapproximation because the annualization of an arithmetic difference between terms is not the arithmetic difference ofthe annualized terms.[2] Since the denominator is here taken to be the annualized standard deviation of the arithmeticdifference of these series, which is a standard measure of annualized risk, and since the ratio of annualized terms isthe annualization of their ratio, the annualized information ratio provides the annualized risk-adjusted active returnof 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 overthe 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 ortracking 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. Thiscan lead to the Information Ratio calculated for a manager being negative when the manager produces alpha to thebenchmark and vice-versa. A better measure of the alpha produced by the manager is the Geometric InformationRatio.[3]

Information ratio 2

Characteristics of Information RatioThe 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.

Notes[1] Richard C. Grinold and Ronald N. Kahn, Active Portfolio Management, Second Edition, page 114.[2] The Annualization of Attribution by Andre Mirabelli in Advanced Portfolio Attribution Analysis edited by Carl Bacon.[3] "How to Calculate Alpha: Geometric Information Ratio" (http:/ / www. automated-trading-system. com/ geometric-information-ratio/ #start).

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Article Sources and ContributorsInformation ratio Source: http://en.wikipedia.org/w/index.php?oldid=524034134 Contributors: Amirab, Benabramov, Big el57, Btyner, Fouraker, Kavalina, Math+Finance, Mgarrett6,Mpacanovsky, MrOllie, Octopus-Hands, Outbox4, Pgk, Plastikspork, Shareman, Snakemike, Wstrong, Zfeinst, 27 anonymous edits

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