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Paathshaala : Information Ratio

Information Ratio( IR )

The Information Ratio measures the excess return of an investment manager divided by the amount of risk the manager takes relative to a benchmark. It is used in the analysis of performance of mutual funds etc. Specifically, the information ratio is defined as excess return divided by Tracking Error.Excess return is the amount of performance over or under a given benchmark index. Thus, excess return can be positive or negative. Tracking error is the standard deviation of the excess return. An alternative calculation of Information ratio is alpha divided by tracking error, although it is preferable to use pure excess return in the calculation.

The ratio compares the annualized returns of the Fund in question with those of a selected benchmark (e.g, 3 month Treasury Bills ). Since this ratio considers the annualized standard deviation of both series (as measures of risks inherent in owning either the fund or the benchmark), the ratio shows the risk-adjusted excess return of the Fund over the benchmark. The higher the Information Ratio, the higher the excess return of the Fund, given the amount of risk involved, and the better a Fund manager.

The Information Ratio of a manager series vs. a benchmark series is the quotient of the annualized excess return and the annualized standard deviation of excess return.

Information Ratio = (AnnRtn(r1, ..., rn) - AnnRtn(s1, ..., s,n)) / AnnStdDev(e1, ..., en)

where:
r1, ..., rn = manager return series
s1, ..., sn = benchmark return series
e1, ..., en = r1 - s1, ..., rn - sn

The Information ratio is similar to the Sharpe ratio, but there is a major difference. The Sharpe ratio compares the return of an asset against the return of Treasury bills, but the Information Ratio compares excess return to the most relevant equity (or debt) benchmark index.

The Information Ratio measures the consistency with which a manager beats a benchmark.

It is very important to realize that annualized and cumulative excess return are not calculated in the naive way, by taking the annualized or cumulative return of the excess return series. Instead, one must take the annualized and cumulative return of the two original series and then form the difference between the two:

AnnExRtn = AnnRtn(r1, ..., rn) - AnnRtn(s1, ..., sn)

The annualized standard deviation is the standard deviation multiplied by the square root of the number of periods in one year.

AnnStdDev(r1, ..., rn) = StdDev(r1, ..., rn) *

where r1, ..., rn is a return series, i.e., a sequence of returns for n time periods.

Standard deviation of return measures the average deviations of a return series from its mean, and is often used as a measure of risk. A large standard deviation implies that there have been large swings in the return series of the manager.

There exists a close connection between the Information Ratio and the statistical significance of excess returns. The hypothesis that the set of relative returns is positive and statistically significant on average can be tested with the t-statistic.

The t-Statistic of a manager series vs a benchmark series is the information ratio multiplied by the square root of the number of years.

t-Statistic = (Information Ratio) *

If a fund's beta is close to one, its information ratio times the square root of the number of observations is about equal to the t-statistic for testing the significance of positive relative returns. A statistical test for over performance is therefore also a test for a significant information ratio.


 
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