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
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)
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, ...,
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.