Information Ratio (IR)

August 24, 2024 Portfolio Management

Benchmark-relative performance ratio comparing mean active return with the volatility of active return, called tracking error.

On this page

The Information Ratio (IR) measures average portfolio return above a benchmark per unit of tracking error. It evaluates the consistency of benchmark-relative performance, not the portfolio’s total risk or absolute return.

Key Takeaways

The numerator is the arithmetic mean of periodic active returns.
The denominator is the standard deviation of that same active-return series.
Portfolio and benchmark returns must be aligned by date, currency, frequency, and return basis.
A higher historical ratio can indicate more active return per unit of active risk, but there is no universal cutoff that proves skill.

Formula

First calculate active return for each period:

AR_t=R_{p,t}-R_{b,t}

Then calculate the common active-return form of the Information Ratio:

IR=\frac{\overline{AR}}{s(AR_t)}

Where:

(R_{p,t}) is portfolio return in period (t)
(R_{b,t}) is benchmark index return in the same period
(\overline{AR}) is mean active return
(s(AR_t)) is the sample standard deviation of active returns, or tracking error

Some sources use a residual-return version based on regression residuals rather than total active return. A report should state which version it uses because the results can differ.

Worked Example

Assume twelve aligned monthly observations produce:

average monthly portfolio return: 0.75%
average monthly benchmark return: 0.60%
average monthly active return: 0.15%
monthly tracking error: 0.75%

The monthly Information Ratio is:

IR_{monthly}=\frac{0.15\%}{0.75\%}=0.20

Under the simplifying square-root-of-time convention, approximate annual active return is 1.80% and annualized tracking error is:

TE_{annual}\approx0.75\%\sqrt{12}=2.60\%

The approximate annualized Information Ratio is:

IR_{annual}\approx\frac{1.80\%}{2.60\%}=0.69

Equivalently, 0.20 x sqrt(12) is about 0.69. This annualization assumes sufficiently stable, independent periodic active returns. Autocorrelation, changing exposures, or smoothed valuations can invalidate the shortcut.

How to Interpret the Information Ratio

A positive ratio means average portfolio return exceeded benchmark return during the sample. A negative ratio means average underperformance. A ratio near zero means little average active return relative to its variability.

There is no universal value that makes an Information Ratio good. Interpretation depends on:

strategy type and opportunity set
benchmark suitability
sample length and market regimes
gross- or net-of-fee return basis
data frequency and annualization method
portfolio constraints and active-risk budget

A high ratio estimated from a short sample may be less persuasive than a lower but stable estimate across multiple regimes. The ratio is dimensionless, but its inputs and methodology still require disclosure.

Information Ratio vs. Nearby Measures

Measure	Numerator	Denominator or model	Main question
Information Ratio	Mean active return	Tracking error	How much average benchmark-relative return accompanied active risk?
Sharpe Ratio	Mean return above a reference rate	Total standard deviation	How much excess return accompanied total volatility?
Jensen’s Alpha	Portfolio return minus CAPM-implied return	CAPM and beta	How much return was unexplained by market beta?
Active return	Portfolio return minus benchmark return	None	How far did the portfolio finish above or below its benchmark?

Risks and Limitations

Benchmark dependence

An unsuitable benchmark can make both active return and tracking error misleading. The benchmark should represent the portfolio’s mandate and investable opportunity set.

Low tracking error can inflate the ratio

When the denominator is close to zero, small return differences can produce an unstable ratio. A very high value based on limited variation is not automatically evidence of low risk or repeatable skill.

The ratio can hide the path of losses

IR treats positive and negative deviations from the benchmark symmetrically in its denominator. It does not show drawdown, tail loss, liquidity, leverage, or total portfolio volatility.

Historical results are uncertain

Changing the sample, fee basis, benchmark, or observation frequency can alter the result. Backtests also require review for survivorship, look-ahead bias, model selection, and transaction costs.

Practical Review Checklist

Before comparing Information Ratios, verify:

the benchmark and why it fits each portfolio
aligned portfolio and benchmark total-return observations
mean active return and tracking error calculated from the same series
gross-versus-net fee treatment
the data frequency, sample dates, and annualization convention
whether the calculation uses active return or residual return
total risk, drawdown, liquidity, capacity, and leverage outside the ratio

Tracking Error: Measures the active-return volatility in the denominator.
Alpha: Describes benchmark- or model-relative value added.
Benchmark Index: Supplies the comparison return used to form active returns.
Sharpe Ratio: Uses a reference rate and total volatility instead of a benchmark and active risk.
Jensen’s Alpha: Evaluates return relative to CAPM rather than tracking error.

Sources

FAQs

Is an Information Ratio above 1 always excellent?

No universal threshold applies. A value must be evaluated with its benchmark, sample length, methodology, fee basis, strategy constraints, and estimation uncertainty.

Can an index fund have an Information Ratio?

It can be calculated if there are return differences, but an index fund is generally evaluated for tracking quality and costs rather than intentional benchmark outperformance.

Why might two providers report different Information Ratios?

They may use different benchmarks, return frequencies, samples, fee bases, annualization rules, or active-versus-residual definitions.

This page is for financial education and does not recommend a manager, fund, benchmark, or strategy.

Alpha Generation

Jensen's Alpha