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Information ratio

Mean active return per unit of tracking error relative to a specified benchmark, with explicit statistical and comparability limits.

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Who this is for — Readers evaluating management relative to a benchmark who need to relate mean active return to the variability of that same relative-performance series.

The information ratio (IR) is mean active return divided by tracking error:

ARₜ = Rₚ,ₜ − Rᵦ,ₜ;   IR = mean(ARₜ) / sd(ARₜ)

The numerator describes the average direction of relative performance; the denominator describes its dispersion. Both depend on the same benchmark, frequency and window. Changing the index can change the sign, TE and ratio without changing the portfolio.

Information ratio: active return per tracking error Mean active return is scaled by its dispersion Information ratio: active return per tracking error Mean active return is scaled by its dispersion IR = mean(rₚ − r_b) / TE Benchmark It must represent the mandateand remain coherent in thecomparison. Mean active return Arithmetic mean of periodicdifferences on the same basis. Tracking error Standard deviation of thosesame periodic differences. Uncertainty Sample, autocorrelation andselection affect the estimate. Cyclepedia · educational diagram: state conventions, period and data
The same average active return can have different consistency. IR measures dispersion but does not prove that the mean came from skill.

Ex post and ex ante

Ex-post IR uses realised active returns. Ex-ante IR may use expected active return and forecast tracking error:

IR_ex ante = E[Rₚ − Rᵦ] / TE_forecast

The first is historical; the second embeds forecasts and a risk model. Showing them without labels confuses outcome with expectation. A high ex-ante IR can come from optimistic expected return or underestimated risk.

Uncertainty matters. Mean active return may not be statistically distinguishable from zero, especially with few periods, autocorrelation or selection of the best among many managers.

Benchmark choice

An appropriate benchmark is specified in advance and represents the mandate and opportunity set. Portfolio and reference need consistent currency and hedging; price, gross-total or net-total return; frequency and timestamps; income treatment; gross/net fee basis; economic universe; and rebalancing rule.

CFA Institute notes that even small index-composition differences can materially change IR. An inconsistent benchmark creates misfit return and misfit risk: the ratio may reward or penalise exposure that belongs to the mandate–index gap rather than the quality of implementation.

Information ratio and Sharpe ratio

The structures are similar but baselines differ. Sharpe ratio uses differential return against a benchmark often intended to be risk-free and a consistent variability measure. Information ratio uses active return against a management benchmark and tracking error.

If the Sharpe benchmark were the same index and its denominator the standard deviation of the differences, the mathematical forms would converge. In professional usage the names normally signal different questions. Stating the benchmark removes more ambiguity than the label alone.

Example

Two hypothetical strategies each have mean monthly active return of 0.20%. A has monthly TE of 0.50%; B has 1%:

IR_A = 0.20 / 0.50 = 0.40;   IR_B = 0.20 / 1 = 0.20

Under the square-root-of-time approximation, the annualised values multiply by √12. This is valid only under the chosen assumptions. The example does not prove A will stay more consistent or that either active return is skill rather than factor exposure or luck.

Why there are no universal bands

A “good” threshold would depend on mandate, benchmark, universe, capacity, horizon, number of genuinely independent decisions, cost and fees, permitted active risk, process stability, distribution, autocorrelation and how many managers or strategies were screened.

The same IR over twelve months and ten years carries different uncertainty. An easy-to-beat but unsuitable index does not make management more skilled. A near-zero TE can create an unstable ratio from tiny measurement differences.

Limitations and reporting checklist

IR does not identify sources of active return, separate factors, selection, timing, cost and luck, or correct survivorship and selection bias. It compresses a distribution into mean and standard deviation, may hide tails, is window- and frequency-sensitive, is undefined when TE is zero and is not additive across portfolios or periods.

Attribution can decompose the outcome; factor regressions can estimate beta and alpha. Neither turns a historical relationship into causality.

A complete report gives the exact benchmark and variant; active-return formula; frequency, window and calendar; total/price return, currency and hedge; gross/ net basis; sample or population TE; annualisation and autocorrelation; ex-ante/ex-post status; observation count and uncertainty; and supporting attribution, factor and cost analysis.

Common error — Comparing information ratios calculated against different benchmarks as though the metric were reference-independent. The index and its variant are part of the formula.

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