Formula, in Risk & Portfolio Construction

Information Ratio Formula

The information ratio is the active return of a portfolio relative to its benchmark divided by the tracking error, the standard deviation of that active return. It measures how much excess return a manager generates per unit of benchmark-relative risk, and rewards consistency rather than the size of any single bet.

5 variables. Published May 26, 2026. By AI Fin Hub Research.

Formula

IR = (R_p - R_b) / TE

TE = stdev(R_p - R_b)

Annualized:  IR_annual = IR_period x sqrt(N)

Variables

R_p

Portfolio return

Per-period return of the active portfolio.

R_b

Benchmark return

Per-period return of the reference benchmark over the same window. The benchmark, not the risk-free rate, is the baseline, which is what distinguishes the information ratio from the Sharpe ratio.

R_p - R_b

Active return

The per-period difference between the portfolio and benchmark, sometimes called excess return relative to benchmark. Its mean is the numerator.

Tracking error

Standard deviation of the active return series. A low tracking error with positive active return signals a manager who beats the benchmark steadily; a high tracking error signals lumpy outperformance.

Periods per year

Annualization factor (252 daily, 52 weekly, 12 monthly). The ratio scales by the square root of N under the i.i.d. assumption.

Step by step

1

Compute the active return for each period as portfolio return minus benchmark return.

Portfolio +1.4% versus benchmark +1.0% in a month gives an active return of +0.4%.
2

Take the mean of the active returns across the sample.

Mean active return of 0.30% per month over 36 months.
3

Compute the standard deviation of the active returns to get tracking error.

Standard deviation of the monthly active returns is 1.2%.
4

Divide mean active return by tracking error for the per-period information ratio.

0.30% / 1.2% = 0.25 per month.
5

Annualize by multiplying by the square root of periods per year.

0.25 x sqrt(12) = 0.866 annualized.

Worked example

Active equity fund versus its index, monthly data

Mean monthly active return

0.30%

Tracking error (monthly)

1.2%

Periods per year

Monthly IR = 0.0030 / 0.012 = 0.25. Annualized = 0.25 x sqrt(12) = 0.25 x 3.464 = 0.866.

Annualized information ratio of about 0.87. Grinold and Kahn treat an IR near 0.5 as good and near 1.0 as exceptional for an active manager, so 0.87 would place this fund toward the upper end of skilled active management.

Common variations

Sharpe ratio: uses the risk-free rate as the baseline and total volatility as the denominator instead of benchmark-relative terms.

Appraisal ratio: divides Jensen's alpha by the standard deviation of the residual (non-systematic) returns from a factor regression.

Fundamental law of active management: decomposes the information ratio into information coefficient times the square root of breadth, IR = IC x sqrt(breadth).

Run the numbers next

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Questions people ask next

What is the information ratio and how is it different from the Sharpe ratio?

The information ratio divides active return (portfolio minus benchmark) by tracking error, the standard deviation of that active return series. The Sharpe ratio uses the risk-free rate as the baseline and total volatility as the denominator. Two strategies with the same Sharpe can have very different information ratios depending on how consistently each beats its benchmark.

What counts as a good information ratio for an active manager?

Grinold and Kahn treat an IR near 0.5 as good and near 1.0 as exceptional. The worked example here — 0.30% mean monthly active return against 1.2% tracking error — produces an annualized IR of 0.87, which places the fund toward the upper end of skilled active management.

Why does the information ratio reward consistency over large single bets?

The denominator is tracking error, the standard deviation of active returns. A manager who beats the benchmark by a small, steady margin has lower tracking error than one who alternates large wins and large losses. Lower tracking error for the same mean active return produces a higher ratio, so steady outperformance scores better than lumpy outperformance of the same average size.

How do I annualize the information ratio?

Multiply the per-period ratio by the square root of the number of periods per year: 252 for daily, 52 for weekly, 12 for monthly. The worked example gives a monthly IR of 0.25, which multiplied by sqrt(12) equals about 0.87 annualized, under the assumption that active returns are independent across periods.

Sources

Active Portfolio Management , Richard C. Grinold and Ronald N. Kahn, McGraw-Hill (1999)
The Information Ratio , Thomas H. Goodwin, Financial Analysts Journal 54(4), 34-43 (1998)

Keep the topic connected

Formula Tracking Error Formula
The tracking error formula: the standard deviation of a portfolio's active return versus its benchmark. How tightly a fund tracks its index.
Formula Fundamental Law of Active Management Formula
The fundamental law of active management: information ratio equals information coefficient times the square root of breadth. With an example.
Formula Information Coefficient Formula
The information coefficient formula: correlation between forecast and realized returns. How to measure quant forecasting skill, with a worked example.
Formula Sharpe Ratio Formula
The Sharpe ratio formula: excess return over the risk-free rate divided by return volatility, then annualized. Every variable defined, with a worked example.