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.
Formula
Copy the exact expression or work through it step by step below.
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.
TE
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.
N
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
12
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
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Sources & References
- Active Portfolio Management — Richard C. Grinold and Ronald N. Kahn, McGraw-Hill (1999)
- The Information Ratio — Thomas H. Goodwin, Financial Analysts Journal (1998)
Related Content
Keep the topic connected
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.
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.
Information Coefficient Formula
The information coefficient formula: correlation between forecast and realized returns. How to measure quant forecasting skill, with a worked example.
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.