On This Page
- What is the information ratio?
- How is the information ratio calculated?
- Information ratio example: two managers
- The fundamental law of active management
- Annualizing the information ratio and counting costs
- How to use the information ratio to evaluate a process
- Limitations of the information ratio
- Bottom line
- FAQ
Key Takeaways
- Compute period-by-period portfolio return minus benchmark return, then divide its arithmetic mean by its standard deviation.
- It is the benchmark-relative analogue of the Sharpe ratio: the benchmark replaces the risk-free rate in the numerator and active risk replaces total volatility in the denominator.
- The fundamental-law framework relates expected active performance to forecast quality, effective breadth and how the portfolio expresses the forecasts.
- In the independent-bet version, quadrupling breadth doubles modeled IR when the information and transfer coefficients remain fixed.
- Compare mean active return, tracking error and portfolio exposures on the same benchmark and return basis.
- Changing the benchmark changes the numerator and the denominator at once, so two information ratios are comparable only when the index, the frequency and the window match.
What is the information ratio?
The information ratio (IR) is a measure of active return per unit of active risk. It divides the arithmetic mean of a portfolio’s period-by-period return minus its benchmark’s return by the standard deviation of that active-return series, called tracking error. A higher positive ratio means more benchmark-relative return for each unit of variation around the benchmark.
How is the information ratio calculated?
Subtract the benchmark’s return from the portfolio’s return in every period. Then divide the arithmetic mean of that active-return series by its standard deviation.
Use matching total-return definitions, dates and currencies. Sharpe uses a risk-free baseline instead of a benchmark. Regression alpha divided by residual volatility is the related appraisal-ratio construction.
Formula
Active return at t = portfolio return at t − benchmark return at t; information ratio = mean(active return) ÷ standard deviation(active return)- Rp,t and Rb,t are the portfolio and benchmark returns in period t, both total returns over identical windows, so their difference is the active return for that period.
- The numerator is the mean of the active return series and TE is its standard deviation, taken with the n minus 1 sample divisor used for standard deviation elsewhere in this glossary. Both come from the same series, so a single pair of annual returns produces no ratio at all.
- In the fundamental-law model, IC measures the relationship between forecasts and outcomes. It is a correlation measure, not a trade win probability.
- Breadth counts effective independent opportunities in the selected model. A raw position count and correlation-adjusted breadth are different quantities.
- TC measures how the implemented portfolio expresses the optimal forecast portfolio on a common risk basis. In the unrestricted optimum, TC is 1.
- The usual annualized convention multiplies monthly IR by √12. Its additive-return scaling uses zero serial correlation; evaluate serial dependence and compounding in the corresponding horizon calculation.
- Use IR ≈ TC × IC × √BR for the simplified expected-performance model. In a correlated matrix formulation, apply the model’s signal-adjusted IC and covariance-based TC.
Information ratio example: two managers
Use 60 monthly observations with the same total-return benchmark. Annualized arithmetic mean returns are 8% for the benchmark, 3% for the risk-free baseline, 10.40% for Manager A and 11.60% for Manager B. Annualized excess-return volatility is 15% for A and 17.20% for B; tracking error is 3% for A and 6% for B.
- A mean active return: 10.40% − 8% = 2.40% annualized
- A information ratio: 2.40% ÷ 3% = 0.80
- B mean active return: 11.60% − 8% = 3.60% annualized
- B information ratio: 3.60% ÷ 6% = 0.60
- A Sharpe: 7.40% ÷ 15% = 0.49; B Sharpe: 8.60% ÷ 17.20% = 0.50
- Separate model illustration: 0.40 × 0.10 × √400 = 0.80; 0.60 × 0.10 × √100 = 0.60
B has 1.20 percentage points more annualized mean active return, while A has the higher information ratio because B’s tracking error is twice as large. The separate fundamental-law examples illustrate model inputs that produce the same two ratios.
A has 2.40% annualized mean active return and 3% tracking error, giving 0.80. B has 3.60% and 6%, giving 0.60. These are annualized arithmetic inputs from the same monthly-return basis.
Against a 3% risk-free baseline, the separate Sharpe calculations give A 0.4933 and B 0.5000. Keep compounded ending wealth distinct from the arithmetic means used in these ratios.
The two measures rank the managers differently: Sharpe puts B slightly ahead, while the information ratio puts A ahead because B’s tracking error is twice as large.
The fundamental law of active management
The simplified fundamental law expresses expected IR as transfer coefficient × information coefficient × square root of breadth. Inputs of 0.40, 0.10 and 400 give 0.80; inputs of 0.60, 0.10 and 100 give 0.60.
These are model illustrations. In correlated formulations, use the model’s adjusted information coefficient and risk-adjusted implementation measure. A forecast correlation is distinct from the probability of a profitable trade.
Annualizing the information ratio and counting costs
The usual √12 scaling of monthly IR follows the additive, serially uncorrelated convention. Calculate horizon returns separately when assessing compounding or serial dependence.
Include trading costs in the net portfolio-return series. Variable costs can change both its mean active return and tracking error, so calculate the net ratio from that series directly.
How to use the information ratio to evaluate a process
Compare benchmark-relative return, tracking error, factor exposures, holding time and drawdown. Examine candidate selection, portfolio construction and execution separately when comparing a model with its completed record.
Limitations of the information ratio
- The ratio belongs to its benchmark. Changing the index changes the numerator and the denominator at once, so two ratios compare only on the same benchmark, frequency and window.
- Use a long enough record. Short histories give unstable readings, and a single pair of annual returns produces no ratio at all.
- Check active returns for autocorrelation before annualizing. The √12 scaling assumes serially uncorrelated active returns, so autocorrelation distorts the annualized figure.
- Negative readings need care. With a negative mean, a larger tracking error produces a less negative ratio, so compare the mean and tracking error separately.
- A high ratio still needs a source. Factor exposures produce it as well as security selection, so check the exposures before you credit the manager’s skill.
Bottom line
The information ratio measures a portfolio’s average return above its benchmark relative to how much that active return varies from period to period. Use it to compare managers or strategies on the same benchmark, frequency and window, and read it alongside mean active return, tracking error and factor exposures.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- CFA Institute: The Sharpe Ratio and the Information Ratio (Deborah Kidd, CFA)
- CFA Institute: Technical Appendix to Analysis of Active Portfolio Management
- Zhang, Wang and Cao: Turnover-Adjusted Information Ratio
How entries are sourced, calculated and updated: editorial methodology.