Information Ratio — Measuring Active Return and Its Variability
Suppose fund A's annual return differences from its benchmark were +5, +6, and +7 percentage points, while fund B's were +25, −15, and +8. Both averages are +6pp, but the variation differs. Information Ratio (IR) compares this average with the variability of the return differences. A hypothetical three-year example explains the calculation, how it differs from the Sharpe Ratio, and what it can tell us. IR alone cannot distinguish luck from skill or predict next year's performance.
1. Definition — Mean active return divided by TE
This article uses the difference between portfolio and benchmark returns measured over the same periods and in the same currency.
IR = Mean active return (ā) / Tracking Error (TE)
Mean active return (ā)
The arithmetic mean of the period-by-period return differences aₜ. This is distinct from beta-adjusted regression alpha. Dividing regression alpha by the TE defined here would mix different definitions. For that separate concept, see The True Meaning of Alpha.
Tracking Error (TE)
The standard deviation of the same active returns aₜ. The hypothetical example treats the observations as the complete set and uses population standard deviation, dividing by n. Using sample standard deviation, which divides by n−1, changes TE and IR, so comparisons must use the same convention.
TE = √[Σ(aₜ − ā)² / n]
Active return and TE are expressed in percentage points (pp); IR has no units. For a fixed positive mean, a smaller TE gives a higher IR. Definition reference: CFA Institute, Using Multifactor Models.
2. Intuition — by example
Two hypothetical funds illustrate the calculation. Each has three annual active returns, and TE uses the population standard deviation above. Inputs and TE are in pp.
| Fund | Year 1 | Year 2 | Year 3 | Mean | TE | IR |
|---|---|---|---|---|---|---|
| A | +5 | +6 | +7 | +6 | 0.81650 | 7.34847 |
| B | +25 | −15 | +8 | +6 | 16.39105 | 0.36605 |
These figures are invented, not the record of any real fund. Displayed values are rounded to five decimal places, but IR is calculated from unrounded TE. The inputs are annual, so no further annualization is applied.
B: TE = √[(361 + 441 + 4) / 3], IR = 6 / √(806 / 3)
Both funds have a mean active return of +6pp, but A's IR is roughly 20 times B's.
- A's return differences stay close to their mean over these three years.
- B's return differences vary more, and B underperforms its benchmark in year 2.
3. Interpreting IR levels
When TE is positive, the sign and size of IR have the following meanings. These are explanations of the ratio, not manager rankings or universal quality thresholds.
| IR | Mathematical meaning |
|---|---|
| < 0 | Mean active return is negative. This does not mean the fund underperformed in every period. |
| 0 | Mean active return is zero. |
| 0.5 | Mean active return is half the TE. |
| 1.0 / 2.0 | Mean active return is one / two times the TE. |
Comparisons need matching measurement windows, data frequency, annualization, benchmarks, and fee treatment. A high IR alone does not establish statistical significance or future repeatability.
4. IR vs Sharpe Ratio
Sharpe and IR look similar in form but measure different things:
| Metric | Numerator | Denominator | What it measures |
|---|---|---|---|
| Sharpe | Mean of (return − risk-free return for the same period) | Std. dev of those excess returns | Efficiency relative to a risk-free asset |
| IR | Mean of (return − benchmark return) | Std. dev of the same active returns (TE) | Efficiency relative to the benchmark |
Sharpe compares returns with a risk-free asset; IR compares them with the selected benchmark. If the risk-free return is constant across periods, Sharpe's denominator equals the standard deviation of portfolio returns.
- An index ETF can have different returns from the index it tracks because of fees and tracking differences. Its IR is not zero by definition.
- A portfolio can have a positive IR in a falling market if it loses less than its benchmark. A positive IR does not necessarily mean the portfolio itself made money.
On Sharpe's limits and how Sortino / Calmar differ, see The Sharpe Ratio Trap.
5. Four IR-calculation pitfalls
① Measurement window and observation count
With few observations, individual values can strongly affect both the mean and TE. A longer record may span changes in market conditions or strategy, so no fixed number of years establishes skill. Report the window, observation count, and missing data.
② Benchmark choice
Choose a benchmark suited to the investment universe, region, currency, and dividend treatment. For example, the S&P 500 may be a candidate for a US large-cap fund, but the actual mandate and treatment of dividends still matter. Changing the benchmark changes both mean active return and TE.
③ Return frequency — daily / monthly / annual
Use the same data frequency for numerator and denominator. With m periods per year, stable period distributions, no serial correlation, and an additive approximation to returns, annualization multiplies the mean by m, TE by √m, and IR by √m. Monthly data uses m=12; if daily data uses m=252, state that assumption. Compounding or serial correlation can make this simple conversion inappropriate.
④ Fees — gross vs net
Mean active return differs before and after fees. In a simplified calculation that subtracts the same return amount each period, TE is unchanged, but the fall in IR depends on TE. A 1% annual fee does not imply a fixed reduction in IR.
6. Practical IR for individual investors
IR can be useful in the following comparisons when its calculation conditions are available:
- Comparing active funds / robo-advisors — check the benchmark, window, frequency, standard deviation convention, and fee treatment alongside IR or TE.
- Self-assessment — compare returns adjusted for deposits and withdrawals with benchmark returns in the same currency and periods.
- Strategy comparison — when backtesting momentum, value, or dividend strategies, examine actual gains and losses, maximum drawdown, and trading costs alongside IR. A high historical IR does not guarantee future performance.
Multifolios provides visual benchmark comparison through Return mode and the SPY / KOSPI lines. This article's hypothetical example explains how to read IR.
Summary
- IR = Mean active return / TE. Calculate both from the same return differences.
- The same mean with a different TE gives a different IR. This hypothetical example produces a roughly 20-fold gap.
- IR alone cannot establish skill or forecast next year. Zero TE prevents calculation of a finite IR.
- Sharpe and IR use different comparisons: a risk-free asset and a selected benchmark.
- Match the window, benchmark, frequency, standard deviation, annualization, and fees.