What Is the Information Ratio? Tracking Error and Sharpe Ratio Compared

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The information ratio (IR) measures how much return a portfolio earns above its benchmark for each unit of tracking error, the volatility of that excess return. It answers two questions about an active manager: did the portfolio beat its benchmark, and did it do so consistently enough to suggest skill rather than a few lucky periods? A higher information ratio means more outperformance per unit of active risk.

What the information ratio measures

Every active fund sets itself a benchmark, such as the S&P 500 for a large-cap U.S. equity fund. The gap between the fund’s return and the benchmark’s return in a period is the active return or excess return. A fund can produce a large average active return from a few exceptional years amid long stretches of underperformance, or a smaller one that shows up period after period.

The information ratio separates those two patterns: it rewards the size of the average excess return and penalizes how much that excess return swings. Investors paying active management fees use it to judge whether outperformance is reliable rather than the product of one good year.

Information ratio formula

The standard formula is:

IR = (Portfolio return − Benchmark return) ÷ Tracking error

where:

• Portfolio return is the return of the fund or portfolio over each period
• Benchmark return is the return of the chosen index or reference portfolio over the same periods
• Tracking error is the standard deviation of the differences between portfolio and benchmark returns

In practice the ratio is calculated over a series of periods (months, quarters or years) in three steps:

1. For each period, subtract the benchmark return from the portfolio return.
2. Average those differences to get the mean excess return.
3. Take the standard deviation of the differences and divide the mean by it.

Tracking error in the formula vs. tracking error for index funds

The term “tracking error” is used in two settings. For a passive index fund or ETF, it describes how closely the fund follows its index, and a small figure is the goal. In the information ratio, it is the risk an active manager deliberately takes by deviating from the benchmark, often called active risk.

What tracking error measures is consistency, not distance from the benchmark. A fund that beats its benchmark by exactly 2% every month has a tracking error close to zero, even though it is clearly not trying to match the index. A fund that beats the benchmark by 10% one month and lags it by 6% the next has a much higher tracking error, even if its average outperformance ends up similar.

Annualizing the ratio

Information ratios are usually quoted on an annual basis. If the inputs are monthly, the mean monthly excess return is multiplied by 12 and the monthly tracking error by the square root of 12. The net effect is that a monthly IR is multiplied by √12 (about 3.46). This conversion assumes monthly excess returns are roughly independent of one another. When excess returns are serially correlated, the scaled figure can overstate or understate the true annual ratio.

Worked example: two hypothetical funds

Hypothetical example for illustration only. Two funds both claim to beat a benchmark that returned 10% a year over the same period.

Fund A (Steady)

• Average annual return: 12%
• Tracking error: 4%
• IR: (12% − 10%) ÷ 4% = 0.50

Fund B (Volatile)

• Average annual return: 15%
• Tracking error: 15%
• IR: (15% − 10%) ÷ 15% = 0.33

Fund B has the higher return and the larger average excess return, but Fund A earns more excess return per unit of active risk. Its steadier outperformance gives more reason to believe it reflects repeatable decisions rather than a few large bets, while Fund B’s wider swings make longer or deeper stretches of underperformance more likely.

Calculating from a return series

Hypothetical example. A fund’s annual excess returns over five years are +4%, −1%, +3%, +2% and −3%.

1. Mean excess return: (4 − 1 + 3 + 2 − 3) ÷ 5 = 1.0%
2. Tracking error: the deviations from the mean are 3, −2, 2, 1 and −4. Their squares sum to 34. Using the sample standard deviation (dividing by n − 1 = 4) gives a variance of 8.5 and a tracking error of about 2.92%.
3. Information ratio: 1.0% ÷ 2.92% ≈ 0.34

The fund lagged its benchmark in two of the five years, yet the ratio is positive because the good years outweighed the bad. This uses the arithmetic average of yearly differences. Comparing the fund’s CAGR with the benchmark’s would give a slightly different numerator, so use the same method for every fund being compared.

Interpreting the information ratio

• Above zero: the portfolio beat its benchmark on average over the period.
• Zero: no average outperformance.
• Below zero: the portfolio trailed the benchmark. A negative IR is common for active funds after fees.

Practitioners often treat an IR around 0.5 as good and figures near 1.0 as exceptional when sustained over many years. These are rules of thumb, not standards. The ratio is most useful when comparing funds measured against the same benchmark, over the same dates and with the same return frequency.

The measurement window matters. A one-year IR built from twelve monthly observations can be dominated by a single market episode, so analysts often compare three-, five- and ten-year figures. A ratio that holds up across all three is stronger evidence of skill. Too long a window has its own problem: the manager, strategy or market environment may have changed.

Information ratio vs. Sharpe ratio

Both are risk-adjusted return measures, and their formulas look similar, which is why they are often confused.

Sharpe ratio = (Portfolio return − Risk-free rate) ÷ Standard deviation of portfolio returns

Information ratio = (Portfolio return − Benchmark return) ÷ Standard deviation of excess returns over the benchmark

The two can rank the same funds differently. A fund that hugs a volatile stock index while adding a small, steady edge may have a respectable IR but a Sharpe ratio driven mainly by the market’s own volatility. A low-volatility portfolio might have an excellent Sharpe ratio but a poor IR against an equity benchmark it could not keep up with. Use the Sharpe ratio to judge how much total risk a portfolio carries for its return, and the information ratio to judge whether an active manager adds value over the passive alternative.

Active vs. residual information ratio

The version above is sometimes called the active information ratio, because it uses raw active returns. In quantitative portfolio management, a residual information ratio is also used. It first regresses portfolio returns on benchmark returns, then divides the regression’s alpha by the standard deviation of the residual returns:

Residual IR = α ÷ σ(residual)

The difference matters when a portfolio’s beta to the benchmark is not 1. A fund with a beta of 1.2 will show positive active returns in rising markets simply from extra market exposure. The active IR counts that as outperformance; the residual IR strips it out and credits only the return not explained by market exposure.

The fundamental law of active management

Richard Grinold and Ronald Kahn connected the information ratio to the inputs of an investment process:

IR ≈ IC × √Breadth

• Information coefficient (IC) is the correlation between a manager’s forecasts and the outcomes that follow.
• Breadth is the number of independent bets made per year.

Hypothetical example: a manager with an IC of 0.05 making 400 independent bets a year has an expected IR of about 0.05 × √400 = 1.0. A manager with an IC of 0.15 but only 16 bets a year gets 0.15 × 4 = 0.6. This is why quantitative strategies favor many small, independent forecasts. The law is an approximation that assumes the bets are truly independent and that portfolio constraints do not block forecasts. Because the IC is a correlation and cannot exceed 1, a stated IR implies a combination of skill and breadth that should be plausible for the strategy.

Limitations of the information ratio

• Benchmark choice drives the result. Measuring a small-cap fund against a large-cap index can flatter or punish it for reasons unrelated to skill.
• A high IR can sit beside a small alpha. A fund beating its index by 0.3% a year with 0.3% tracking error has an IR of 1.0, but the dollar benefit may be smaller than the fee difference against an index fund.
• Scale does not change it. Doubling every active position doubles both average excess return and tracking error, so the IR says nothing about whether the amount of active risk suits an investor. A cash holding, by contrast, is itself an active position against an equity benchmark and does change the ratio.
• Standard deviation treats upside and downside alike. The measure assumes excess returns are reasonably symmetric, so strategies with rare, sharp losses can look better than they are until a loss occurs.
• Short histories are noisy. With few observations, the estimated IR has a wide margin of error, and a strong-looking figure may not survive a longer sample.

FAQs

The Bottom Line

The information ratio matters most to investors paying active management fees who want to know whether a manager adds value over a passive alternative. Compare funds against the same benchmark, over the same dates and return frequency, and check three-, five- and ten-year figures. Treat a high ratio with care when the history is short, the benchmark is a poor fit, or the excess return is too small to cover fees.