Information Ratio and Tracking Error

Most professional investors are judged against a benchmark, such as the S&P 500 for a US equity fund. Two numbers describe that relationship. Tracking error measures how much the portfolio's returns differ from the benchmark's. The information ratio divides the average excess return over the benchmark, called active return, by tracking error. It answers a key question: how much extra return does the manager earn for each unit of risk taken in departing from the benchmark?

The formulas#

Active return = Portfolio return - Benchmark return
Tracking error = Standard deviation of active returns (annualised)
Information ratio = Average active return / Tracking error

Tracking error levels#

Index funds aim for tracking error close to zero. Active managers take tracking error deliberately, hoping to earn active return. See Active vs Passive Investing.

What is a good information ratio?#

Sustained information ratios above 0.5 are uncommon among active managers, especially after fees.

The fundamental law of active management#

Richard Grinold proposed a link between skill, breadth and the information ratio:

Information ratio ≈ Information coefficient × Square root of Breadth

• Information coefficient (IC): the correlation between forecasts and outcomes, a measure of skill.
• Breadth: the number of independent bets per year.

A small edge applied to many independent bets can produce a strong information ratio. An IC of 0.05 across 400 independent bets a year gives an information ratio of about 0.05 times 20, or 1.0. In practice, bets are rarely fully independent, so real breadth is smaller than the raw count. This logic underlies many quantitative strategies. See Quantitative Trading and Combining Signals.

Information ratio versus Sharpe ratio#

For a market neutral fund with a cash benchmark, the two are nearly the same. See Sharpe Ratio.

Pitfalls#

1. Wrong benchmark: a fund holding small stocks measured against a large cap index shows misleading active returns.
2. Short periods: active returns are noisy; several years are needed. See Statistical Significance in Trading.
3. Closet indexing: very low tracking error with fees produces a negative information ratio.
4. Hidden factor bets: active return may come from factor exposures rather than skill. See Factor Models and P&L and Performance Attribution.

Information ratio for your own trading#

Individual traders can use the same idea by choosing a benchmark that matches what they could have earned passively, such as a broad index fund for a stock trader or simply holding Bitcoin for a crypto trader. Compute your monthly returns minus the benchmark's, then the average and standard deviation of those differences. If your active return is small relative to its variability, trading actively may not be worth the time, costs and stress compared with the passive alternative. See Investing vs Trading.

Frequently asked questions#

What is the information ratio?#

Active return over a benchmark divided by tracking error, measuring how much excess return a portfolio earns per unit of benchmark relative risk.

What is tracking error?#

The standard deviation of the difference between a portfolio's returns and its benchmark's returns.

What is a good information ratio?#

Above 0.5 sustained over several years is considered very good; above 1.0 is rare.

Next, learn a ratio that measures return per unit of market risk in Treynor Ratio.