Information ratio

Information ratio (IR) is a measure of the risk-adjusted performance of an investment portfolio relative to its benchmark. It compares the average active return generated by a portfolio with the variability of those active returns, commonly measured by tracking error.

Calculation

The information ratio is commonly calculated as:

$Information Ratio = \frac{Average Active Return}{Tracking Error}$

Since active return is the difference between portfolio return and benchmark return:

$Information Ratio = \frac{R_{p} - R_{b}}{σ (R_{p} - R_{b})}$

where:

$R_{p}$ = portfolio return;
$R_{b}$ = benchmark return;
$σ (R_{p} - R_{b})$ = standard deviation of active returns.

When multiple periods are used, the numerator is generally the average active return over the measurement period.

Example

Suppose a portfolio has an average annual active return of 3% and an annualized tracking error of 6%.

$Information Ratio = \frac{3 %}{6 %} = 0.5$

The information ratio is therefore 0.5.

A higher positive information ratio generally indicates that a portfolio generated more active return relative to the variability of that active return.

Interpretation

A positive information ratio indicates that the portfolio generated positive average active return relative to its benchmark.

A negative information ratio indicates that the portfolio underperformed its benchmark on average.

A value close to zero indicates that the portfolio generated relatively little average active return compared with the variability of its active returns.

The information ratio should generally be interpreted in conjunction with the investment strategy, benchmark, measurement period, and calculation methodology.

Information ratio and tracking error

The information ratio combines active return and tracking error.

Active return measures relative performance:

$Active Return = R_{p} - R_{b}$

Tracking error measures the variability of active returns:

$Tracking Error = σ (R_{p} - R_{b})$

The information ratio relates the two:

$Information Ratio = \frac{Average Active Return}{Tracking Error}$

Thus, the information ratio measures active performance relative to the risk taken through deviations from the benchmark.

Active management

The information ratio is commonly used to evaluate actively managed investment portfolios.

An active manager may take positions that differ from the benchmark in an attempt to generate excess returns. The information ratio evaluates the average excess return relative to the variability of those excess returns.

A manager with a higher information ratio has historically generated greater active return for a given level of tracking error, although past performance does not guarantee future results.

Passive management

For passive investment strategies, the information ratio is generally less central because the objective is usually to minimize deviations from the benchmark rather than generate positive active returns.

A passive fund may have a negative active return because of:

management fees;
transaction costs;
taxes;
cash holdings;
portfolio-rebalancing costs;
other implementation costs.

Annualization

When active returns and tracking error are calculated using periodic observations, the information ratio can be annualized using consistent return and risk measures.

For example, if monthly observations are used, annualized tracking error can be approximated as:

$Annualized Tracking Error = Monthly Tracking Error \times \sqrt{12}$

The numerator should be annualized consistently with the denominator.

Information ratio and Sharpe ratio

The information ratio is conceptually related to the Sharpe ratio, but the two measures use different reference points.

The Sharpe ratio measures excess return relative to a risk-free rate:

$Sharpe Ratio = \frac{R_{p} - R_{f}}{σ (R_{p})}$

The information ratio measures excess return relative to a benchmark:

$Information Ratio = \frac{R_{p} - R_{b}}{σ (R_{p} - R_{b})}$

where:

$R_{p}$ = portfolio return;
$R_{b}$ = benchmark return;
$R_{f}$ = risk-free rate;
$σ (R_{p})$ = standard deviation of portfolio returns;
$σ (R_{p} - R_{b})$ = standard deviation of active returns.

Portfolio management

Portfolio managers can use the information ratio to evaluate the efficiency of active investment decisions.

It can be considered alongside:

The information ratio does not by itself establish whether an investment strategy is appropriate or whether its historical performance will continue.

Importance

The information ratio is an important measure of active investment performance because it relates a portfolio's average active return to the variability of that return. It is particularly useful for comparing active portfolios that use the same or comparable benchmarks and for assessing how efficiently portfolio managers have historically converted deviations from a benchmark into active returns.