Information Ratio

A performance metric that evaluates active return per unit of risk relative to a benchmark index

Overview

Information Ratio (IR) is a key performance metric used to evaluate the skill of active portfolio managers or investment strategies. It measures how much excess return (active return) a portfolio manager generates relative to a benchmark, per unit of additional risk (tracking error) taken.

The Information Ratio provides insight into a manager's ability to generate consistent outperformance through active decisions, while accounting for the additional risk assumed in deviating from the benchmark. This makes it particularly valuable for institutional investors and asset allocators evaluating active management capabilities.

Unlike the Sharpe ratio, which measures excess return over the risk-free rate per unit of total risk, the Information Ratio focuses specifically on active management decisions by measuring excess return over a benchmark per unit of active risk. This distinction is crucial for isolating and evaluating the true value added by active management.

Intuitive Explanation

Imagine you've hired two different guides to take you through a forest. Both guides deviate from the main trail (the benchmark) in search of better views or shortcuts:

Guide A takes you on paths that frequently offer slightly better views than the main trail, with minimal additional hiking difficulty.

Guide B takes you on paths that occasionally offer spectacular views, but also involve significant additional climbing and rough terrain.

The Information Ratio helps determine which guide provides better value. Guide A might have a higher Information Ratio because they consistently deliver modest improvements with minimal extra effort. Guide B might provide occasional amazing experiences but with inconsistent results and much more exertion.

Financial analogy: In investing terms, the Information Ratio rewards consistent, reliable outperformance over a benchmark relative to the additional risk taken. A high Information Ratio indicates a manager who efficiently converts active risk (deviations from the benchmark) into active return (outperformance), demonstrating skill rather than luck.

Detailed Mathematical Explanation

The Information Ratio quantifies the relationship between the active return of a portfolio and the active risk taken to achieve that return.

Core Formula

The Information Ratio is defined as:

Information Ratio Formula

IR = \frac{\text{Active Return}}{\text{Active Risk}} = \frac{R_p - R_b}{\sigma_{p-b}}

where Active Return is the portfolio return minus the benchmark return, and Active Risk (tracking error) is the standard deviation of the active return.

Formal Definition

More precisely, the Information Ratio is calculated as:

IR = \frac{R_p - R_b}{\sqrt{\frac{1}{T}\sum_{t=1}^{T}[(R_{p,t} - R_{b,t}) - (R_p - R_b)]^2}}

Where:

$R_p$ is the average return of the portfolio
$R_b$ is the average return of the benchmark
$R_{p,t}$ is the return of the portfolio at time t
$R_{b,t}$ is the return of the benchmark at time t
$\sigma_{p-b}$ is the tracking error (standard deviation of the difference between portfolio and benchmark returns)
$T$ is the number of observation periods

Alternative Formulation

The Information Ratio can also be expressed in terms of active returns:

Information Ratio using Active Returns

IR = \frac{\alpha}{\sigma_{\alpha}}

where $\alpha$ represents the active return and $\sigma_{\alpha}$ is the standard deviation of active returns (tracking error).

Relationship to Other Metrics

The Information Ratio relates to other performance metrics as follows:

Sharpe Ratio: $\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}$ uses risk-free rate as benchmark and total volatility as risk measure
Information Ratio: $\text{Information Ratio} = \frac{R_p - R_b}{\sigma_{p-b}}$ uses market index as benchmark and tracking error as risk measure

The key difference is that the Information Ratio focuses specifically on active management decisions relative to a benchmark, while the Sharpe ratio measures total risk-adjusted performance regardless of benchmark.

Implementation in Portfolio Analysis

Our implementation of the Information Ratio involves the following steps:

Define the Benchmark: We select an appropriate benchmark that represents the investment universe and risk exposures relevant to the portfolio. Common choices include:
- Broad market indices (e.g., S&P 500, Russell 3000)
- Style-specific indices (e.g., Russell 1000 Growth, MSCI Value)
- Custom composite benchmarks to match portfolio allocation
Calculate Active Returns: We compute the difference between portfolio returns and benchmark returns for each period.
Determine Tracking Error: We calculate the standard deviation of these active returns over the measurement period.
Compute the Ratio: We divide the average active return by the tracking error.

In portfolio evaluation, we use the Information Ratio to:

Assess Manager Skill: Identifying fund managers with consistent outperformance per unit of active risk.
Portfolio Construction: Allocating more capital to strategies with higher Information Ratios.
Risk Budgeting: Determining how much active risk to take in different parts of a portfolio based on expected Information Ratios.

Worked Example

Let's calculate and compare the Information Ratio for two hypothetical fund managers relative to their benchmark.

Step 1: Historical Returns Data

Suppose we have the following quarterly returns for two active managers and their benchmark over a 3-year period (12 quarters):

Benchmark: 2.1%, -1.5%, 3.0%, 1.8%, 2.5%, -2.0%, 4.1%, 0.9%, 3.2%, -1.1%, 2.7%, 1.6%

Manager A: 2.5%, -1.2%, 3.8%, 1.5%, 3.2%, -1.6%, 4.7%, 1.5%, 3.0%, -1.5%, 3.5%, 2.0%

Manager B: 3.1%, -2.5%, 5.0%, 0.5%, 3.5%, -1.0%, 6.1%, -0.5%, 5.2%, -3.0%, 4.2%, 3.0%

Step 2: Calculate Active Returns

First, we calculate the active returns (portfolio return minus benchmark return) for each quarter:

Manager A Active Returns

0.4%, 0.3%, 0.8%, -0.3%, 0.7%, 0.4%, 0.6%, 0.6%, -0.2%, -0.4%, 0.8%, 0.4%

Manager B Active Returns

1.0%, -1.0%, 2.0%, -1.3%, 1.0%, 1.0%, 2.0%, -1.4%, 2.0%, -1.9%, 1.5%, 1.4%

Step 3: Calculate Average Active Return and Tracking Error

Now we calculate the mean active return and the standard deviation of active returns (tracking error):

For Manager A:

Average Active Return = (0.4 + 0.3 + 0.8 + ... + 0.4) / 12 = 3.7 / 12 = 0.31%

Tracking Error = Standard Deviation of Active Returns = 0.43%

For Manager B:

Average Active Return = (1.0 + (-1.0) + 2.0 + ... + 1.4) / 12 = 6.3 / 12 = 0.53%

Tracking Error = Standard Deviation of Active Returns = 1.44%

Step 4: Calculate Information Ratio

Using our formula IR = Average Active Return / Tracking Error:

Manager A: IR = 0.31% / 0.43% = 0.72

Manager B: IR = 0.53% / 1.44% = 0.37

Step 5: Interpretation

While Manager B generated a higher average active return (0.53% vs. 0.31%), Manager A has a much higher Information Ratio (0.72 vs. 0.37). This indicates that Manager A is more skilled at generating consistent outperformance per unit of risk taken.

Manager A's returns show lower but more consistent outperformance with less tracking error, while Manager B takes larger active bets with higher volatility in results. For risk-conscious investors seeking reliable alpha, Manager A would be the preferred choice despite the lower absolute outperformance.

This example illustrates how the Information Ratio helps investors distinguish between managers based on skill (consistent outperformance) rather than just raw returns or willingness to deviate dramatically from the benchmark.

Practical Applications

Manager Selection

The Information Ratio is extensively used in the institutional investment community for evaluating and selecting active managers. Higher Information Ratios indicate managers who more efficiently convert active risk into active return, suggesting greater skill rather than luck or excessive risk-taking.

Performance Evaluation

By focusing on risk-adjusted active returns, the Information Ratio provides a more comprehensive assessment of manager performance than simple outperformance metrics. It helps distinguish between managers who achieve outperformance through skill versus those who rely on taking outsized risks.

Portfolio Construction

In a multi-manager portfolio, capital can be allocated to different strategies based on their historical Information Ratios, with more capital assigned to managers with higher ratios. This approach optimizes the overall portfolio's active risk-return profile.

Risk Budgeting

Investment committees use the Information Ratio to allocate active risk budgets across different portfolio segments. Areas with historically higher Information Ratios may be granted larger risk budgets, as they have demonstrated better conversion of risk into return.

Fee Evaluation

The Information Ratio helps investors assess whether the higher fees charged by active managers are justified by their skill in generating risk-adjusted outperformance. Managers with consistently high Information Ratios may warrant higher fees than those with lower ratios.

Advantages and Limitations

Advantages

Focus on Active Management: Directly measures the value added by active decisions, isolating manager skill from market movements.
Risk Adjustment: Accounts for the additional risk taken to achieve outperformance, not just the magnitude of returns.
Consistency Evaluation: Rewards consistent outperformance over sporadic high returns, aligning with institutional investors' preference for reliability.
Comparability: Provides a standardized way to compare managers across different strategies and market environments.

Limitations

Benchmark Sensitivity: Results are highly dependent on the choice of benchmark, which may not always perfectly represent the investment universe.
Assumes Normal Distribution: Like many traditional risk metrics, the Information Ratio implicitly assumes that returns are normally distributed, which may not hold true in practice.
Time Period Dependency: Information Ratios can vary significantly across different time periods, making it important to evaluate over multiple market cycles.
Ignores Higher Moments: Doesn't account for skewness or kurtosis in return distributions, which can be important risk factors.
No Absolute Risk Consideration: Focuses solely on relative risk (tracking error) rather than absolute risk, potentially overlooking total portfolio risk exposure.

References

Goodwin, T. H. (1998). "The Information Ratio." Financial Analysts Journal, 54(4), 34-43.
Grinold, R. C., & Kahn, R. N. (2000). "Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk." McGraw-Hill.
Gupta, F., Prajogi, R., & Stubbs, E. (1999). "The Information Ratio and Performance." Journal of Portfolio Management, 26(1), 33-39.
Sharpe, W. F. (1994). "The Sharpe Ratio." Journal of Portfolio Management, 21(1), 49-58.
Amenc, N., & Le Sourd, V. (2003). "Portfolio Theory and Performance Analysis." Wiley Finance.
Treynor, J. L., & Black, F. (1973). "How to Use Security Analysis to Improve Portfolio Selection." Journal of Business, 46(1), 66-86.

Related Metrics

Sharpe Ratio

The classic risk‐adjusted return metric that divides excess portfolio return by total volatility.

Treynor Ratio

A portfolio performance metric that measures returns earned in excess of the risk-free rate per unit of market risk (beta).

Modigliani Risk-Adjusted Performance (M²)

A measure that adjusts portfolio returns to match market volatility, allowing direct comparison with benchmark returns.