INFORMATION RATIO

Definition

The Information Ratio (IR) is a risk-adjusted performance metric that measures the excess return of an investment or portfolio relative to a benchmark, divided by the tracking error (the standard deviation of excess returns).

It evaluates the consistency and efficiency of active management—how much excess return a manager generates per unit of active risk taken.

• Higher IR → better active management skill.
• IR close to zero or negative → little to no value added vs. benchmark.

Origins

The term "Information Ratio" evolved from the concept of an "information coefficient" and gained widespread use in institutional asset management during the 1990s. Its development was a natural progression from other risk-adjusted metrics like the Sharpe Ratio, as investors sought a more direct way to evaluate a manager's performance relative to a specific benchmark.

Usage

• Portfolio Management – Compare active fund managers vs. benchmarks.

• Institutional Investing – Assess skill in pension and endowment management.

• Risk Attribution – Separate value added from systematic vs. unsystematic risk.

• Performance-Based Fees – Used in hedge fund evaluations.
  
  

How Information Ratio Works

1. Excess return = Portfolio return – Benchmark return.

2. Tracking error = Standard deviation of excess returns.

3. Divide excess return by tracking error.

4. Interpretation: Higher IR → manager consistently beats the benchmark with controlled risk.
   
   

Key Takeaway

• Measures active return per unit of active risk.

• Complements Sharpe Ratio (which uses risk-free rate, not benchmark).

• A common benchmark: IR > 0.5 = good, IR > 1 = excellent.

• Widely used by institutional investors and consultants.

Context in Financial Modeling

• Manager Selection – Rank investment funds relative to benchmarks.

• Portfolio Optimization – Allocate capital to maximize IR.

• Risk Budgeting – Allocate “active risk” across strategies.

• Factor Investing – Evaluate alpha generation after controlling for factor exposures.
  
  

Types of Information Ratio

1. Ex-Post IR – Based on historical returns and volatility.

2. Ex-Ante IR – Forecasted IR using expected returns and risks.

3. Appraisal Ratio – Variant using Jensen’s Alpha instead of raw excess return.
   
   

Nuances & Complexities

• Benchmark choice matters – Poorly chosen benchmarks distort IR.

• Short track records – Low statistical reliability.

• Non-normal returns – IR assumes symmetric distributions.

• Skill vs. luck – High IR over short time frames may not persist.
  
  

Mathematical Formulas

$$IR = \frac{R_p - R_b}{\sigma_{(R_p - R_b)}}$$

Where:

• $R_p$ = Portfolio return

• $R_b$ = Benchmark return

• $\sigma_{(R_p - R_b)}$ = Tracking error (std. deviation of excess return)

$$\text{Credit Spread} = Y_{\text{corporate bond}} - Y_{\text{risk-free bond}}$$

Related Terms

• Sharpe Ratio

• Alpha (α)

• Tracking Error

• Treynor Ratio

• Active Risk

• Benchmarking
  
  

Real-World Applications

Mutual Fund Manager

Portfolio = 10% annual return, Benchmark = 8%, Tracking error = 4% →

$$IR = \frac{10\% - 8\%}{4\%} = 0.50 \quad (\text{good})$$

Hedge Fund Strategy

Portfolio = 12% return, Benchmark = 7%, Tracking error = 3% →

$$IR = \frac{12\% - 7\%}{3\%} = 1.67 \quad (\text{excellent})$$

References & Sources

• Super Money: Information Ratio (IR)