18.2 The Information Ratio & Selecting the Right Risk-Adjusted Metric
Key Takeaways
- The information ratio divides annualized active return by tracking error, the standard deviation of active return.
- Tracking error near zero makes the information ratio unstable and effectively meaningless for a closet indexer.
- The correct metric depends on the question: total risk for a whole portfolio, beta for a component, tracking error for benchmark-relative skill.
- No single risk-adjusted measure is universally superior; each embeds a different definition of risk.
Last updated: August 2026
18.2 The Information Ratio & Selecting the Right Risk-Adjusted Metric
1. Benchmark-Relative Active Measures: Information Ratio (IR)
When evaluating active managers hired to outperform a specific assigned benchmark (e.g., a Russell 2000 Value manager against the Russell 2000 Value Index), traditional CAPM metrics may fail if the manager's mandate deviates from broad market beta. The Information Ratio (IR) evaluates active return per unit of active risk (tracking error).
Mathematical Formulation
Where:
- $\overline{R_p - R_b}$ = Mean active return (arithmetic excess return over benchmark $R_b$)
- $\text{Tracking Error (TE)} = \sigma_{(R_p - R_b)} = \sqrt{\frac{1}{T-1} \sum_{t=1}^{T} \left( (R_{p,t} - R_{b,t}) - \overline{R_p - R_b} \right)^2}$ = Annualized standard deviation of excess returns
The Information Ratio Architecture
Active Return (Rp - Rb) ──► Value added from stock/sector bets
───────────────────────── = Information Ratio (IR)
Tracking Error (TE) ──► Volatility of excess returns (Active Risk)
IR Tier Manager Quality Assessment
─────── ──────────────────────────
< 0.00 Destructive / Underperforming Benchmark
0.00 – 0.49 Mediocre / Inconsistent Value Added
0.50 – 0.74 Good / Strong Institutional Manager
0.75 – 0.99 Very Good / Top-Decile Performance
≥ 1.00 Exceptional / Rare Elite Skill
The Fundamental Law of Active Management (Grinold & Kahn)
Richard Grinold and Ronald Kahn established that a manager's Information Ratio is driven by two independent components: forecasting skill and breadth of independent investment decisions:
Where:
- Information Coefficient (IC): Correlation between manager forecasts and actual realized returns (measures depth of skill, typically $0.03$ to $0.08$).
- Breadth (BR): Number of independent investment decisions made per year.
2. Comprehensive Comparison & Metric Selection Framework
Comparative Matrix: Risk-Adjusted Metrics
| Metric | Risk Measure | Benchmark | Best Utilized When... | Key Formula |
|---|---|---|---|---|
| Sharpe Ratio | Total Risk ($\sigma$) | Cash ($R_f$) | Evaluating entire wealth, standalone portfolios, or undiversified assets | $S_p = \frac{R_p - R_f}{\sigma_p}$ |
| $M^2$ Measure | Total Risk ($\sigma$) | Market Volatility ($\sigma_m$) | Presenting total risk-adjusted results in clear percentage terms to clients | $M^2 = R_f + S_p \cdot \sigma_m$ |
| Treynor Ratio | Systematic Risk ($\beta$) | Cash ($R_f$) & Market ($M$) | Evaluating a manager being added as a sub-allocation to a diversified master fund | $T_p = \frac{R_p - R_f}{\beta_p}$ |
| Jensen's Alpha | Systematic Risk ($\beta$) | CAPM Required Return | Measuring absolute excess alpha percentage and statistical significance | $\alpha_p = R_p - [R_f + \beta_p(R_m - R_f)]$ |
| Information Ratio | Active Risk ($\text{TE}$) | Specific Assigned Benchmark ($R_b$) | Evaluating active manager skill against a mandate-specific benchmark | $\text{IR} = \frac{R_p - R_b}{\text{TE}}$ |
Institutional Metric Selection Decision Tree
Institutional Metric Selection Decision Tree
│
What is the role of the portfolio being evaluated?
│
┌───────────────────────────────────┼───────────────────────────────────┐
▼ ▼ ▼
[ Entire Client Wealth / ] [ Sub-Allocation in a ] [ Active Manager Hired ]
[ Standalone Portfolio ] [ Diversified Portfolio] [ vs. Specific Mandate ]
│ │ │
Does uncompensated unique Idiosyncratic risk is Evaluated against assigned
risk matter? YES. diversified away. style benchmark (Rb).
│ │ │
┌─────┴─────┐ ┌─────┴─────┐ ▼
▼ ▼ ▼ ▼ [ INFORMATION RATIO ]
[ SHARPE ] [ M² ] [ TREYNOR ] [ JENSEN'S α ] IR = (Rp - Rb) / TE
Ratio: Return in % Slope in Alpha in %
Sp = M² = Rf + Tp = α = Rp - CAPM
(Rp-Rf)/σp Sp · σm (Rp-Rf)/βp (Verify t-stat)
Worked Example: Multi-Manager Institutional Evaluation
An endowment consultant reviews three candidate large-cap equity managers. Current market data: $R_f = 2.0%$, $R_m = 10.0%$, $\sigma_m = 15.0%$.
| Manager | Realized Return ($R_p$) | Total Volatility ($\sigma_p$) | Market Beta ($\beta_p$) | Benchmark Return ($R_b$) | Tracking Error ($\text{TE}$) | Correlation ($\rho_{pm}$) |
|---|---|---|---|---|---|---|
| Manager A | 13.0% | 18.0% | 1.10 | 10.0% | 4.0% | 0.92 |
| Manager B | 11.5% | 14.0% | 0.85 | 10.0% | 3.0% | 0.91 |
| Manager C | 15.0% | 25.0% | 1.20 | 10.0% | 7.5% | 0.72 |
-
Sharpe Ratios:
- $S_A = (13.0 - 2.0) / 18.0 = 11.0 / 18.0 = \mathbf{0.611}$
- $S_B = (11.5 - 2.0) / 14.0 = 9.5 / 14.0 = \mathbf{0.679}$
- $S_C = (15.0 - 2.0) / 25.0 = 13.0 / 25.0 = \mathbf{0.520}$
- Standalone Ranking (Total Risk): Manager B > Manager A > Manager C
-
Treynor Ratios:
- $T_A = (13.0 - 2.0) / 1.10 = 11.0 / 1.10 = \mathbf{10.00%}$
- $T_B = (11.5 - 2.0) / 0.85 = 9.5 / 0.85 = \mathbf{11.18%}$
- $T_C = (15.0 - 2.0) / 1.20 = 13.0 / 1.20 = \mathbf{10.83%}$
- Sub-Allocation Ranking (Systematic Risk): Manager B > Manager C > Manager A
- Insight: Manager C ranks 2nd under Treynor because Treynor ignores its high idiosyncratic risk, but ranks lowest under Sharpe because its total volatility is 25% due to poor diversification ($\rho = 0.72$).
-
Jensen's Alphas:
- $\alpha_A = 13.0 - [2.0 + 1.10(10.0 - 2.0)] = 13.0 - 10.8 = \mathbf{+2.20%}$
- $\alpha_B = 11.5 - [2.0 + 0.85(10.0 - 2.0)] = 11.5 - 8.8 = \mathbf{+2.70%}$
- $\alpha_C = 15.0 - [2.0 + 1.20(10.0 - 2.0)] = 15.0 - 11.6 = \mathbf{+3.40%}$
-
Information Ratios:
- $\text{IR}_A = (13.0 - 10.0) / 4.0 = 3.0 / 4.0 = \mathbf{0.750}$ (Very Good)
- $\text{IR}_B = (11.5 - 10.0) / 3.0 = 1.5 / 3.0 = \mathbf{0.500}$ (Good)
- $\text{IR}_C = (15.0 - 10.0) / 7.5 = 5.0 / 7.5 = \mathbf{0.667}$ (Good)
- Benchmark Mandate Ranking: Manager A > Manager C > Manager B
Test Your Knowledge
An institutional pension plan hires an active global equity manager who generates an annualized return of 13.5% against the assigned MSCI World benchmark return of 11.0%. Over the 5-year evaluation period, the annualized standard deviation of excess returns (tracking error) was 3.125%. In accordance with Grinold and Kahn's Fundamental Law of Active Management, how should the plan sponsor evaluate this manager's Information Ratio?
A
B
C
D