How is the information ratio calculated, and what does it reveal about active management skill that the Sharpe ratio misses?

Question

AcadiFi · Accepted Answer

The **information ratio (IR)** measures the active return (excess return over the benchmark) per unit of active risk (tracking error):

**IR = (R_p - R_b) / Tracking Error**

where:
- **R_p - R_b** = active return (portfolio return minus benchmark return)
- **Tracking Error** = standard deviation of active returns = sigma(R_p - R_b)

**Why IR Captures What Sharpe Misses**

The Sharpe ratio measures total excess return (over risk-free) per unit of total risk. It doesn't distinguish between:
- Returns earned passively from benchmark beta exposure
- Returns earned actively from manager decisions (stock selection, sector tilts, timing)

The IR isolates the **active component** — the value added (or destroyed) by manager decisions.

**Worked Example**

Meridian Capital runs an active US equity fund benchmarked to the S&P 500.

| Year | Fund Return | Benchmark Return | Active Return |
|---|---|---|---|
| 2021 | 28.4% | 26.9% | +1.5% |
| 2022 | -16.2% | -19.4% | +3.2% |
| 2023 | 24.8% | 24.2% | +0.6% |
| 2024 | 12.1% | 10.6% | +1.5% |
| 2025 | 18.7% | 17.5% | +1.2% |

**Average active return:** (1.5 + 3.2 + 0.6 + 1.5 + 1.2) / 5 = **1.60%**

**Tracking error (std dev of active returns):** sqrt(variance of {1.5, 3.2, 0.6, 1.5, 1.2}) = **0.93%**

**IR = 1.60% / 0.93% = 1.72**

**Interpretation Benchmarks**

| IR | Assessment |
|---|---|
| < 0.0 | Active management is destroying value |
| 0.0 - 0.25 | Marginal skill — fees likely consume the active return |
| 0.25 - 0.50 | Decent — above-average active manager |
| 0.50 - 0.75 | Very good — consistently adding value |
| > 0.75 | Exceptional (rare over multi-year periods) |
| > 1.0 | Extremely rare — verify data quality |

Meridian's IR of 1.72 is extraordinary and likely benefits from a short sample period. Over 10+ years, IRs above 0.75 are uncommon.

```mermaid
flowchart TD
    A["Information Ratio"] --> B["Numerator: Active return = R_p - R_b"]
    A --> C["Denominator: Tracking error = sigma(R_p - R_b)"]
    B --> D["Measures: How much value is the manager adding?"]
    C --> E["Measures: How consistently are they adding it?"]
    D --> F["IR = Skill per unit of active risk"]
    E --> F
```

**The Fundamental Law of Active Management**

Grinold and Kahn showed that:

**IR ≈ IC x sqrt(BR)**

where:
- **IC** = Information Coefficient (correlation between forecasts and outcomes; ~0.02-0.10 for most managers)
- **BR** = Breadth (number of independent bets per year)

This means a manager can achieve a high IR either through better forecasts (higher IC) or more independent decisions (higher BR) — or both.

**Key Exam Points:**
- IR and Sharpe give different rankings when managers have different benchmark exposures
- IR is the correct metric for evaluating an active manager who will be combined with other investments
- Tracking error can be decomposed into systematic (factor tilts) and idiosyncratic (stock selection) components

For more on active management, check our CFA Level III materials.

How is the information ratio calculated, and what does it reveal about active management skill that the Sharpe ratio misses?

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