What is the Treynor ratio, and when should you use it instead of the Sharpe ratio?

Question

AcadiFi · Accepted Answer

The **Treynor ratio** measures excess return per unit of **systematic (market) risk**, using beta as the risk denominator:

**Treynor Ratio = (R_p - R_f) / Beta_p**

Unlike the Sharpe ratio, which uses total risk (standard deviation), the Treynor ratio assumes the investor holds a **well-diversified portfolio** where unsystematic risk has been eliminated.

**When to Use Treynor vs. Sharpe**

| Situation | Preferred Metric | Reasoning |
|---|---|---|
| Evaluating a standalone investment | **Sharpe** | Total risk matters when the investment IS the portfolio |
| Evaluating a fund within a diversified portfolio | **Treynor** | Only systematic risk matters; unsystematic risk is diversified away |
| Comparing funds with different diversification levels | **Treynor** | Avoids penalizing concentrated funds that will be blended |
| Non-normal returns | Neither is ideal | Consider Sortino, Omega, or conditional measures |

**Worked Example**

Three funds evaluated over 5 years (risk-free rate = 4.0%):

| Fund | Return | Std Dev | Beta | Sharpe | Treynor |
|---|---|---|---|---|---|
| Pemberton Growth | 12.5% | 18.0% | 1.15 | 0.472 | 7.39% |
| Ashworth Value | 10.8% | 12.5% | 0.85 | 0.544 | 8.00% |
| Kingsley Balanced | 9.2% | 9.0% | 0.70 | 0.578 | 7.43% |

**Sharpe ranking:** Kingsley > Ashworth > Pemberton
**Treynor ranking:** Ashworth > Kingsley > Pemberton

```mermaid
flowchart TD
    A["Which metric?"] --> B{"Is the fund the entire portfolio?"}
    B -->|Yes| C["Use Sharpe ratio: total risk matters"]
    B -->|No: part of diversified allocation| D["Use Treynor ratio: only systematic risk matters"]
    D --> E["Ashworth best: highest excess return per unit of beta"]
    C --> F["Kingsley best: highest excess return per unit of total risk"]
```

**Interpretation**

A Treynor ratio of 8.00% for Ashworth means: for every unit of beta exposure, Ashworth generates 8.00% of excess return. If the market's excess return is 6.5% (market beta = 1.0, so market Treynor = 6.5%), Ashworth is adding 1.50% of value per unit of systematic risk.

**Numerical Pitfalls:**
- Treynor is undefined for beta = 0 (market-neutral funds)
- Like Sharpe, it gives perverse rankings when excess returns are negative
- Beta must be estimated accurately — an unstable beta estimate produces a misleading Treynor ratio
- Does not account for beta timing (changing beta strategically)

**Relationship to the Security Market Line (SML):**

Funds plotting **above** the SML have positive alpha and high Treynor ratios. The Treynor ratio is essentially the slope from the risk-free rate to the fund's point in (beta, return) space. A higher slope means better risk-adjusted performance relative to systematic risk.

For more on performance metrics, explore our CFA Level III materials.

What is the Treynor ratio, and when should you use it instead of the Sharpe ratio?

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