Treynor Ratio
Excess return per unit of systematic (market) risk. Numerator is the same as Sharpe; denominator is beta instead of total volatility.
When to use: Use when comparing well-diversified portfolios (where idiosyncratic risk has been mostly diversified away, leaving only systematic risk). Sharpe is more appropriate for concentrated portfolios; Treynor for diversified ones.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Treynor | Treynor Ratio | Excess return per unit of systematic risk (beta) | integer |
| Rp | Portfolio Return | Periodic mean return of the portfolio as a decimal | % |
| Rf | Risk-Free Rate | Per-period risk-free rate as a decimal (use the same period as the returns) | % |
| Beta | Beta | Portfolio beta against the relevant market | integer |
Real-Life Examples
Example 1: Diversified Equity Fund
Portfolio earns 12% annual return, beta 1.2, risk-free rate 3%.
Given
Step-by-Step
Treynor of 0.075 means the fund earned 7.5 percentage points of excess return per unit of beta — comparable to a fund earning 7.5% on a beta-1 portfolio.
Example 2: Low-Beta Defensive Fund
Returns 8%, beta 0.6, risk-free rate 3%.
Given
Step-by-Step
Treynor of 0.083 — slightly higher than the previous example despite lower absolute return. The defensive fund extracts more excess return per unit of market risk.
Frequently Asked Questions
When the portfolio is well-diversified — most large equity mutual funds, broad index ETFs, or any portfolio where idiosyncratic risk has been diversified to near zero. For undiversified portfolios (single-stock concentrated, narrow sector, etc.) Sharpe is better because it captures total risk, not just market risk.
Negative beta means the portfolio moves opposite the market — rare but possible (e.g. inverse ETFs, gold in some regimes). Treynor remains defined but interpretation flips: a positive excess return with negative beta would be highly attractive (insurance-like).
Closely related. Jensen's alpha = Rp − [Rf + β(Rm − Rf)] — the absolute excess return after CAPM-implied baseline. Treynor is the same idea normalized per unit of beta. Both reward beta-efficient strategies.