Treynor Ratio

The Treynor ratio (reward-to-volatility ratio) measures how much excess return a portfolio generates per unit of systematic risk. It adjusts returns for market-related risk (beta), helping investors compare risk-adjusted performance across portfolios exposed to market movements.

Formula

Treynor Ratio = (rp − rf) / βp

where:
rp = portfolio return
 rf = risk-free rate (commonly proxied by Treasury bills)
* βp = portfolio beta (sensitivity to market returns)

The result expresses excess return per unit of market risk.

What it shows

  • A higher Treynor ratio indicates better compensation for market (systematic) risk and is generally more desirable.
  • The ratio focuses only on systematic risk (beta). It assumes diversification has removed idiosyncratic risk.
  • If a portfolio has a negative beta, the Treynor ratio is not meaningful for standard interpretation.

How it works

The Treynor ratio uses beta—how much a portfolio’s returns move with the market—to scale excess return (return above a risk-free asset). It reflects whether an investor was adequately compensated for exposure to market risk. Because it depends on historical returns and beta estimates, it is backward-looking and not a guaranteed predictor of future performance.

Comparison with the Sharpe ratio

  • Treynor: adjusts returns using beta (systematic risk). Best for well-diversified portfolios where idiosyncratic risk is negligible.
  • Sharpe: adjusts returns using standard deviation (total risk). Useful when both systematic and unsystematic risks matter.

Limitations and practical considerations

  • Backward-looking: past beta and returns may not predict future behavior.
  • Benchmark selection matters: beta should be calculated against an appropriate market index for the asset class (e.g., a large-cap fund should use a large-cap benchmark).
  • No absolute scale: a higher Treynor is better when comparing similar investments, but there’s no universal threshold for “good.”
  • Best used alongside other metrics (Sharpe, alpha, drawdown, qualitative factors) rather than alone.

Quick example

Portfolio return = 12% (0.12)
Risk-free rate = 2% (0.02)
Portfolio beta = 1.2

Treynor = (0.12 − 0.02) / 1.2 = 0.0833 → 8.33% excess return per unit of beta

Origin and use

Developed by Jack Treynor, one of the contributors to the Capital Asset Pricing Model (CAPM), the Treynor ratio is a practical tool for evaluating how well a portfolio compensates investors for exposure to market risk. Use it to compare similarly benchmarked, diversified portfolios and as one component of a broader performance analysis.