Calculate the Treynor ratio from portfolio return, risk-free rate, and beta to measure systematic-risk-adjusted performance.
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Portfolio Analysis
The Treynor ratio measures excess return per unit of systematic (market) risk, using beta as the risk denominator. It is ideal for evaluating well-diversified portfolios where unsystematic risk has been eliminated.
Unlike the Sharpe ratio, which penalises all volatility, the Treynor ratio only considers systematic risk (beta). This makes it the appropriate performance metric for portfolios that are part of a larger diversified allocation, where idiosyncratic risk is irrelevant.
Higher Treynor ratios indicate better compensation per unit of market risk taken. A negative Treynor ratio means the portfolio underperformed the risk-free rate.
Simple ratio of excess return to beta.
Treynor Ratio = (Rp − Rf) / β
Rp = portfolio return, Rf = risk-free rate, β = portfolio beta (sensitivity to market movements).
Portfolio return 12%, risk-free rate 4.5%, beta 1.2. Excess return = 7.5%. Treynor = 7.5 / 1.2 = 6.25.
Only meaningful for diversified portfolios where beta captures the relevant risk. Relies on accurate beta estimation, which varies with the chosen benchmark and lookback period. Does not penalise concentration or liquidity risk.
Frequently asked questions
Use Treynor when the portfolio is well-diversified (unsystematic risk is negligible) and you want to evaluate compensation for market risk only. Use Sharpe when the portfolio is standalone and total volatility matters.
There is no universal threshold. Compare against a benchmark’s Treynor ratio and peer portfolios. A portfolio with a higher Treynor than the market is outperforming on a risk-adjusted basis.
Yes. A negative Treynor means the portfolio returned less than the risk-free rate (negative excess return) or has negative beta, which is rare for long-only equity portfolios.
Use the portfolio’s beta relative to an appropriate benchmark (e.g. S&P 500 for US equities). Beta should be estimated over a period consistent with your evaluation horizon, typically 3–5 years of monthly returns.
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