Treynor Ratio Calculator

What Is the Treynor Ratio?

The Treynor Ratio, also known as the reward-to-volatility ratio, measures how much excess return a portfolio generated for each unit of systematic risk it took. Unlike the Sharpe Ratio, which penalizes total volatility (including diversifiable risk), the Treynor Ratio only considers market risk—the risk that cannot be eliminated through diversification.

A higher Treynor Ratio indicates a portfolio has delivered better risk-adjusted performance relative to the market. This metric is particularly useful for evaluating well-diversified portfolios where unsystematic risk has been largely eliminated.

How the Treynor Ratio Is Calculated

The formula subtracts the risk-free rate from the portfolio return, then divides the result by the portfolio's beta:

Treynor Ratio = (Portfolio Return − Risk-Free Rate) ÷ Beta

Each component plays a specific role:

• Portfolio Return — the actual return achieved over the measurement period.
• Risk-Free Rate — the return of a theoretically risk-free asset, typically a short-term government bond yield (e.g., U.S. Treasury bill).
• Beta — a measure of the portfolio's sensitivity to overall market movements. A beta of 1.0 means the portfolio moves in line with the market.

The result is expressed as a ratio. A positive value means the portfolio earned more than the risk-free rate per unit of market risk. A negative value indicates underperformance relative to the risk-free rate.

How to Use This Calculator

Enter three values to compute the Treynor Ratio:

1. Portfolio Return (%) — the total return of your portfolio over the period you are evaluating.
2. Risk-Free Rate (%) — the current yield on a risk-free benchmark, such as a 3-month Treasury bill.
3. Portfolio Beta — the beta coefficient of your portfolio, typically calculated against a broad market index like the S&P 500.

The calculator will return the Treynor Ratio, which you can use to compare the risk-adjusted performance of different portfolios or against a benchmark.

Interpreting the Result

The Treynor Ratio is most meaningful when used for comparison:

• Higher ratio — the portfolio generated more excess return per unit of market risk. This suggests efficient risk-taking.
• Lower or negative ratio — the portfolio did not adequately compensate for the market risk taken. A negative ratio means the portfolio underperformed the risk-free rate.
• Comparison across portfolios — when evaluating multiple portfolios with similar investment mandates, the one with the highest Treynor Ratio is generally considered the best risk-adjusted performer.

Because the Treynor Ratio only accounts for systematic risk, it is most appropriate for evaluating portfolios that are already well-diversified. For concentrated portfolios, the Sharpe Ratio may provide a more complete picture.

Practical Use Cases

The Treynor Ratio is commonly applied in several scenarios:

• Portfolio manager evaluation — assess whether a manager's returns justify the market risk taken.
• Fund comparison — compare mutual funds or ETFs that operate within the same asset class or benchmark.
• Asset allocation decisions — determine which portfolio mix offers the best return per unit of market exposure.
• Performance attribution — separate the effects of market timing from security selection.

Limitations to Consider

The Treynor Ratio has several constraints worth noting:

• Relies on beta accuracy — beta is a historical measure and may not accurately reflect future market sensitivity.
• Ignores unsystematic risk — for portfolios that are not fully diversified, the ratio may overstate risk-adjusted performance.
• Assumes a single risk-free rate — in practice, the appropriate risk-free rate may vary by investor and time horizon.
• Not suitable for negative beta portfolios — the ratio becomes difficult to interpret when beta is negative or near zero.
• Historical bias — past returns and beta do not guarantee future performance.