Treynor Ratio Calculator
From the annualised return, the risk-free rate and beta, compute the excess return per unit of systematic (market) risk.
Input Data
Results
At a glance:The Treynor ratio measures return per unit of systematic risk. Treynor = (return − risk-free rate) ÷ beta. Beta is the portfolio's market sensitivity; the ratio uses market risk, not total volatility, so it fits diversified portfolios. A higher Treynor is better.
Formula
Treynor ratio = (return − risk-free rate) ÷ beta.
How to Use
- Enter the annualised return and the risk-free rate.
- Enter the beta.
- Read the Treynor ratio and the rating reference.
FAQ
What is the difference between Treynor and Sharpe?
The Sharpe ratio's denominator is total risk (including unsystematic risk), while Treynor uses only systematic risk (beta). For a well-diversified portfolio, Treynor is more apt; for a single stock (large unsystematic risk), Sharpe is safer.
What if beta is 0 or negative?
Beta = 0 makes the denominator zero and is not applicable; beta < 0 means the asset moves opposite to the market, so Treynor turns negative and must be read with care (a characteristic of hedging assets).
How high a Treynor is good?
There is no absolute standard; it should be compared with the market or other portfolios. Among similar portfolios, the higher it is, the better the use of systematic risk.
What is its relationship with Alpha?
Alpha is the absolute excess return (%), while Treynor is the excess return per unit of systematic risk (%/β). Both come from CAPM and are complementary in showing the 'amount' and the 'efficiency' of return.
Why emphasise a diversified portfolio?
Treynor assumes unsystematic risk is already removed by diversification, leaving only systematic risk (β). If the portfolio is not diversified, the Sharpe ratio using total risk is more honest.
What does a negative Treynor mean?
When the return is below the risk-free rate and β > 0, you bear systematic risk yet underperform the safest option. Unless for a specific hedging purpose, it is not worth holding.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.