Measure risk-adjusted return by systematic risk (beta): Treynor = (portfolio return − risk-free rate) ÷ beta.
Input Data
Results
At a glance:The Treynor ratio is the excess return over the risk-free rate divided by beta, measuring reward per unit of systematic risk.
Formula
portfolioReturn = (endValue − beginValue) / beginValue × 100%
treynor = (portfolioReturn − riskFreeRate) / beta
$$$R_p = \\dfrac{\\text{Ending} - \\text{Beginning}}{\\text{Beginning}}$$$$$$Treynor = \\dfrac{R_p - R_f}{\\beta}$$$$$$\\dfrac{10\\% - 1.5\\%}{1.25}=6.8\\%$$$How to Use
- Enter the beginning and ending portfolio values.
- Enter the risk-free rate and beta.
- Review the portfolio return and Treynor ratio.
FAQ
When should I use the Treynor ratio versus the Sharpe ratio?
The Sharpe ratio uses total volatility (standard deviation) in the denominator and suits evaluating a single or not-fully-diversified investment. The Treynor ratio uses beta, counting only systematic risk, and suits evaluating a well-diversified portfolio that has only market risk left. A higher ratio means better return per unit of systematic risk.
What is beta?
Beta measures a portfolio's sensitivity to overall market swings: beta = 1 moves with the market, above 1 is more volatile than the market, below 1 is steadier. It represents the systematic risk that cannot be eliminated by diversification.
Is a higher ratio always better?
With positive returns, a higher ratio generally means more excess return per unit of systematic risk, so usually better. But if the portfolio return is negative, the comparison is less meaningful and should be judged with other metrics.
How should I read beta specifically—what do 1.25, 0.8 and negative beta mean?
Beta measures an asset's or portfolio's 'volatility sensitivity relative to the overall market'—i.e. how much 'systematic risk' (market-driven, undiversifiable risk) it carries—with the market (e.g. the Hang Seng Index, S&P 500) as the benchmark at beta = 1. 'Beta = 1' means it moves in sync with the market: up 10%, it rises about 10%; down 10%, it falls about 10%. 'Beta > 1' (e.g. 1.25) means it is 'more volatile and aggressive than the market': up 10%, it climbs about 12.5%; down 10%, it also drops about 12.5%. High-beta assets gain more in bull markets and fall harder in bears—suited to investors bullish on the outlook who accept bigger swings; tech and cyclical stocks often fall here. 'Beta < 1' (e.g. 0.8) means 'less volatile and more defensive': up 10%, it rises only about 8%; down 10%, it drops only about 8%. Utilities, staples and some high-yield stocks behave this way, suiting investors seeking stability. 'Beta = 0' means no correlation with the market—theoretically cash or certain money-market instruments. 'Beta < 0 (negative)' means it 'moves opposite to the market'—when the market falls it rises; such assets (gold at some times, inverse ETFs, some havens) have 'hedging' value, protecting a portfolio in downturns but are relatively rare. Note beta is estimated from historical data (usually a regression of past stock and market returns) and is 'ex post'; past beta does not guarantee the future. In the Treynor ratio beta is the denominator, measuring 'how much excess return per unit of this market risk'.
Why is the Treynor ratio suited to 'well-diversified' portfolios—what is the link between diversification and systematic risk?
Distinguish two kinds of investment risk: 'systematic risk' and 'unsystematic risk'. Systematic risk (market risk) comes from factors affecting the whole market—interest-rate moves, recessions, policy changes, geopolitics—and 'cannot be eliminated by diversification' because it hits all assets; beta measures exactly this. Unsystematic risk (specific risk) comes from a particular company or industry—management scandals, product failures, sector-specific regulation—and 'can be largely reduced or eliminated by diversification', because when you hold enough, well-spread assets, one company's bad news is diluted by others performing normally. The key point: diversification eliminates unsystematic risk but not systematic risk. A 'well-diversified' portfolio (dozens of stocks across sectors, or an index fund) has its unsystematic risk largely dispersed, leaving 'almost only systematic risk'—so its risk is almost fully described by beta. Then the beta-denominated Treynor ratio fits best, measuring the return efficiency from the only remaining risk. Conversely, an 'under-diversified' portfolio (one or two stocks) still carries large unsystematic risk that beta does not cover; relying on Treynor alone understates true risk, and you should use the Sharpe ratio with 'total standard deviation' (both systematic and unsystematic) as the denominator. In short: high diversification → unsystematic risk gone → risk is mainly beta → use Treynor; low diversification → unsystematic risk remains → risk is total volatility → use Sharpe. This is why fund-manager stock-picking and timing skill is often judged by Treynor (assuming a diversified fund), while individual investments are more often evaluated with Sharpe.
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.