Treynor Ratio Calculator

The Treynor Ratio Calculator measures how much extra return a portfolio earns per unit of systematic risk. Developed by Jack Treynor in 1965, the ratio divides the portfolio's excess return (return minus risk-free rate) by its beta — the slope of the portfolio's returns regressed against a market benchmark. Unlike the Sharpe ratio, which divides by total volatility, the Treynor ratio focuses only on market-driven risk and is therefore the right yardstick when the portfolio sits inside a larger diversified pool. This calculator supports three input paths — direct values, paired periodic return series, or side-by-side comparison of up to five portfolios — and reports the Treynor decimal, Treynor in percentage points per unit of beta, the Sharpe ratio for context, CAPM required return, Jensen alpha, and an asset-class benchmark lane.

How to Use

1. Pick an input mode: Direct inputs when you already have R_p, R_f, and β; From returns series when you only have periodic returns; Compare portfolios to rank up to five at a time.
2. Fill in the highlighted fields. In compare mode, leave entire rows blank to skip them.
3. Optionally add the portfolio standard deviation to unlock the Sharpe-vs-Treynor twin panel.
4. Optionally add the expected market return to unlock CAPM required return and Jensen alpha.
5. Read the gauge, the classification, the excess-return decomposition, and the step-by-step breakdown.

Treynor Ratio Formula

Treynor vs Sharpe — Which Should You Use?

	Treynor	Sharpe
Risk in denominator	Systematic only (β)	Total risk (σ)
Best for	Diversified portfolios inside a larger pool	Standalone or concentrated portfolios
Diversifies away	Idiosyncratic risk before scoring	Nothing — penalises all volatility
Comparable across	Sub-portfolios of one large mandate	Funds with very different mandates
Fails when	β ≈ 0 (denominator vanishes)	σ ≈ 0 (very stable cash-like asset)

How to Read the Number

• T > equity risk premium (~0.06) — the portfolio earned more per unit of beta than the broad market would have predicted. Jensen alpha is positive.
• T ≈ equity risk premium — fair compensation for the systematic risk taken; no measurable manager skill.
• 0 < T < equity risk premium — beat cash but underperformed the market on a beta-adjusted basis. Jensen alpha is negative.
• T < 0 — failed to beat the risk-free rate. The portfolio took systematic risk for no premium.
• β < 0 — the portfolio is an inverse hedge. A negative Treynor here can actually be good news (the hedge worked); read it together with Sharpe and alpha.

What Makes This Treynor Calculator Different

• Three input modes — direct, paired returns series (β auto-derived), or multi-portfolio comparison. Most calculators only support direct mode.
• Twin gauge: Treynor and Sharpe side-by-side when you supply σ. Diagnose whether your portfolio is concentrated or diversified at a glance.
• CAPM excess-return decomposition bar splits the realised return into R_f, β × ERP, and Jensen alpha so you can see where the performance came from.
• Multi-portfolio ranking with animated bars and a gold winner highlight — useful for picking between funds with different betas.
• Asset-class benchmark lane — long-run typical Treynor values for cash, bonds, balanced, equity, and active funds with your computed position pinned across each lane.
• Sample vs population denominator toggle in series mode, matching CFA and industry conventions.
• Step-by-step breakdown with formulas in LaTeX so you can verify every number by hand or in a spreadsheet.

When the Treynor Ratio Can Mislead

• Tiny beta — a market-neutral fund with β ≈ 0.05 can show a sky-high Treynor that says little about real performance. Cross-check with Sharpe.
• Short windows — beta estimates with fewer than 30 observations are noisy. A reliable Treynor ratio needs a stable beta.
• Wrong benchmark — a small-cap value fund regressed against the S&P 500 produces a misleading beta and therefore a misleading Treynor. Use a style-matched benchmark.
• Non-stationary risk — beta drifts through regimes. A Treynor ratio computed across a regime change can over- or understate forward-looking performance.
• Negative beta with positive excess return — produces a negative Treynor that looks bad but actually reflects a successful hedge. Read alongside Jensen alpha.

Tips for a Reliable Estimate

• Use at least 30 paired observations — CFA convention is 60 monthly returns over five years.
• Match the return frequency for both series (daily with daily, monthly with monthly) and align by date.
• Use the same risk-free rate frequency as the returns frequency, or annualise everything before computing.
• Pick a benchmark that matches the portfolio's style — broad equity, sector, country, or factor index.
• Stress-test the Treynor ratio across two or three windows; persistent ranking matters more than a single window result.

Worked Example

Suppose a balanced fund returned 12.5% last year against a 4.5% Treasury yield, with a beta of 1.20 vs the S&P 500. Plugging into the formula:

FAQ

What is the Treynor ratio?

The Treynor ratio is a risk-adjusted return measure defined as the portfolio's excess return over the risk-free rate divided by its beta. It tells you how much extra return per unit of systematic (market) risk a portfolio delivered.

How is Treynor different from Sharpe?

Both ratios use excess return in the numerator. Sharpe divides by the portfolio's total standard deviation (systematic plus unsystematic risk). Treynor divides by beta (systematic risk only). Treynor is more meaningful for already-diversified portfolios; Sharpe is more meaningful for concentrated or stand-alone positions.

What is a good Treynor ratio?

There is no universal threshold. Compare it to the equity risk premium per unit of beta — historically about 0.05 to 0.07 for broad equity indices. Above that suggests the portfolio earned a premium relative to the market; below that suggests it underperformed on a beta-adjusted basis.

Can the Treynor ratio be negative?

Yes. A negative Treynor means either the portfolio returned less than the risk-free rate, or it had a negative beta and a positive excess return. The second case usually indicates a successful hedge and should be read alongside Sharpe and Jensen alpha.

What happens when beta is zero?

The Treynor ratio is undefined when beta equals zero because the denominator vanishes. In that case use the Sharpe ratio, which divides by total volatility and is well-defined for market-neutral or cash-equivalent positions.

How does Treynor connect to CAPM and Jensen alpha?

CAPM says the required return equals the risk-free rate plus beta times the equity risk premium. If the Treynor ratio exceeds the equity risk premium then the portfolio's Jensen alpha is positive. Jensen alpha equals the realised return minus the CAPM required return.

Should I annualise the inputs?

Use a consistent frequency. If you compute beta from monthly returns, multiply the mean monthly excess return by 12 before dividing by beta to get an annualised Treynor ratio. The returns series mode handles this automatically.

Is a high Treynor ratio always better?

Not unconditionally. Very high ratios often come from very small betas, which can be noisy and easy to misestimate. A robust assessment combines Treynor, Sharpe, Jensen alpha, information ratio, and multiple time windows.