Treynor Ratio Calculator

Frequently Asked Questions

What does the Treynor ratio measure?

Excess return per unit of systematic (market) risk: (portfolio return − risk-free rate) ÷ beta. It rewards return earned for market exposure rather than total volatility.

When should I use Treynor instead of Sharpe?

Treynor is best for well-diversified portfolios where unsystematic risk is already removed, so beta is the relevant risk measure. Sharpe suits undiversified or standalone portfolios.

What does a negative Treynor ratio mean?

Either the portfolio underperformed the risk-free rate, or beta is negative. Negative-beta cases make the ratio hard to interpret and should be flagged.

What is a good value?

Higher is better, and it is most meaningful when ranking funds against each other or against the market portfolio over the same window.

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Estimates only. Not investment advice.

Investment Disclaimer: Estimates only. Not investment advice.

This calculator provides estimates for educational purposes only and is not investment advice. Past performance does not guarantee future results. Consult with a qualified financial advisor before making investment decisions. All investments carry risk, including potential loss of principal.

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How This Calculator Works

This tool computes two CAPM-based performance measures. The Treynor ratio is (R_p − R_f) ÷ β - excess return per unit of systematic (market) risk rather than total risk. Jensen's alpha is R_p − [R_f + β(R_m − R_f)], the return earned above what the Capital Asset Pricing Model predicts for the portfolio's beta. Beta measures sensitivity to the market: β = 1 moves with the index, β > 1 amplifies it, β < 1 dampens it. Because Treynor uses beta in the denominator it assumes the portfolio is well diversified so that unsystematic risk has been removed; the Sharpe ratio, by contrast, divides by total standard deviation and is the right choice for an undiversified or single-strategy book.

Worked Numeric Example

Take R_p = 11%, R_f = 4%, β = 1.2, R_m = 9%. Treynor = (11 − 4) ÷ 1.2 = 7 ÷ 1.2 ≈ 5.83. CAPM expected return = 4 + 1.2 × (9 − 4) = 4 + 6 = 10%. Jensen's alpha = 11 − 10 = +1.0%, meaning the manager beat the risk-adjusted benchmark by one percentage point. The market's own Treynor (beta = 1) is 9 − 4 = 5.0, so the portfolio's 5.83 indicates superior reward for the systematic risk taken.

Real-World Use

Treynor and Jensen's alpha are the standard yardsticks when a fund is one sleeve inside a larger diversified portfolio - the investor already holds many funds, so only systematic risk matters at the margin. Mutual-fund analysts, plan sponsors, and academic performance studies (Jensen's 1968 paper launched modern fund evaluation) lean on alpha to separate genuine skill from leveraged market exposure that merely looks impressive in raw return terms. Manager-selection committees routinely rank a peer group by Treynor to neutralize the fact that some managers simply ran higher beta in a rising market; two funds with identical raw returns can have very different Treynor ratios if one achieved its number by quietly dialing up market exposure rather than by stock selection. Smart-beta and factor-fund due diligence starts from exactly this decomposition - is the return alpha, or is it beta wearing a costume?

Common Mistakes

Using Treynor on an undiversified portfolio - beta only captures market risk, so idiosyncratic risk is invisible and the ratio flatters concentrated bets.

Estimating beta over a window that does not match the evaluation period, or against the wrong benchmark index.

Treating a single positive alpha as proof of skill; alpha has wide standard errors and often reverses.

Forgetting that leverage scales beta, inflating both raw return and CAPM-expected return so the apparent edge can vanish.

Comparing Treynor across funds with very different betas without checking that each is genuinely diversified - the ratio is only meaningful when unsystematic risk has been removed.

Limitations & Related Ratios

Both measures inherit CAPM's assumptions: a single market factor, stable beta, and mean-variance investors. Beta itself is estimated with error and is famously unstable across regimes, so a precise-looking alpha can rest on a shaky denominator. Multi-factor models (Fama-French three-factor, Carhart four-factor) frequently reveal that apparent alpha was really uncompensated exposure to size, value, or momentum - what looked like skill was a factor tilt that any cheap index could have delivered. Alpha estimates also carry wide confidence intervals; several years of data are usually needed before a positive alpha is statistically distinguishable from luck. Pair Treynor with the Sharpe ratio (total risk), the information ratio (active risk versus a benchmark), the Sortino ratio (downside risk), and maximum drawdown for a rounded view. This is an educational estimate, not investment advice; consult a qualified professional before acting on any performance metric.

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