Alpha and Beta Calculator
Free alpha and beta calculator. Measure your portfolio's market sensitivity (beta) and excess risk-adjusted return (alpha) against a benchmark index.
Treynor Ratio Calculator
Calculate the Treynor ratio for risk-adjusted portfolio evaluation. Compare funds, benchmark vs market, and analyze beta sensitivity with Jensen's alpha.
Treynor Ratioโง
8.64
โ
Outperforming market on a risk-adjusted basis
Market Treynorโง
5.50
Benchmark: (Rm โ Rf) / 1.0
Comparison Treynorโง
5.50
โ
Your fund wins
Excess Returnโง
9.50%
Return above risk-free rate
Jensen's Alphaโง
3.45%
CAPM expected: 10.6%
Required Returnโง
10.55%
To match market Treynor at your ฮฒ
Treynor Ratio Comparison
Your Portfolio
8.64
Comparison Fund
5.50
Market (ฮฒ=1)
5.50
Fund Performance Comparison
| Fund | Return | Beta | Treynor | vs Market |
|---|---|---|---|---|
| Your Portfolio | 14.00% | 1.10 | 8.64 | โฒ 3.14 |
| Comparison Fund | 10.00% | 1.00 | 5.50 | โผ 0.00 |
| Market (ฮฒ=1) | 10.00% | 1.00 | 5.50 | โ |
| Risk-Free | 4.50% | 0.00 | โ | โ |
Beta Sensitivity
| Beta | Treynor | CAPM Expected | Alpha |
|---|---|---|---|
| 0.30 | 31.67 | 6.15% | +7.85% |
| 0.50 | 19.00 | 7.25% | +6.75% |
| 0.70 | 13.57 | 8.35% | +5.65% |
| 0.90 | 10.56 | 9.45% | +4.55% |
| 1.00 | 9.50 | 10.00% | +4.00% |
| 1.10 | 8.64 | 10.55% | +3.45% |
| 1.30 | 7.31 | 11.65% | +2.35% |
| 1.50 | 6.33 | 12.75% | +1.25% |
| 2.00 | 4.75 | 15.50% | -1.50% |
Planning notes, formulas, and examples
About the Treynor Ratio Calculator
The Treynor ratio measures how much excess return a portfolio earns per unit of systematic risk (beta). Named after Jack Treynor, it's the go-to metric for evaluating well-diversified portfolios where unsystematic risk has been diversified away, leaving only market (beta) risk.
The formula is simple: (Portfolio Return โ Risk-Free Rate) / Portfolio Beta. A fund returning 14% with ฮฒ = 1.1 when the risk-free rate is 4.5% has a Treynor ratio of 8.64. Compare this to the market's Treynor (market return โ risk-free rate) to determine if the fund manager added value. Higher Treynor = better risk-adjusted performance.
This calculator computes the Treynor ratio for your portfolio and a comparison fund, benchmarks against the market, calculates Jensen's alpha, and provides beta sensitivity analysis. It answers the critical question: is your fund manager generating excess returns, or just taking on more market risk? Use the beta sensitivity view to see how the ratio shifts with different market exposure assumptions.
When This Page Helps
Use Treynor when you want to judge performance against market risk, not total volatility. It is the right lens for diversified portfolios, where beta captures the risk that matters and a simple return comparison can overstate skill. It also helps separate a manager who is genuinely adding alpha from one who is just taking a larger market bet.
How to Use the Inputs
- Enter your portfolio's return, beta, and the risk-free rate.
- Enter the expected market return for benchmark comparison.
- Add a comparison fund's return and beta for head-to-head analysis.
- Review the Treynor ratio and Jensen's alpha.
- Compare visual bars to see which fund earns more per unit of risk.
- Check the beta sensitivity table to understand how Treynor changes with risk.
Formula used
Treynor Ratio = (Rp โ Rf) / ฮฒp
Market Treynor = (Rm โ Rf) / 1.0
Jensen's Alpha = Rp โ [Rf + ฮฒp ร (Rm โ Rf)]
Excess Return = Rp โ Rf
Required Return = Rf + Market Treynor ร ฮฒpExample Calculation
Result: Treynor: 8.64, Market Treynor: 5.50, Alpha: +3.45%
Excess return = 14% โ 4.5% = 9.5%. Divided by beta 1.1 = Treynor of 8.64. The market Treynor is only 5.50, so this fund significantly outperforms on a risk-adjusted basis. Jensen's alpha of +3.45% confirms genuine outperformance.
Tips & Best Practices
- A fund can have high returns but low Treynor if it achieves those returns through excessive market exposure (high beta).
- When comparing mutual funds in the same asset class, rank by Treynor rather than raw return.
- The Treynor ratio assumes well-diversified portfolios. For concentrated portfolios, use the Sharpe ratio.
- Check that beta is measured over the same period as returns for consistent results.
- Declining Treynor over time may signal a manager losing their edge or taking on more risk without proportional returns.
Treynor Ratio Interpretation
Compare the Treynor ratio only across portfolios with meaningful market exposure. A higher value means more excess return per unit of beta, but the ratio is only useful when the portfolio is diversified enough that unsystematic risk is not dominating outcomes.
Practical Checks
Make sure the return period matches the beta measurement window and the risk-free rate is quoted on the same basis. If beta is near zero, the ratio becomes unstable and Sharpe ratio is usually the better benchmark. If the market Treynor exceeds the portfolio Treynor, the benchmark is earning more return for each unit of systematic risk.
Sources & Methodology
Last updated:
Methodology
This calculator divides excess portfolio return by beta to estimate return earned per unit of systematic market risk. It also compares the same ratio against the benchmark market input and shows Jensen-style residual return for context.
The worksheet is only meaningful when beta comes from the same return window as the portfolio return. It is best used for diversified portfolios rather than concentrated bets.
Sources
- Beta (Investor.gov / U.S. Securities and Exchange Commission)
- Capital Asset Pricing Model (CAPM) (Investor.gov / U.S. Securities and Exchange Commission)
- Risk and Return (Investor.gov / U.S. Securities and Exchange Commission)
Frequently Asked Questions
There's no absolute threshold. A positive Treynor means the portfolio earned above the risk-free rate. A Treynor above the market Treynor means the fund outperformed on a risk-adjusted basis.
Treynor is best for diversified portfolios (evaluates systematic risk only). Sharpe is best for total portfolio evaluation or undiversified holdings (considers total risk via standard deviation).
Yes โ if the portfolio return is below the risk-free rate OR if beta is negative with positive excess returns. A negative Treynor usually means poor performance.
Treynor becomes undefined or extreme. The ratio only works for portfolios with meaningful market exposure. For market-neutral strategies, use Sharpe ratio instead.
Both measure risk-adjusted performance. Treynor gives a ratio (return per unit of beta). Alpha gives a percentage (actual return minus CAPM expected return). Both use beta as the risk measure.
Annually for long-term evaluation. Quarterly Treynor can be noisy. Use 3-5 year periods for meaningful fund manager evaluation.
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