Risk-Adjusted Performance Calculator
Use the Risk-Adjusted Performance Calculator with your own values for Calculation mode, Portfolio return, Risk-free rate, Portfolio standard deviation, Portfolio beta, and Market return. It reports Sharpe ratio, Treynor ratio, and Jensen alpha, shows the formula and worked example, and does not fetch live market or account data.
Learn the method: step-by-step examples and practice ↓
Calculate, then understand
Step-by-step learning lab
Identify whose cash flow this is and when it occurs. Enter the given values, then follow the calculation as each number changes.
Sharpe ratio
How much excess return does the portfolio earn per unit of total volatility?
When to use it and why it works
An investor gives up the risk-free alternative to bear portfolio volatility. Subtract that alternative return, then divide the excess by return standard deviation to compare reward relative to total risk.
Sharpe = (Rp − Rf) / σ
Work through an example
Annual portfolio return is 12%, risk-free return 3%, and annualized standard deviation 10%. Find Sharpe.
Read this example’s explanation
(12% − 3%) ÷ 10% = 0.9, with no percent sign.
Your calculated answer
- Sharpe ratio
- 0.9
Follow each step
Subtract the matching risk-free return from the portfolio return.
12 − 3 = 9Divide excess return by matching return standard deviation; the percentage units cancel.
9 / 10 = 0.9
Intermediate calculations retain precision; displayed values are rounded. Follow the precision requested by your question.
What the result means
Sharpe has no percent sign. The default 0.9 means 0.9 units of excess return per unit of total volatility. A negative value means underperformance versus the selected risk-free benchmark.
Mistakes to watch for
- Returns and standard deviation must use the same frequency; do not divide annual return by monthly volatility.
- This textbook version treats the risk-free return as constant and uses supplied return and volatility estimates. It does not estimate volatility from a time series or promise future performance.
- Compare only on consistent assumptions. With negative excess returns, more volatility can push the ratio toward zero without making the investment better.
Try another question on your own
At the same annual frequency, portfolio return is 8%, risk-free return 2%, and standard deviation 12%. Find Sharpe.
Set up the formula first. Answers rounded to two decimals are accepted; use six decimals for absolute values below 0.01. For percentages, enter the number before the percent sign.
How to use this calculator
Enter Calculation mode, Portfolio return, Risk-free rate, Portfolio standard deviation, Portfolio beta, and Market return.
Review the model boundary before calculating: Return, risk-free rate, volatility, beta, and market return must cover the same period and frequency.
Read Sharpe ratio, Treynor ratio, and Jensen alpha, then compare the result with the cited source and governing product terms.
Formula
Formula used: Sharpe = (Rₚ − Rf) / σₚ; Treynor = (Rₚ − Rf) / βₚ; Jensen α = Rₚ − [Rf + βₚ(Rm − Rf)]. Percentages are converted to decimals before calculation.
Worked example
Example: with Portfolio return = 12%, Risk-free rate = 3%, and Portfolio standard deviation = 15%, the calculated Sharpe ratio is 0.60.
Assumptions and limits
- Return, risk-free rate, volatility, beta, and market return must cover the same period and frequency.
- Historical risk-adjusted performance does not predict future returns.
- This educational estimate is not investment, tax, accounting, or legal advice.
Sources
- William F. Sharpe: The Sharpe RatioThe Sharpe ratio definition and consistent return and risk measurement. Reviewed 2026-08-24.
- The Journal of Finance: The Performance of Mutual Funds in the Period 1945–1964Jensen alpha and benchmark-adjusted performance measurement. Reviewed 2026-08-24.
- OpenStax, Rice University: Principles of Finance — Applications in Performance MeasurementOfficial formula or method source used by this calculator. Reviewed 2026-08-24.
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Verification
How this calculator is checked
Trust comes from reproducible evidence, not model confidence. You can inspect the formula, assumptions, worked example, and cited sources on this page.
- Versioned calculationFormula logic is kept separate from the interface and covered by automated registry and behavior checks.
- Cited evidenceSources linked for independent checking: 3.
- Transparent AI useAI may assist drafting or adversarial review. Agreement between models is not proof, and no human expert review is claimed unless a named reviewer is shown.
Frequently asked questions
How does the Risk-Adjusted Performance Calculator work?
Formula used: Sharpe = (Rₚ − Rf) / σₚ; Treynor = (Rₚ − Rf) / βₚ; Jensen α = Rₚ − [Rf + βₚ(Rm − Rf)]. Percentages are converted to decimals before calculation.
What should I enter in the Risk-Adjusted Performance Calculator?
Enter Calculation mode, Portfolio return, Risk-free rate, Portfolio standard deviation, Portfolio beta, and Market return using one consistent currency and time basis.
What should I verify before using the Risk-Adjusted Performance Calculator result?
Verify these limits: Return, risk-free rate, volatility, beta, and market return must cover the same period and frequency. Historical risk-adjusted performance does not predict future returns. This educational estimate is not investment, tax, accounting, or legal advice.
Last updated 2026-08-25 · sharpe-treynor-jensen-v1 · content-2026-08-24 · Published by YunFanLabs