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.
Jensen's Alpha Calculator
Calculate Jensen's Alpha, Treynor Ratio, Sharpe Ratio, and Information Ratio to evaluate risk-adjusted portfolio performance against the CAPM benchmark.
Annualized standard deviation
Std dev of excess returns vs benchmark
Jensen's Alphaโง
2.50%
โ
Positive alpha โ manager added value
CAPM Expected Returnโง
11.50%
Rf + ฮฒร(Rm โ Rf) = 5 + 1.3ร(10โ5)
Treynor Ratioโง
6.92
Excess return per unit of systematic risk (beta)
Sharpe Ratioโง
0.50
Excess return per unit of total risk (volatility)
Information Ratioโง
0.80
Active return per unit of tracking error
Mยฒ Returnโง
14.00%
Modigliani risk-adjusted performance
Return Attribution
Risk-Free
+5.00%
Beta Contribution
+6.50%
Alpha (Skill)
+2.50%
$10,000 Growth Comparison (10 Years)
| Year | Portfolio (14%) | CAPM Expected (11.5%) | Market (10%) |
|---|---|---|---|
| 1 | $11,400 | $11,150 | $11,000 |
| 2 | $12,996 | $12,432 | $12,100 |
| 3 | $14,815 | $13,862 | $13,310 |
| 4 | $16,890 | $15,456 | $14,641 |
| 5 | $19,254 | $17,234 | $16,105 |
| 6 | $21,950 | $19,215 | $17,716 |
| 7 | $25,023 | $21,425 | $19,487 |
| 8 | $28,526 | $23,889 | $21,436 |
| 9 | $32,519 | $26,636 | $23,579 |
| 10 | $37,072 | $29,699 | $25,937 |
Planning notes, formulas, and examples
About the Jensen's Alpha Calculator
Jensen's Alpha measures a portfolio manager's ability to generate returns above what the Capital Asset Pricing Model (CAPM) would predict for the portfolio's level of systematic risk (beta). A positive alpha indicates the manager generated excess return through skill โ stock selection, market timing, or both.
The CAPM says your expected return should equal the risk-free rate plus beta times the market risk premium. Any return above (or below) this is alpha. A fund with 14% return, 1.3 beta, 10% market return, and 5% risk-free rate has a CAPM expectation of 11.5% โ the 2.5% excess is Jensen's Alpha.
This calculator computes alpha alongside four complementary metrics: the Treynor Ratio (excess return per beta), Sharpe Ratio (excess return per unit of total volatility), Information Ratio (active return per tracking error), and Mยฒ (Modigliani risk-adjusted return). Together, they give a complete picture of whether a portfolio manager is truly adding value. Use the example to verify the CAPM math before you compare managers or reporting periods.
When This Page Helps
Raw returns are meaningless without risk adjustment. A 14% return with 1.3 beta tells a completely different story than 14% with 0.8 beta. Jensen's Alpha and related metrics separate luck and leverage from genuine investment skill. Use this when you need a benchmark-adjusted view of performance instead of a simple return ranking. It is especially useful for comparing managers, funds, or strategies with different market exposures.
How to Use the Inputs
- Enter the portfolio's actual return over the measurement period.
- Enter the market benchmark return and the risk-free rate.
- Input the portfolio beta (regression against the market).
- Add portfolio volatility and tracking error for Sharpe and IR calculations.
- Review alpha and performance attribution.
- Compare alpha across multiple periods to see whether outperformance persists after fees.
Formula used
ฮฑ = R_p โ [R_f + ฮฒ ร (R_m โ R_f)]
Treynor = (R_p โ R_f) / ฮฒ
Sharpe = (R_p โ R_f) / ฯ_p
Information Ratio = (R_p โ R_m) / Tracking Error
Mยฒ = R_f + Sharpe ร ฯ_mExample Calculation
Result: Jensen's Alpha = +2.50%
CAPM expected return = 5% + 1.3ร(10%โ5%) = 11.5%. The portfolio earned 14%, so alpha is 14% โ 11.5% = +2.5%. The manager generated 2.5% excess return above the risk-adjusted benchmark.
Tips & Best Practices
- Compare alpha net of management fees โ many funds have negative alpha after fees.
- Check the Information Ratio: above 0.5 suggests genuine skill, above 1.0 is exceptional.
- A high Sharpe but low Treynor may indicate unsystematic risk not captured by beta.
- Look at alpha consistency year-over-year, not just the average.
- Beware survivorship bias โ failed funds with negative alpha disappear from databases.
Interpretation
A positive alpha means the portfolio beat its CAPM expectation for the amount of systematic risk it carried. A negative alpha means the return was lower than the benchmark-adjusted target.
Comparison Notes
Use the same benchmark, time period, and fee basis when comparing managers. A change in beta or a different index can make two alpha figures look comparable when they are not.
Reading the Output
Look at Treynor, Sharpe, and Information Ratio alongside alpha. Together they show whether outperformance came from skill, leverage, or broad market exposure.
Sources & Methodology
Last updated:
Methodology
This worksheet takes the user-entered portfolio return, market return, risk-free rate, beta, volatility, and tracking error, then computes CAPM-expected return, Jensen's Alpha, Treynor Ratio, Sharpe Ratio, Information Ratio, and an Mยฒ-style risk-adjusted return. It treats all returns as being measured over the same period and does not attempt to estimate beta, volatility, or tracking error from raw return history.
That means the page is a benchmarking worksheet, not a performance-attribution engine. The output is only as reliable as the return, beta, and risk estimates supplied by the user, and short measurement windows can make alpha look more stable than it really is.
Sources
- Glossary: Alpha (Investor.gov) โ SEC investor-education glossary entry defining alpha as risk-adjusted performance relative to a benchmark.
- Glossary: Beta (Investor.gov) โ SEC investor-education glossary entry defining beta as a measure of market risk.
- Calculating a Company's Cost of Capital (New York University) โ NYU corporate-finance reference showing the CAPM benchmark used in alpha calculations.
Frequently Asked Questions
Consistently positive alpha (above 0%) is good. Alpha above 2% annually is exceptional and rare over long periods.
Yes โ negative alpha means the portfolio underperformed what CAPM predicted for its risk level. The manager destroyed value.
Excess return is simply portfolio return minus benchmark return. Alpha adjusts for risk โ a high-beta fund should earn higher returns, so excess return alone doesn't prove skill.
Treynor measures return per unit of beta. Alpha is the absolute excess return above CAPM. A positive alpha implies a Treynor ratio above the market's.
Short-period alpha (1 year) is unreliable. Persistent positive alpha over 5+ years with a strong Information Ratio is more meaningful.
Only if you use net-of-fee returns. Always compare alpha after fees to get a true picture of manager value-add.
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