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.

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 — 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% — 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 M² (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.

Why Use This Jensen's Alpha Calculator?

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 This Calculator

  1. Enter the portfolio's actual return over the measurement period.
  2. Enter the market benchmark return and the risk-free rate.
  3. Input the portfolio beta (regression against the market).
  4. Add portfolio volatility and tracking error for Sharpe and IR calculations.
  5. Review alpha and performance attribution.
  6. Compare alpha across multiple periods to see whether outperformance persists after fees.

Formula

α = R_p − [R_f + β × (R_m − R_f)] Treynor = (R_p − R_f) / β Sharpe = (R_p − R_f) / σ_p Information Ratio = (R_p − R_m) / Tracking Error M² = R_f + Sharpe × σ_m

Example Calculation

Result: Jensen's Alpha = +2.50%

CAPM expected return = 5% + 1.3×(10%−5%) = 11.5%. The portfolio earned 14%, so alpha is 14% − 11.5% = +2.5%. The manager generated 2.5% excess return above the risk-adjusted benchmark.

Tips & Best Practices

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

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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 M²-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

Frequently Asked Questions

What is a good Jensen's Alpha?

Consistently positive alpha (above 0%) is good. Alpha above 2% annually is exceptional and rare over long periods.

Can alpha be negative?

Yes — negative alpha means the portfolio underperformed what CAPM predicted for its risk level. The manager destroyed value.

What's the difference between alpha and excess return?

Excess return is simply portfolio return minus benchmark return. Alpha adjusts for risk — a high-beta fund should earn higher returns, so excess return alone doesn't prove skill.

How is alpha related to the Treynor Ratio?

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.

How reliable is alpha measurement?

Short-period alpha (1 year) is unreliable. Persistent positive alpha over 5+ years with a strong Information Ratio is more meaningful.

Does alpha account for fees?

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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