Jensen's Alpha Calculator

What does Jensen’s alpha estimate?

Jensen’s alpha estimates the portion of a portfolio’s return that remains after allowing for the return expected from its market exposure. It is a risk-adjusted performance measure: instead of asking only whether a portfolio made money, it asks whether the portfolio earned more or less than the Capital Asset Pricing Model, or CAPM, would imply for its beta.

A positive alpha means the realized portfolio return was above the CAPM benchmark for the selected period. A negative alpha means the portfolio fell short of that benchmark. An alpha near zero means performance was broadly consistent with the return implied by the chosen risk-free rate, market return, and beta. The measure is useful for structured comparison, but a single period cannot distinguish repeatable investment skill from luck, timing, unmeasured factors, fees, or data noise.

How should each input be used?

Beginning portfolio value

Enter the market value at the start of the measurement period. This field is required and must be greater than zero because it is the denominator of the portfolio-return calculation. A larger starting value does not change the percentage alpha when all returns stay the same, but it increases the displayed “alpha on starting capital” amount. Do not mix a start-of-day value with an end-of-month value unless the other rates cover that same interval.

Ending portfolio value

Enter the portfolio’s value at the end of the period. This field is required and cannot be negative. The calculator assumes there were no external deposits or withdrawals. If cash was added or removed, use a time-weighted return or another cash-flow-adjusted method first; otherwise the computed portfolio return can be materially distorted. Higher ending value raises the portfolio return and, all else equal, raises alpha.

Risk-free rate

Enter a rate for a low-credit-risk instrument with a maturity or measurement horizon reasonably aligned with the analysis. Analysts often reference U.S. Treasury yields, which are published by the U.S. Department of the Treasury, or market series available through the Federal Reserve Bank of St. Louis. A higher risk-free rate generally raises the CAPM expected return, which lowers alpha when other inputs are unchanged.

Portfolio beta

Beta measures sensitivity to market movements. A beta of 1.00 implies market-like exposure; above 1.00 indicates greater sensitivity; below 1.00 indicates lower sensitivity; and a negative beta indicates movement that has historically tended to oppose the market. Beta is required but may be negative. Use a beta estimated over a period, return frequency, and benchmark consistent with the rest of the analysis. When the market risk premium is positive, a higher beta raises expected return and reduces alpha.

Market rate of return

Enter the return of a broad benchmark over the same period as the portfolio return. This is a realized or assumed market return, not necessarily a long-run average. Using an annual market figure with a quarterly portfolio result is a common mistake. Higher market return increases the market risk premium and usually increases the CAPM benchmark for positive-beta portfolios, reducing alpha.

How does the calculation work?

The calculator first derives the portfolio return from beginning and ending values. It then computes the CAPM expected return and subtracts that benchmark from the portfolio return.

For the initial example, the portfolio return is 20.00%. With a 2.00% risk-free rate, 1.12 beta, and 11.00% market return, CAPM implies 12.08%. The resulting Jensen’s alpha is therefore 7.92%.

How should the results, chart, and table be interpreted?

The primary result is Jensen’s alpha in percentage terms. Positive values indicate outperformance relative to the selected CAPM assumptions; negative values indicate underperformance. The portfolio return is the raw holding-period gain or loss. The CAPM expected return is the risk-adjusted benchmark. The market risk premium is the market return minus the risk-free rate and represents the extra return assigned to market risk.

“Alpha on starting capital” multiplies the alpha rate by beginning value. It is an intuitive scale indicator, not a separate cash-flow attribution model. The bar chart compares realized return with the CAPM benchmark using the same live values. The calculation table exposes each intermediate so you can audit the arithmetic. The downloaded workbook contains the current inputs, outputs, comparison values, and scenario notes in a valid Excel file.

What are the main limitations and common mistakes?

• Using mismatched periods for portfolio, market, and risk-free returns.
• Ignoring deposits, withdrawals, fees, taxes, or leverage that changed the realized result.
• Treating beta as stable even though it can vary with the estimation window and benchmark.
• Assuming a positive one-period alpha proves persistent manager skill.
• Comparing alphas calculated with different market indexes or risk-free assumptions.

CAPM is a simplified model and does not capture every source of return. The U.S. Securities and Exchange Commission’s Investor.gov glossary provides a concise definition of alpha, while the CFA Institute Research and Policy Center offers broader educational material on investment analysis and risk concepts.