Jensen's Alpha Calculator
Using CAPM, measure excess return: Alpha = portfolio return − [Rf + beta × (Rm − Rf)].
Input Data
Results
At a glance:Jensen's Alpha measures the part of a portfolio's actual return that exceeds 'the CAPM return for its risk': Alpha = actual return − [Rf + β × (Rm − Rf)]. The bracket is the CAPM expected return (the fair reward for bearing systematic risk β). Alpha > 0 means the manager created extra value beyond risk (beat the benchmark); Alpha < 0 means lagging the deserved level. It strips out the return earned merely by taking more risk, highlighting true active-management skill.
Formula
Portfolio return = (ending value − beginning value) ÷ beginning value.
CAPM expected return = Rf + beta × (Rm − Rf).
Jensen's alpha = actual return − CAPM expected return.
$$E(R_p) = R_f + \beta (R_m - R_f)$$$$\alpha = R_p - [R_f + \beta (R_m - R_f)]$$$$\text{Example: } 20\% - [2\% + 1.12(11\%-2\%)] = 7.92\%$$How to Use
- Enter the beginning and ending portfolio values.
- Enter the risk-free rate, market return and portfolio beta.
- View the portfolio return, CAPM expected return and Jensen's alpha instantly.
Jensen's alpha under different portfolios (Rf = 2%)
| Actual Rp | Market Rm | beta | CAPM expected | Alpha |
|---|---|---|---|---|
| 20% | 11% | 1.12 | 12.08% | +7.92% (beat) |
| 15% | 11% | 1.12 | 12.08% | +2.92% (slight) |
| 25% | 9% | 0.90 | 8.30% | +16.70% (strong) |
Case Studies
Case 1: Computing Jensen's alpha
A fund starts at HK$1,000,000 and ends at HK$1,200,000; risk-free 2%, market 11%, beta 1.12.
Actual return = (1,200,000 − 1,000,000) ÷ 1,000,000 = 20%; CAPM expected = 2% + 1.12 × (11% − 2%) = 2% + 10.08% = 12.08%; Jensen's alpha = 20% − 12.08% = +7.92%.
Interpretation: the fund earned 20%, but given its systematic risk (beta 1.12) CAPM says it 'should' earn 12.08%. The extra +7.92% is alpha — the manager created risk-free extra value via stock-picking or timing, beating the benchmark.
Case 2: Low beta, high alpha is the real skill
Compare two funds (Rf = 2%). A: actual 20%, beta 1.12, market 11%, alpha = 20 − [2 + 1.12 × 9] = +7.92%. B: actual 25%, but market 9%, beta only 0.9, CAPM expected = 2 + 0.9 × 7 = 8.3%, alpha = 25 − 8.3 = +16.7%.
By return alone: B (25%) > A (20%); by alpha: B (+16.7%) far beats A (+7.92%), and B used lower beta 0.9 (less market risk) to earn more.
Interpretation: the value of alpha is that it 'strips out the risk-deserved part'. A earned a lot but had high beta so should have; B earned more at lower risk — clearly stronger active skill. So compare managers by 'what remains after the risk-deserved return', not headline returns. ⚠️ Alpha depends on beta, market return and the period; past performance is not future — combine with information ratio, Sharpe, etc.
FAQ
What does positive alpha mean?
It means the actual return exceeds the return CAPM predicts from its risk (beta) — the manager created extra value (beat the market's fair reward) through stock-picking or timing.
How is alpha related to beta?
Beta measures the systematic risk the portfolio bears (amplifying or damping market moves) and produces the CAPM expected return; alpha is the actual return minus that expectation, measuring the 'extra' performance beyond risk.
Why use CAPM as the benchmark?
CAPM gives the 'fair reward' from the portfolio's systematic risk. Using it as a benchmark removes the return merely from higher risk, highlighting true active-management ability.
Is negative alpha necessarily a bad manager?
Negative alpha literally means 'actual return below what CAPM says beta deserves' — bearing that much risk but underperforming. But whether to call the manager 'bad' needs caution, as alpha is highly sensitive to estimates. (1) Beta estimation period and market index hugely affect it; (2) market return Rm choice sets the CAPM baseline; (3) too short a period is noisy (luck, not skill); (4) style/constraints may cause short-run negative alpha. So negative alpha is a 'needs investigation' signal, not a verdict. Confirm beta/benchmark/period are reasonable, check multi-period alpha consistency, and combine with information ratio, Sharpe and max drawdown. Only persistent negative alpha across regimes suggests weak active management.
How do alpha, beta, CAPM and Sharpe relate and combine?
They form the risk-adjusted performance framework. Beta & CAPM: beta measures systematic risk; CAPM uses beta to compute the fair return (expected = Rf + β(Rm − Rf)); alpha = actual − CAPM expected, the excess beyond risk. Sharpe also risk-adjusts but differs: Sharpe = excess return ÷ total std dev (all risk), good for undiversified portfolios; alpha uses beta (systematic only) and is a percentage, good for diversified vs CAPM. Combine: (1) CAPM+beta set the 'deserved' baseline; (2) alpha for active value; (3) information ratio for stability of that alpha; (4) Sharpe/Sortino cross-check from total/downside risk; (5) max drawdown for tail risk. Multiple indicators avoid single-number misjudgement.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.