Jensen's Alpha Calculator
Calculate Jensen's Alpha to measure a portfolio's risk-adjusted performance relative to its expected return based on the Capital Asset Pricing Model (CAPM). A positive alpha indicates outperformance.
How to use this tool
- Enter portfolio return, risk-free rate, market return and portfolio beta in the fields above.
- Results update instantly as you type โ or click Calculate.
- Read your jensen's alpha and the full breakdown beneath it.
โ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation โ verify with a qualified professional.
Formula
ฮฑ = Rp โ [Rf + ฮฒ ร (Rm โ Rf)]
Where Rp = portfolio return, Rf = risk-free rate, Rm = market return, ฮฒ = portfolio beta.
How it works
Jensen's Alpha compares a portfolio's actual return to the return predicted by the Capital Asset Pricing Model (CAPM). The CAPM expected return accounts for systematic (market) risk via beta: higher-beta portfolios are expected to earn higher returns. A positive alpha means the manager added value beyond what market risk alone would predict; a negative alpha indicates underperformance on a risk-adjusted basis.
Worked example
Portfolio Returning 12% with Beta of 1.2
- Portfolio return = 12%; Risk-free rate = 2%; Market return = 9%; Beta = 1.2
- Market risk premium = 9% โ 2% = 7%
- CAPM expected return = 2% + 1.2 ร 7% = 2% + 8.4% = 10.4%
- Jensen's Alpha = 12% โ 10.4% = 1.6%
Jensen's Alpha = 1.60%. The portfolio outperformed its CAPM benchmark by 1.60 percentage points on a risk-adjusted basis.
Common mistakes to avoid
- Using arithmetic average returns instead of matching the return frequency to the beta source โ mixing monthly beta with annual returns produces a meaningless alpha.
- Forgetting to use the risk-free rate that corresponds to the holding period; using a 10-year Treasury rate for a monthly return series overstates the hurdle.
- Interpreting a positive alpha as skill without checking statistical significance โ with a short track record, alpha can easily be noise rather than manager outperformance.
Key terms
- What is Jensen's Alpha?
- Jensen's Alpha (or Jensen's measure) is a risk-adjusted performance metric that compares a portfolio's actual return to the return predicted by the CAPM given the portfolio's beta. A positive alpha indicates outperformance.
- What is Beta?
- Beta measures a portfolio's sensitivity to market movements. A beta of 1.2 means the portfolio is expected to move 1.2% for every 1% move in the market. Higher beta = more market risk.
- What is the risk-free rate?
- The risk-free rate is the theoretical return on a zero-risk investment, typically approximated by the yield on short-term US Treasury bills or notes.
- What is the market risk premium?
- The market risk premium is the excess return of the market over the risk-free rate (R_m โ R_f). It compensates investors for taking on the risk of investing in equities rather than risk-free assets.
- Does a positive alpha guarantee future outperformance?
- No. Alpha is a historical measure. Past alpha does not guarantee future outperformance; it may reflect luck, a temporary edge, or unrecognized risks not captured by beta.
Frequently asked questions
- What does a negative Jensen's Alpha mean?
- A negative alpha means the portfolio underperformed what the CAPM predicted given its level of systematic risk. The manager added less return than expected per unit of beta exposure.
- How is Jensen's Alpha different from the Sharpe ratio?
- The Sharpe ratio measures return per unit of total (standard deviation) risk. Jensen's Alpha measures excess return over the CAPM benchmark, using only systematic (beta) risk. A fund can have a high Sharpe but a negative alpha if its beta is high.
- What beta should I use if I manage a multi-asset portfolio?
- You should estimate a portfolio-level beta by regressing your portfolio returns against the chosen market index. Using a simple average of individual asset betas ignores correlation effects and is less accurate.