Jensen's Alpha Calculator

What is Jensen's Alpha?

Jensen's Alpha (also known as Jensen's Performance Index or ex-post alpha) is a risk-adjusted performance measure that represents the average return on a portfolio over what was predicted by the Capital Asset Pricing Model (CAPM), given the portfolio's beta and the average market return.

Developed by economist Michael Jensen in 1968, it's one of the most widely used metrics for evaluating portfolio manager performance.

The Jensen's Alpha Formula

Calculate Jensen's Alpha

α = Rp - [Rf + β × (Rm - Rf)]

Where:

• α (Alpha) = Jensen's Alpha (excess return)
• Rp = Realized Portfolio Return
• Rf = Risk-Free Rate (e.g., Treasury bill rate)
• β (Beta) = Portfolio's systematic risk (sensitivity to market)
• Rm = Market Return (benchmark return)
• (Rm - Rf) = Market Risk Premium

Alternative Forms

Expected Return = Rf + β × (Rm - Rf)

Required Return for Target Alpha = α + Rf + β × (Rm - Rf)

How to Use This Calculator

1. Select your calculation mode (Alpha, Required Return, or Beta)
2. Enter your portfolio return (actual performance)
3. Enter the risk-free rate (typically 3-5%)
4. Enter the market return (benchmark like S&P 500)
5. Enter the portfolio beta (sensitivity to market)
6. View your Jensen's Alpha and interpretation

Interpreting Jensen's Alpha

Typical Alpha Values

When to Use Jensen's Alpha

• Portfolio Evaluation: Assess if your investments beat the market on a risk-adjusted basis
• Fund Manager Comparison: Compare performance of different fund managers
• Investment Selection: Choose funds that consistently generate positive alpha
• Performance Attribution: Separate skill from market movements

Jensen's Alpha vs. Other Metrics

Jensen's Alpha

Measures absolute excess return over CAPM prediction. Best for: evaluating manager skill.

Sharpe Ratio

Measures risk-adjusted return per unit of total risk. Best for: comparing investments with different risk levels.

Treynor Ratio

Measures risk-adjusted return per unit of systematic risk (beta). Best for: well-diversified portfolios.

Information Ratio

Measures excess return relative to tracking error. Best for: comparing active managers to benchmarks.

Limitations of Jensen's Alpha

1. CAPM Assumptions: Relies on CAPM which has known limitations
2. Historical Data: Based on past performance, not predictive
3. Beta Instability: Beta can change over time
4. Single Factor: Only considers market risk, not other factors
5. Benchmark Selection: Results depend on appropriate benchmark choice

Frequently Asked Questions

What is a good Jensen's Alpha?

A positive alpha indicates outperformance. An alpha of 1% or higher is generally considered good for actively managed funds, though consistency matters more than magnitude.

How is beta calculated?

Beta is calculated as the covariance of the portfolio returns with market returns, divided by the variance of market returns. A beta of 1 means the portfolio moves with the market.

What risk-free rate should I use?

Typically, the 3-month Treasury bill rate is used. As of recent years, this has ranged from 0% to 5% depending on economic conditions.

Note: This calculator provides estimates for educational and analysis purposes. Past performance does not guarantee future results. Consult a financial advisor for investment decisions.