Enter Values

%
Actual portfolio return (annualized)
%
Treasury or T-Bill rate (annualized)
Systematic risk relative to market (β=1 is market average)
%
Benchmark market return (annualized)
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Quick Reference

  • Positive alpha = Outperformed CAPM expectations
  • Negative alpha = Underperformed CAPM expectations
  • All inputs must be annualized from the same period
  • Measures manager skill vs passive market exposure

Jensen's Alpha Result

Jensen's Alpha 2.00% Above Expected
-5% 0% +10%
Expected Return (CAPM) 10.00%
Market Risk Premium 5.50%

Formula Breakdown

α = Rp − [Rf + β(Rm − Rf)]
Step 1: Market Premium = 10.00% − 4.50% = 5.50%
Step 2: Expected Return = 4.50% + 1.00 × 5.50% = 10.00%
Step 3: Alpha = 12.00% − 10.00% = 2.00%

Interpretation

Your portfolio generated 2.00% more return than CAPM predicted for its level of systematic risk. This positive alpha suggests the portfolio outperformed risk-adjusted expectations.

Rating Guide

These are general guidelines for context. Meaningful alpha analysis requires comparing portfolios with similar objectives over identical time periods.

< -3% Negative Significant underperformance
-3% to 0% Below Expected Underperforming expectations
0% to 1% At Expected In line with CAPM
1% to 3% Above Expected Moderate outperformance
3% to 5% Good Strong outperformance
≥ 5% Exceptional Verify data accuracy

Understanding Jensen's Alpha

What is Jensen's Alpha?

Jensen's alpha measures portfolio performance relative to what the Capital Asset Pricing Model (CAPM) predicts. Introduced by Michael Jensen in his 1968 paper "The Performance of Mutual Funds," it quantifies the excess return above or below what would be expected given the portfolio's systematic risk (beta).

In simple terms, alpha answers: "Did this portfolio outperform or underperform what CAPM predicted, given the market risk it took on?"

Key Insight: Positive alpha suggests "manager skill"—the ability to generate returns beyond what passive market exposure would provide. Negative alpha suggests underperformance relative to risk-adjusted expectations.

Understanding the Formula

Jensen's alpha uses CAPM to calculate what return you should have earned, then compares it to what you actually earned:

  1. Calculate Market Risk Premium: Rm − Rf (how much the market returned above the risk-free rate)
  2. Calculate Expected Return: Rf + β × (Rm − Rf) (what CAPM predicts for your beta level)
  3. Calculate Alpha: Actual Return − Expected Return (the difference is your alpha)
Time Period Matters: All inputs must be annualized from the same measurement period. A 2% alpha over 1 year may be statistical noise; over 10 years, it's more meaningful.

Alpha vs Other Metrics

Jensen's alpha is one of several risk-adjusted performance measures:

  • Sharpe Ratio: Excess return per unit of total risk (standard deviation)
  • Treynor Ratio: Excess return per unit of systematic risk (beta)
  • Jensen's Alpha: Absolute performance vs CAPM benchmark (measures skill)

While Sharpe and Treynor are ratios that help compare portfolios, alpha is an absolute measure of outperformance or underperformance in percentage points.

Interpreting Results

  • α > 0: Portfolio beat CAPM predictions—suggests good stock selection, market timing, or both
  • α = 0: Portfolio matched CAPM predictions—no value added beyond market exposure
  • α < 0: Portfolio missed CAPM predictions—could indicate poor decisions, high fees, or bad luck

Limitations

While valuable, Jensen's alpha has important limitations:

  • CAPM assumptions: The model assumes market efficiency, single-period returns, and no transaction costs
  • Beta estimation: Alpha is only as reliable as your beta estimate, which varies with methodology
  • Statistical significance: Short-term alpha may be luck; only sustained alpha over multiple years is meaningful
  • Past performance: Historical alpha doesn't guarantee future alpha

Consider using Jensen's alpha alongside the Sharpe ratio, Treynor ratio, and CAPM calculator for a complete picture of portfolio performance.

Frequently Asked Questions

Jensen's alpha measures portfolio performance relative to what the Capital Asset Pricing Model (CAPM) predicts. Named after Michael Jensen who introduced it in 1968, it represents the excess return above or below the theoretical risk-adjusted expectation. Positive alpha indicates outperformance, suggesting manager skill, while negative alpha indicates underperformance.

Jensen's alpha formula is: Alpha = Portfolio Return − [Risk-Free Rate + Beta × (Market Return − Risk-Free Rate)]. First calculate the expected return using CAPM, then subtract it from the actual portfolio return. For example, if your portfolio returned 12%, risk-free rate is 4.5%, beta is 1.0, and market returned 10%, alpha = 12% − [4.5% + 1.0 × (10% − 4.5%)] = 12% − 10% = 2%.

Any positive alpha suggests outperformance versus CAPM expectations. Generally, alpha between 1-3% indicates moderate outperformance, while above 3% suggests strong performance. However, alpha interpretation depends heavily on the time period, benchmark selection, and statistical significance. Short-term alpha may be noise; sustained alpha over 5+ years is more meaningful.

Beta measures systematic risk—how much a portfolio moves relative to the market. Beta of 1 means market-equivalent volatility. Alpha measures excess performance above what beta-adjusted risk would predict. A portfolio can have high beta (risky) but positive alpha (skilled management), or low beta (conservative) but negative alpha (underperforming). They measure different aspects of portfolio characteristics.

Yes, Jensen's alpha can be negative. Negative alpha indicates the portfolio underperformed what CAPM predicted given its risk level. This could indicate poor stock selection, bad market timing, high fees eroding returns, or simply bad luck over the measurement period. Many actively managed funds show negative alpha after accounting for fees.

Jensen's alpha is derived directly from CAPM. CAPM predicts expected return as: E(R) = Rf + Beta × (Rm − Rf). Alpha is the difference between actual return and this CAPM-predicted return. If markets were perfectly efficient and CAPM perfectly accurate, all portfolios would have zero alpha. Persistent non-zero alpha challenges the efficient market hypothesis.
Disclaimer

This calculator is for educational and informational purposes only. Jensen's alpha is a historical measure that uses past data and may not predict future performance. The rating thresholds are educational approximations, not fixed industry standards. Alpha significance depends on measurement period, statistical significance, and benchmark selection. Investment decisions should consider multiple factors beyond risk-adjusted returns. Always consult with a qualified financial advisor before making investment decisions.

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