Skip to main content
◆ ARIA
Log inSign up free
  1. Home
  2. /
  3. Glossary
  4. /
  5. Alpha (Jensen's Alpha)
Risk & Statistics

Alpha (Jensen's Alpha)

Excess return above what CAPM predicts given the asset’s beta — the manager’s skill.

Definition

Jensen's Alpha is the return of an investment minus the return predicted by CAPM for its level of beta. Positive alpha means the asset beat the market on a risk-adjusted basis — interpreted as manager skill or a genuine factor edge. Negative alpha means underperformance. Alpha must be measured net of fees and tested for statistical significance: a positive alpha over 12 months on a single asset is rarely real.

Formula

Alpha = R_p - [ Rf + Beta * (R_m - Rf) ]

where:
  R_p  = portfolio return
  Rf   = risk-free rate
  R_m  = market return
  Beta = portfolio beta

Worked example

A fund returns 16% over a year with beta 1.2 while the market returned 10% and Rf = 4%. CAPM predicts: 4% + 1.2 * (10% - 4%) = 11.2%. Alpha = 16% - 11.2% = 4.8%. The fund generated 4.8% of risk-adjusted excess return.

How ARIA Analyst uses it

ARIA computes rolling alpha versus a chosen benchmark in the Performance Agent and shows whether observed alpha is statistically significant via bootstrap resampling.

Related terms

  • Beta (β)

    Sensitivity of an asset to moves in a benchmark — typically the broad market.

  • Sharpe Ratio

    Risk-adjusted return measured as excess return per unit of total volatility.

  • Walk-Forward Analysis

    A backtesting procedure that retrains the model on a rolling window and tests on the next out-of-sample period.

See Alpha (Jensen's Alpha) in action on any asset

ARIA Analyst computes Alpha (Jensen's Alpha) automatically as part of a hybrid multi-agent investment report — 5 deterministic scoring agents plus AI augmentation (ML ensemble, Bull vs Bear debate, 10 Deep Search agents on Premium). Get yours in seconds.

Try ARIA Analyst free →
← Back to full glossary