Abnormal Return

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Abnormal Return

Definition

An abnormal return is the difference between an investment’s realized return and its expected return over a specified period. It indicates whether an asset or portfolio performed unusually well or poorly relative to what was anticipated.

Formula:
* Abnormal return = Realized return − Expected return

Why it matters

  • Measures risk-adjusted performance relative to a benchmark or model.
  • Helps evaluate a manager’s skill versus market-driven returns.
  • Can signal chance events, structural shifts, or potential fraud and market manipulation.
  • Positive abnormal return = outperformance; negative abnormal return = underperformance.

How expected return is estimated

Expected return is typically estimated using an asset-pricing model or historical averages. A common model is the Capital Asset Pricing Model (CAPM):

CAPM expected return = Risk-free rate + Beta × (Market expected return − Risk-free rate)

Once the expected return is computed, subtract it from the realized return to get the abnormal return.

Cumulative Abnormal Return (CAR)

Cumulative abnormal return (CAR) is the sum of abnormal returns over a chosen event window:
* CAR = Σ (Abnormal returns over the window)

CAR is often measured over short windows (days) to assess the impact of events such as earnings announcements, lawsuits, buyouts, or regulatory changes. Using longer windows or compounding daily abnormal returns can introduce bias.

Examples

  1. Portfolio example:
  2. Risk-free rate = 2%, Market expected return = 15%, Portfolio beta = 1.25, Portfolio realized return = 25%
  3. CAPM expected return = 2% + 1.25 × (15% − 2%) = 18.25%

  4. Abnormal return = 25% − 18.25% = 6.75% (positive outperformance)

  5. Stock example:

  6. Risk-free rate = 5%, Market expected return = 12%, Stock beta = 2, Stock realized return = 9%
  7. CAPM expected return = 5% + 2 × (12% − 5%) = 19%
  8. Abnormal return = 9% − 19% = −10% (underperformance)

Key takeaways

  • Abnormal return quantifies the gap between realized and expected performance.
  • It can be positive or negative and reflects both skill and external factors.
  • CAR aggregates abnormal returns to measure cumulative event effects.
  • Accurate assessment depends on an appropriate model for expected returns.