What Is the Abnormal Return Formula and How Is It Calculated?

Investors and analysts use abnormal return to measure how a stock or portfolio performs compared to expectations. This helps determine whether an investment’s gains or losses stem from market movements or specific factors like company news, economic events, or investor sentiment. Understanding how to calculate abnormal return is essential for evaluating investment performance beyond general market trends.

Formula Breakdown

Abnormal return is calculated by comparing an asset’s actual performance to its expected performance based on historical data or market conditions. This requires three components: actual return, expected return, and the difference between them.

Actual Return

Actual return represents the percentage change in an investment’s value over a specific period, including both price appreciation and dividends. The formula is:

Actual Return = [(Ending Price – Beginning Price) + Dividends] / Beginning Price × 100

For example, if an investor buys a stock at $50, it rises to $55, and they receive a $2 dividend, the actual return is:

[(55 – 50) + 2] / 50 × 100 = 14%

This figure shows how much the investment’s value changed over the period but does not account for broader market trends, which is why it must be compared to the expected return.

Expected Return

Expected return estimates what an investment should earn based on historical data, market models, or financial theories. One common method for calculating it is the Capital Asset Pricing Model (CAPM):

Expected Return = Risk-Free Rate + Beta × (Market Return – Risk-Free Rate)

Where:
– Risk-Free Rate is typically represented by government bond yields.
– Market Return is measured using a broad index like the S&P 500.
– Beta represents the stock’s sensitivity to market movements.

For instance, if the risk-free rate is 2%, the market return is 8%, and a stock has a beta of 1.2, the expected return is:

2% + 1.2 × (8% – 2%) = 9.2%

This provides a benchmark for how the investment should have performed given its risk level and market conditions.

Abnormal Return

Abnormal return is the difference between actual and expected return:

Abnormal Return = Actual Return – Expected Return

Using the previous examples, if a stock’s actual return was 14% and its expected return was 9.2%, the abnormal return is:

14% – 9.2% = 4.8%

A positive abnormal return suggests the investment outperformed expectations, possibly due to company-specific events or investor optimism. A negative abnormal return indicates underperformance, which could be due to adverse news or broader economic concerns.

Adjusting for Market Benchmarks

Comparing a stock’s performance to broader market benchmarks helps determine whether an abnormal return is due to company-specific factors or general market trends. Investors often use indices like the S&P 500, Dow Jones Industrial Average, or Nasdaq Composite as reference points. If a stock’s return deviates significantly from the market, it suggests influences beyond overall economic conditions.

One method for adjusting for benchmarks is market-adjusted return, which subtracts the market index return from the stock’s return. For example, if a stock gained 12% while the S&P 500 rose 8%, the market-adjusted return is 4%. This isolates the stock’s unique performance by filtering out general market movements.

Another approach involves risk-adjusted measures like the Sharpe ratio, which accounts for volatility. A stock that generates higher returns but with excessive risk may not be as attractive as one with steadier gains. By incorporating standard deviation into the analysis, investors can determine whether higher returns were achieved efficiently or resulted from excessive risk.

Interpreting the Results

Understanding abnormal returns requires more than just calculating the difference between actual and expected performance. The reasons behind an investment’s deviation matter. A positive abnormal return might indicate strong fundamentals, such as revenue growth or cost efficiency, but it could also result from short-term speculation. A pharmaceutical company’s stock might surge after FDA approval of a new drug, reflecting a justified gain, whereas a sudden spike due to social media hype may not be sustainable.

The duration and consistency of abnormal returns also provide insight. A one-time deviation may not hold much predictive value, but repeated outperformance or underperformance suggests underlying trends. Persistent positive abnormal returns could indicate strong fundamentals, while continuous negative deviations may point to structural weaknesses, such as declining market share or poor management decisions.

Market efficiency plays a role as well. In highly efficient markets, abnormal returns are often short-lived because new information is quickly priced in. If a stock consistently generates excess returns, it may indicate inefficiencies or undiscovered value. In contrast, in less efficient markets, price discrepancies can persist, creating opportunities for investors who can identify mispricings before they are corrected.