Abnormal return

What Is Abnormal Return?

An abnormal return is the difference between the actual return of an investment and its Expected Return, given a specific risk model. This concept is fundamental in Portfolio Theory and financial economics, as it helps measure an investment's performance beyond what would be anticipated based on its inherent risk. When an asset generates an abnormal return, it implies that it has outperformed or underperformed its benchmark after accounting for risk. This metric is crucial for evaluating investment performance, identifying potential market inefficiencies, and assessing the impact of specific events on asset prices.

History and Origin

The concept of abnormal return is deeply intertwined with the development of the Efficient Market Hypothesis (EMH), a theory that postulates asset prices fully reflect all available information, making it impossible to consistently "beat the market" through active management. Eugene Fama significantly contributed to this theory, notably with his influential 1970 paper, "Efficient Capital Markets: A Review of Theory and Empirical Work," which formalized the concept of market efficiency and its implications for asset pricing²⁰, ²¹, ²².

Following the EMH, the idea emerged that any deviation from an asset's expected return, after adjusting for risk, could be considered an abnormal return. This led to the widespread use of models like the Capital Asset Pricing Model (CAPM), developed independently by William Sharpe, Jack Treynor, John Lintner, and Jan Mossin in the early 1960s, to estimate the expected return of an asset¹⁷, ¹⁸, ¹⁹. The CAPM provided a coherent framework for relating an investment's required return to its risk, a critical step in calculating abnormal returns.

The application of abnormal returns became particularly prominent in the Event Study methodology, a research technique developed to examine how asset prices react to specific corporate or macroeconomic events¹⁴, ¹⁵, ¹⁶. Pioneered by researchers building on Fama's work, event studies measure the abnormal change in stock prices around an event, allowing financial economists to infer the economic impact of that event¹², ¹³.

Key Takeaways

• An abnormal return is the difference between an investment's actual return and its expected return, adjusted for risk.
• It serves as a measure of an asset's performance relative to its risk profile.
• The concept is central to assessing Investment Performance and identifying market inefficiencies.
• Abnormal returns are widely used in event studies to quantify the impact of specific information or events on asset prices.
• A positive abnormal return suggests outperformance, while a negative abnormal return indicates underperformance.

Formula and Calculation

The calculation of abnormal return typically involves determining an asset's expected return based on a financial model, then subtracting it from the actual observed return. The most common model used to estimate expected returns is the Capital Asset Pricing Model (CAPM).

The formula for Abnormal Return (AR) is:

Where:

• (AR_t) = Abnormal Return at time t
• (R_t) = Actual Return of the asset at time t
• (E(R_t)) = Expected Return of the asset at time t

When using the CAPM to calculate the expected return, the formula for (E(R_t)) is:

Where:

• (R_f) = Risk-free rate of return
• (\beta_i) = Beta of the asset, representing its Systematic Risk
• (R_m) = Expected market return
• ((R_m - R_f)) = Market risk premium

Therefore, combining these, the abnormal return can also be expressed as:

This calculation allows analysts to isolate the portion of an asset's return that cannot be explained by market movements and its inherent risk.

Interpreting the Abnormal Return

Interpreting an abnormal return requires understanding the context in which it is calculated. A positive abnormal return suggests that the asset or portfolio performed better than what would be predicted by the model, given its level of risk. This outperformance is often referred to as Alpha, and it can indicate a manager's skill, the presence of a market anomaly, or simply luck. Conversely, a negative abnormal return means the investment underperformed its expected benchmark, indicating that it delivered less return than anticipated for its risk.

In the realm of Security Analysis, a consistently positive abnormal return might draw attention to a potential mispricing or an informational advantage. However, due to the concept of Market Efficiency, sustained positive abnormal returns are theoretically difficult to achieve in well-functioning markets.

Hypothetical Example

Consider an investor who purchased shares of Tech Innovations Inc. for a specific period.
Let's assume the following:

• Actual Return ((R_t)) of Tech Innovations Inc. = 15%
• Risk-free rate ((R_f)) = 3%
• Beta ((\beta_i)) of Tech Innovations Inc. = 1.2
• Expected Market Return ((R_m)) = 10%

First, calculate the expected return of Tech Innovations Inc. using the CAPM:
(E(R_t) = R_f + \beta_i (R_m - R_f))
(E(R_t) = 0.03 + 1.2 \times (0.10 - 0.03))
(E(R_t) = 0.03 + 1.2 \times 0.07)
(E(R_t) = 0.03 + 0.084)
(E(R_t) = 0.114) or 11.4%

Next, calculate the abnormal return:
(AR_t = R_t - E(R_t))
(AR_t = 0.15 - 0.114)
(AR_t = 0.036) or 3.6%

In this hypothetical example, Tech Innovations Inc. generated an abnormal return of 3.6%. This means the stock's actual return exceeded its expected return by 3.6 percentage points, after accounting for its systematic risk. This positive abnormal return could be a point of interest for Financial Modeling and further analysis.

Practical Applications

Abnormal returns are a core component of various analyses within finance and investing. One of their most significant applications is in Event Study analysis. Researchers use event studies to determine the impact of corporate actions (like mergers, acquisitions, or earnings announcements), regulatory changes, or macroeconomic shocks on a company's stock price¹⁰, ¹¹. By calculating the abnormal return around the announcement date, they can quantify the market's reaction to the specific event. For instance, an academic paper on event studies outlines how they measure abnormal changes in stock prices associated with events, such as a corporate decision⁹.

Furthermore, abnormal returns are utilized in assessing active Portfolio Management strategies. Investment managers often aim to generate positive abnormal returns (alpha) for their clients, signifying that their active decisions have added value beyond passive market exposure. This is a key metric in evaluating a fund manager's skill rather than simply benefiting from overall market movements. They also play a role in identifying potential Arbitrage opportunities or persistent market anomalies, although the efficient market hypothesis suggests such opportunities should be rare or quickly eliminated.

Limitations and Criticisms

Despite its utility, the concept of abnormal return, particularly in proving sustained outperformance, faces several limitations and criticisms, primarily stemming from challenges in accurately measuring Expected Return and the ongoing debate surrounding Market Efficiency.

One significant challenge is the "joint hypothesis problem." Any test for abnormal returns implicitly tests two hypotheses simultaneously: the efficiency of the market and the correctness of the asset pricing model used to calculate expected returns (e.g., CAPM). If an abnormal return is observed, it's difficult to ascertain whether it's due to market inefficiency or simply an inadequacy in the chosen pricing model⁷, ⁸. The Capital Asset Pricing Model itself has faced empirical challenges and criticisms regarding its simplifying assumptions, such as the assumption that investors can borrow and lend at a risk-free rate or that all investors have homogenous expectations⁶.

Furthermore, the influence of Behavioral Finance has highlighted how psychological biases can lead to temporary deviations from rational pricing, creating apparent abnormal returns that may not be consistently exploitable⁴, ⁵. Critics of strict market efficiency, such as Nobel laureate Richard Thaler, argue that markets can exhibit inefficiencies due to human behavior, leading to phenomena like overreaction that contradict the predictions of the EMH², ³. While some studies attribute forecastability in stock prices to overreaction, suggesting systematic deviations from fundamental values, the evidence does not always create actionable trading opportunities for investors to earn extraordinary Risk-Adjusted Return¹.

Abnormal Return vs. Expected Return

Abnormal return and Expected Return are distinct but related concepts in finance. The expected return is the anticipated rate of return that an investment is projected to yield, typically based on its level of Systematic Risk and the prevailing market conditions. It represents the return an investor should expect to earn for taking on a certain amount of risk, according to a financial model like the Capital Asset Pricing Model.

In contrast, abnormal return is the difference between this anticipated expected return and the actual return achieved by the investment over a given period. It quantifies the degree to which an investment has overperformed or underperformed its theoretical expectation. While expected return is a forward-looking prediction, abnormal return is a backward-looking measurement that indicates the presence of unexpected performance, whether positive or negative, after accounting for the asset's risk. The existence of consistent, positive abnormal returns would challenge the strong forms of the Efficient Market Hypothesis, which suggests that all available information is already reflected in asset prices, leaving no room for sustained outperformance beyond that explained by risk.

FAQs

What does a positive abnormal return indicate?

A positive abnormal return indicates that an investment has generated a return greater than what would be predicted by its risk profile, typically as modeled by the Capital Asset Pricing Model. This outperformance, often referred to as Alpha, can suggest that the investment manager added value, or that there was an unexpected positive event influencing the asset's price.

How is abnormal return different from total return?

Total return is the overall gain or loss of an investment over a period, expressed as a percentage of the initial investment, encompassing all income and capital appreciation. Abnormal return, however, specifically measures the portion of that total return that cannot be explained by the asset's Expected Return for a given level of risk. It isolates the "unexpected" component of performance.

Can abnormal returns be consistently achieved?

Theoretically, in perfectly Market Efficiency, consistently achieving positive abnormal returns is difficult because asset prices are presumed to reflect all available information, making it challenging to find undervalued assets or exploit mispricings. However, some market participants and academics, particularly those in Behavioral Finance, argue that temporary inefficiencies due to investor biases can lead to fleeting opportunities for abnormal returns.

Why is abnormal return important for investors?

For investors, understanding abnormal return is vital for evaluating the true skill of an investment manager, rather than simply attributing good performance to a rising market or higher Systematic Risk. It helps in assessing whether an active management strategy genuinely adds value beyond what could be achieved through passive investing.