7.5 Event Study Methodology

"Event studies are a way of measuring the impact of an economic event on the value of a firm."— Eugene Fama, 2013 Nobel Laureate in Economics

Evaluating causal effects of specific events: From financial markets to policy evaluation

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Section Objectives

Upon completing this section, you will be able to:

• Understand the basic framework and application scenarios of event study methodology
• Master the calculation of abnormal returns (AR) and cumulative abnormal returns (CAR)
• Build market models to estimate normal returns
• Conduct statistical significance testing (t-test, cross-sectional test)
• Implement complete event study analysis workflow
• Evaluate the impact of merger announcements, policy changes, and other events
• Complete event study implementation using Python

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What is Event Study?

Core Idea

Event Study: Evaluating the impact of a specific event on a variable (usually stock returns).

Basic Logic:

1. If the event hadn't occurred, the outcome variable would follow a "normal" pattern
2. After the event occurs, the difference between observed actual values and "normal" expected values is the event effect
3. This difference is called Abnormal Return

Mathematical Expression:

Classic Application Areas

Field	Typical Events	Research Question
Financial Markets	Merger announcements, earnings announcements, stock splits	Does the event affect stock prices?
Corporate Governance	CEO changes, board restructuring	How do governance changes affect firm value?
Regulatory Policy	New regulations, policy changes	What is the regulatory impact on markets?
Macroeconomics	Central bank rate cuts, fiscal stimulus	Policy impact on asset prices?
Public Policy	Education reforms, environmental regulations	Policy impact on socioeconomic indicators?

Foundational Study: Fama et al. (1969)

Paper: The Adjustment of Stock Prices to New Information

Research Question: How do stock splits affect stock prices?

Findings:

• Before split announcement, stocks show significant abnormal returns (about 33% over 30 months)
• After split announcement, abnormal returns disappear
• Conclusion: Market is efficient, stock prices quickly reflect new information

Impact:

• Pioneered event study methodology
• Provided empirical support for efficient market hypothesis
• Became one of the most commonly used methods in financial economics

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Basic Framework of Event Study

Timeline Design

Timeline
├── Estimation Window
│   ├── T0 to T1 (typically 120-250 days)
│   └── Purpose: Estimate "normal" return model parameters
│
├── Event Window
│   ├── T1 to T2 (typically -10 to +10 days around event)
│   ├── Event Day: t = 0
│   └── Purpose: Calculate abnormal returns
│
└── Post-Event Window
    ├── T2 to T3 (optional)
    └── Purpose: Evaluate long-term effects

Symbol Definitions:

• : Estimation window start
• : Estimation window end = Event window start
• : Event window end
• : Post-event window end
• : Event day

Typical Parameter Choices:

• Estimation window: (250 to 11 trading days before event)
• Event window: (10 trading days before and after event)

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Step 1: Normal Return Models

Common Normal Return Models

1. Market Model (Most Common ⭐)

Definition:

Where:

• : Return of stock at time
• : Market portfolio return at time (e.g., CSI 300 Index)
• : Parameters estimated from estimation window data

Advantages:

• Accounts for overall market volatility
• Eliminates systematic risk
• Simple estimation, intuitive interpretation

2. Mean-Adjusted Return Model

Definition:

Where is the average return of stock in the estimation window.

Normal Return Expectation:

Advantages: Simple, suitable for limited data situations

Disadvantages: Does not account for overall market volatility

3. Market-Adjusted Return Model

Definition:

Assumes all stocks' expected returns equal market return ().

Advantages: No parameter estimation needed

Disadvantages: Assumption too simplified

Model Comparison

Model	Parameters	Advantages	Disadvantages	Use Cases
Market Model		Accounts for market risk	Needs estimation window	⭐ Standard choice
Mean-Adjusted		Simple and intuitive	Ignores market volatility	Limited data
Market-Adjusted	None	No estimation needed	Assumption too strong	Quick analysis

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Step 2: Calculate Abnormal Returns (AR)

Definition of Abnormal Returns

Abnormal Return (AR):

Using Market Model:

Where are parameters estimated by OLS in the estimation window.

Calculate Cumulative Abnormal Returns (CAR)

Cumulative Abnormal Return (CAR):

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Multiple Event Study

Cross-sectional Averaging

When we have multiple events (e.g., multiple company merger announcements), we need to calculate Average Abnormal Return (AAR) and Cumulative Average Abnormal Return (CAAR).

Average Abnormal Return (AAR)

Where is the number of events.

Cumulative Average Abnormal Return (CAAR)

Cross-sectional t-test

Standard Error:

t-statistic:

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Section Summary

Core Steps of Event Study

1. Design Time Windows

   • Estimation window:
   • Event window:

2. Estimate Normal Return Model

   • Market model (recommended):
   • Mean-adjusted model:

3. Calculate Abnormal Returns

   • AR:
   • CAR:

4. Statistical Testing

   • Single-day AR:
   • CAR:
   • Multiple events: Cross-sectional testing of AAR and CAAR

5. Visualization and Interpretation

   • AR bar chart
   • CAR cumulative chart
   • Confidence intervals

Practice Points

Question	Solution
How to choose estimation window length?	Usually 120-250 days, need sufficient data but avoid structural breaks
How long should event window be?	Short-term events (earnings announcements): ±3 days; long-term events (mergers): ±20 days
What if β is unstable?	Use market-adjusted model or Fama-French three-factor model
How to handle event clustering?	Use calendar-time portfolio method
How to test long-term effects?	Use BHAR (Buy-and-Hold Abnormal Returns)

Extensions

1. Fama-French Three-Factor Model

2. Conditional Event Study

   • Group by firm characteristics (size, industry)
   • Group by event characteristics (transaction amount, payment method)

3. Long-term Abnormal Returns

   • BHAR (Buy-and-Hold Abnormal Returns)
   • Calendar-time portfolio method

Next Section Preview

In the next section, we will summarize all content of time series analysis and provide 10 high-difficulty practice exercises.

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Extended Reading

Classic Literature

1. Fama, E. F., Fisher, L., Jensen, M. C., & Roll, R. (1969). "The Adjustment of Stock Prices to New Information." International Economic Review, 10(1), 1-21.

   • Seminal work on event study methodology

2. Brown, S. J., & Warner, J. B. (1985). "Using Daily Stock Returns: The Case of Event Studies." Journal of Financial Economics, 14(1), 3-31.

   • Systematic summary of event study methodology

3. MacKinlay, A. C. (1997). "Event Studies in Economics and Finance." Journal of Economic Literature, 35(1), 13-39.

   • Authoritative review article, must-read

4. Kothari, S. P., & Warner, J. B. (2007). "Econometrics of Event Studies." In Handbook of Corporate Finance: Empirical Corporate Finance, 3-36.

   • Latest methodological review

Applied Literature

1. Andrade, G., Mitchell, M., & Stafford, E. (2001). "New Evidence and Perspectives on Mergers." Journal of Economic Perspectives, 15(2), 103-120.

   • Classic merger event study

2. Kothari, S. P., & Warner, J. B. (1997). "Measuring Long-Horizon Security Price Performance." Journal of Financial Economics, 43(3), 301-339.

   • Long-term abnormal return measurement

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Event Study: Revealing how markets digest new information!