Long-Run Event Studies

Long-run event studies measure the impact of an event over months or years rather than days. They are essential for answering whether the market fully and correctly prices an event at the time of announcement or whether abnormal performance persists afterward. This page covers the three main approaches — Buy-and-Hold Abnormal Returns (BHAR), Cumulative Abnormal Returns (CAR), and the Calendar-Time Portfolio method — along with the methodological challenges that make long-run studies more difficult than short-run analyses.

When Are Long-Run Event Studies Needed?

Use a long-run event study when your research question concerns the market's long-term assessment of an event, not just the immediate reaction. Typical applications include:

• Post-merger performance: Do acquiring firms earn positive or negative abnormal returns in the 1-3 years after a merger?
• Post-IPO returns: Do IPO firms underperform their benchmarks in the long run (the "IPO underperformance" puzzle)?
• Post-earnings announcement drift (PEAD): Do firms with positive earnings surprises continue to outperform for 60-90 trading days?
• SEO underperformance: Do firms that issue seasoned equity offerings underperform afterward?
• Spin-offs and divestitures: What is the long-run value creation from corporate restructuring?

Buy-and-Hold Abnormal Returns (BHAR)

The BHAR approach computes the difference between the compounded return of the event firm and the compounded return of a benchmark over the same holding period. It reflects the actual experience of an investor who buys the stock on the event date and holds it for T periods.

The BHAR for firm i over horizon T is:

BHAR_i(T) = Product(1 + R_i,t) - Product(1 + R_benchmark,t)

where the product runs from t = 1 to T (e.g., T = 12 months or 36 months). The benchmark can be a market index, a matched firm, or a portfolio of matched firms.

# Configure the EventStudy package for BHAR
ps <- ParameterSet$new(return_model = BHARModel$new())

# Set long event window in the request table
request <- tibble(
  event_id = 1:50,
  firm_symbol = firms,
  index_symbol = "SP500",
  event_date = event_dates,
  group = "PostMerger",
  event_window_start = 0,
  event_window_end = 252,   # ~12 months of trading days
  shift_estimation_window = -10,
  estimation_window_length = 250
)

task <- EventStudyTask$new(firm_data, index_data, request)
task <- run_event_study(task, ps)

# Retrieve BHAR for each event
task$get_car()  # CAR over the long window = BHAR

Cumulative Abnormal Returns (CAR)

The CAR approach sums daily or monthly abnormal returns over the holding period without compounding. It is simpler to compute and has better statistical properties than BHAR (the distribution is closer to normal), but it does not reflect the actual investor experience because it ignores compounding.

CAR_i(T) = Sum of AR_i,t from t = 1 to T

For short horizons (up to about 12 months), CAR and BHAR produce similar results. Over longer horizons, the compounding difference grows, and BHAR is generally preferred because it represents the economically relevant quantity (investor wealth).

Calendar-Time Portfolio Approach

The calendar-time portfolio approach avoids many problems of the BHAR and CAR methods by aggregating event firms into a portfolio. Each calendar month, the portfolio includes all firms that experienced the event within the past T months. The portfolio return is then regressed on a factor model (e.g., Fama-French three-factor or five-factor), and the intercept (alpha) measures the abnormal return.

# Step 1: For each calendar month, identify event firms
#   (firms with events in the past 36 months)

# Step 2: Compute equal-weighted or value-weighted portfolio return

# Step 3: Regress portfolio excess returns on factor model
library(lmtest)
library(sandwich)

# Example: Fama-French 3-factor regression
ct_model <- lm(
  portfolio_excess ~ mkt_rf + smb + hml,
  data = calendar_time_data
)

# Use Newey-West standard errors for autocorrelation
coeftest(ct_model, vcov = NeweyWest(ct_model, lag = 3))

# The intercept (alpha) is the monthly abnormal return
# Multiply by T for cumulative abnormal return

Comparing the Three Approaches

Methodological Challenges

Long-run event studies face several well-documented problems that do not arise in short-run studies. Being aware of these challenges is essential for producing credible results.

New Listing Bias

When the benchmark is a market index or broad portfolio, firms that enter the benchmark after the event date are included in the benchmark return but not in the event sample. These new listings tend to be smaller and riskier, which biases the benchmark return. This is particularly problematic for IPO studies where the relevant comparison group (other IPOs) is systematically different from the full market.

Skewness in BHAR Returns

Compounded returns are bounded below at -100% but unbounded above. Over long horizons, this produces a severe right skew in the BHAR distribution. Standard t-tests, which assume symmetry, perform poorly. Solutions include using the skewness-adjusted t-test of Lyon, Barber, and Tsai (1999) or bootstrapped p-values.

Cross-Correlation

With long event windows, multiple events frequently overlap in calendar time. This creates cross-sectional dependence that inflates test statistics. The calendar-time portfolio approach is the most effective solution.

Benchmark Sensitivity

Long-run results are highly sensitive to the choice of benchmark. Small differences in benchmark returns compound over time, producing large differences in measured abnormal performance. A study may find significant underperformance with one benchmark and no abnormal performance with another.

Best Practices

• Report multiple methods: Present BHAR, CAR, and calendar-time portfolio results. If all three agree, the finding is robust. If they disagree, discuss why.
• Use multiple benchmarks: Test with a market index, size-matched firms, and size/book-to-market matched firms. Report all results.
• Address skewness: For BHAR inference, use the skewness-adjusted t-test or bootstrapped p-values rather than standard t-tests.
• Include delisting returns: Firms that delist during the holding period (due to bankruptcy, acquisition, or going private) must be included with their delisting returns. Ignoring them creates survivorship bias.
• Check for confounding: Over 12-36 months, many other events occur. Consider whether your results might be driven by systematic confounding (e.g., all event firms are also in the same industry that experienced a downturn).
• Use the calendar-time approach for clustered events: If your events cluster in time (IPO waves, merger waves), the calendar-time portfolio approach is essential.

Implementation in R

library(EventStudy)
library(tidyverse)

# --- BHAR approach ---
ps_bhar <- ParameterSet$new(return_model = BHARModel$new())

request_long <- tibble(
  event_id = 1:nrow(events),
  firm_symbol = events$symbol,
  index_symbol = "SP500",
  event_date = events$date,
  group = events$group,
  event_window_start = 1,       # Start day after event
  event_window_end = 252,       # 12 months
  shift_estimation_window = -10,
  estimation_window_length = 250
)

task_bhar <- EventStudyTask$new(firm_data, index_data, request_long)
task_bhar <- run_event_study(task_bhar, ps_bhar)

# BHAR results
bhar_results <- tidy.EventStudyTask(task_bhar, type = "ar")

# --- CAR approach (Market Model) ---
ps_car <- ParameterSet$new(return_model = MarketModel$new())

task_car <- EventStudyTask$new(firm_data, index_data, request_long)
task_car <- run_event_study(task_car, ps_car)

car_results <- tidy.EventStudyTask(task_car, type = "aar")

# --- Compare BHAR and CAR ---
cat("Mean BHAR (12 months):", mean(bhar_results$car), "\n")
cat("Mean CAR  (12 months):", tail(car_results$caar, 1), "\n")

# Skewness-adjusted t-test (Lyon, Barber, Tsai 1999)
bhar_values <- bhar_results$car
n <- length(bhar_values)
mean_bhar <- mean(bhar_values)
sd_bhar <- sd(bhar_values)
skew <- (1/n) * sum(((bhar_values - mean_bhar) / sd_bhar)^3)

# Adjusted t-statistic
t_conv <- mean_bhar / (sd_bhar / sqrt(n))
t_adj <- t_conv + (1/3) * skew * (1/sqrt(n)) +
         (1/6) * skew^2 * t_conv / n

cat("Conventional t:", round(t_conv, 3), "\n")
cat("Skewness-adjusted t:", round(t_adj, 3), "\n")
cat("p-value (adjusted):", round(2 * pt(-abs(t_adj), df = n - 1), 4), "\n")

Literature

• Barber, B.M. & Lyon, J.D. (1997). Detecting long-run abnormal stock returns: The empirical power and specification of test statistics. Journal of Financial Economics, 43(3), 341-372.
• Lyon, J.D., Barber, B.M. & Tsai, C.-L. (1999). Improved methods for tests of long-run abnormal stock returns. Journal of Finance, 54(1), 165-201.
• Mitchell, M.L. & Stafford, E. (2000). Managerial decisions and long-term stock price performance. Journal of Business, 73(3), 287-329.
• Fama, E.F. (1998). Market efficiency, long-term returns, and behavioral finance. Journal of Financial Economics, 49(3), 283-306.
• Kothari, S.P. & Warner, J.B. (2007). Econometrics of event studies. In Handbook of Corporate Finance, Vol. 1.

What Should I Do Next?

• Expected Return Models — the BHAR Model and other benchmarks
• Choosing the Right Test Statistic — select appropriate tests for your study design
• Inference & Robustness — bootstrap and multiple testing corrections
• Cross-Sectional Regression — analyze determinants of long-run abnormal returns