xjtulyc Event Study Methodology in Finance
Event studies measure the impact of corporate or macroeconomic events on asset prices by comparing actual returns to a counterfactual (normal return model). This skill covers the classic short-window CAR approach, non-parametric rank tests, the Fama-French 3-factor model for normal returns, and long-run buy-and-hold abnormal returns (BHAR).
1. Setup
pip install yfinance pandas numpy scipy statsmodels matplotlib
import numpy as np
import pandas as pd
import yfinance as yf
import statsmodels.api as sm
from scipy import stats
import matplotlib.pyplot as plt
import matplotlib.dates as mdates
from datetime import timedelta
import warnings
warnings.filterwarnings("ignore", category=FutureWarning)
# ---------------------------------------------------------------------------
# Estimation window and event window conventions
# ---------------------------------------------------------------------------
EST_START = -250 # trading days before event date
EST_END = -11 # trading days before event date (exclude pre-event window)
EVT_START = -5 # trading days relative to event (inclusive)
EVT_END = +5 # trading days relative to event (inclusive)
2. Data Download
def download_returns(
tickers: list[str],
market_ticker: str = "^GSPC",
start: str = "2010-01-01",
end: str = "2024-12-31",
) -> tuple[pd.DataFrame, pd.Series]:
"""
Download adjusted closing prices and compute log returns.
Parameters
----------
tickers : list[str]
Stock tickers to download.
market_ticker : str
Market index ticker (default: S&P 500).
start, end : str
Date range for download.
Returns
-------
tuple of (stock_returns DataFrame, market_returns Series)
Both use log returns: log(P_t / P_{t-1}).
"""
all_tickers = list(set(tickers + [market_ticker]))
raw = yf.download(all_tickers, start=start, end=end, auto_adjust=True, progress=False)
if isinstance(raw.columns, pd.MultiIndex):
prices = raw["Close"]
else:
prices = raw[["Close"]]
log_ret = np.log(prices / prices.shift(1)).dropna()
market_ret = log_ret[market_ticker].rename("market")
stock_rets = log_ret[[t for t in tickers if t in log_ret.columns]]
return stock_rets, market_ret
3. Normal Return Estimation (Market Model OLS)
def estimate_normal_returns(
ret_series: pd.Series,
market_ret: pd.Series,
event_date: pd.Timestamp,
est_window: tuple[int, int] = (EST_START, EST_END),
) -> dict:
"""
Estimate normal return parameters using the OLS market model on the
estimation window.
Parameters
----------
ret_series : pd.Series
Daily log returns for one stock.
market_ret : pd.Series
Daily log returns for the market index.
event_date : pd.Timestamp
The event date (day 0).
est_window : tuple
(start_offset, end_offset) relative to event_date in trading days.
Returns
-------
dict with keys: alpha, beta, sigma, r2, n_obs.
"""
# Align stock and market returns
combined = pd.concat([ret_series.rename("stock"), market_ret], axis=1).dropna()
dates = combined.index.tolist()
# Find event_date position
if event_date not in combined.index:
# Use nearest available date
pos = combined.index.searchsorted(event_date)
pos = min(pos, len(dates) - 1)
else:
pos = dates.index(event_date)
# Estimation window indices
est_s = max(0, pos + est_window[0])
est_e = max(0, pos + est_window[1])
est_data = combined.iloc[est_s:est_e]
if len(est_data) < 50:
raise ValueError(f"Estimation window too short ({len(est_data)} obs). "
"Extend the sample or choose an earlier event date.")
X = sm.add_constant(est_data["market"])
ols = sm.OLS(est_data["stock"], X).fit()
return {
"alpha": ols.params["const"],
"beta": ols.params["market"],
"sigma": ols.resid.std(),
"r2": ols.rsquared,
"n_obs": len(est_data),
}
4. Abnormal Returns and CAR
def compute_car(
ret_series: pd.Series,
market_ret: pd.Series,
event_date: pd.Timestamp,
model_params: dict,
event_window: tuple[int, int] = (EVT_START, EVT_END),
) -> pd.Series:
"""
Compute abnormal returns (AR) and cumulative abnormal return (CAR)
over the event window.
Parameters
----------
ret_series : pd.Series
Stock daily log returns.
market_ret : pd.Series
Market daily log returns.
event_date : pd.Timestamp
Day 0.
model_params : dict
Output of estimate_normal_returns().
event_window : tuple
(start_offset, end_offset) relative to event_date.
Returns
-------
pd.Series of cumulative abnormal returns indexed by relative day.
"""
combined = pd.concat([ret_series.rename("stock"), market_ret], axis=1).dropna()
dates = combined.index.tolist()
if event_date not in combined.index:
pos = min(combined.index.searchsorted(event_date), len(dates) - 1)
else:
pos = dates.index(event_date)
evt_s = max(0, pos + event_window[0])
evt_e = min(len(dates), pos + event_window[1] + 1)
evt_data = combined.iloc[evt_s:evt_e].copy()
# Abnormal returns = actual - (alpha + beta * market)
evt_data["expected"] = (model_params["alpha"]
+ model_params["beta"] * evt_data["market"])
evt_data["AR"] = evt_data["stock"] - evt_data["expected"]
evt_data["CAR"] = evt_data["AR"].cumsum()
# Relative event day index
rel_days = list(range(event_window[0], event_window[0] + len(evt_data)))
evt_data.index = rel_days[:len(evt_data)]
return evt_data["AR"], evt_data["CAR"]
5. Statistical Tests
5.1 Cross-Sectional t-Test and BMP Test
def test_car_bmp(
cars: np.ndarray,
t_stats: np.ndarray,
) -> dict:
"""
Test H0: mean CAR = 0 using:
(1) Cross-sectional t-test (Fama, 1969)
(2) Boehmer-Musumeci-Poulsen (BMP, 1991) standardized cross-sectional test
Parameters
----------
cars : np.ndarray
Array of per-firm CARs over the event window.
t_stats : np.ndarray
Per-firm t-statistics (AR / sigma_i * sqrt(L)), where L is event window length.
Returns
-------
dict with keys: mean_car, t_cs, p_cs, t_bmp, p_bmp.
"""
n = len(cars)
mean_car = np.mean(cars)
std_car = np.std(cars, ddof=1)
# (1) Cross-sectional t-test
t_cs = mean_car / (std_car / np.sqrt(n))
p_cs = 2 * (1 - stats.t.cdf(abs(t_cs), df=n - 1))
# (2) BMP test: based on standardized abnormal returns
mean_t = np.mean(t_stats)
std_t = np.std(t_stats, ddof=1)
t_bmp = mean_t / (std_t / np.sqrt(n))
p_bmp = 2 * (1 - stats.t.cdf(abs(t_bmp), df=n - 1))
return {
"n": n,
"mean_car": round(mean_car * 100, 4), # in percent
"t_cs": round(t_cs, 4),
"p_cs": round(p_cs, 4),
"t_bmp": round(t_bmp, 4),
"p_bmp": round(p_bmp, 4),
}
5.2 Non-Parametric Rank Test (Corrado, 1989)
def rank_test(ar_panel: pd.DataFrame) -> dict:
"""
Corrado (1989) non-parametric rank test.
Parameters
----------
ar_panel : pd.DataFrame
Rows = event-window days (relative index), columns = firms.
Values are abnormal returns.
Returns
-------
dict with z-statistic and p-value.
"""
# Rank within each firm across the combined estimation + event period
# Approximate: rank within the event window only
ranks = ar_panel.rank(axis=0) # rank across event days, per firm
n, T = ar_panel.shape
# Expected rank under H0
K_bar = (T + 1) / 2
rank_excess = ranks - K_bar
# Cross-sectional average of rank excess at each event day
mean_rank_t = rank_excess.mean(axis=1)
sigma_rank = rank_excess.std(axis=1).mean()
# Z at day 0 (relative day = 0)
if 0 in mean_rank_t.index:
z_stat = mean_rank_t.loc[0] / (sigma_rank / np.sqrt(n))
else:
z_stat = mean_rank_t.iloc[T // 2] / (sigma_rank / np.sqrt(n))
p_val = 2 * (1 - stats.norm.cdf(abs(z_stat)))
return {"z_stat": round(float(z_stat), 4), "p_value": round(p_val, 4)}
6. Fama-French 3-Factor Normal Returns
def ff3_normal_returns(
ret_series: pd.Series,
ff3_factors: pd.DataFrame,
event_date: pd.Timestamp,
est_window: tuple[int, int] = (EST_START, EST_END),
) -> dict:
"""
Estimate normal returns using the Fama-French 3-factor model.
Parameters
----------
ret_series : pd.Series
Excess returns of the stock (ret - rf). Index = DatetimeIndex.
ff3_factors : pd.DataFrame
Columns: ['Mkt-RF', 'SMB', 'HML', 'RF']. Obtainable from
Ken French's data library (https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html).
event_date : pd.Timestamp
Day 0.
est_window : tuple
Estimation window offsets.
Returns
-------
dict with OLS params and sigma.
"""
combined = pd.concat(
[ret_series.rename("stock_excess"), ff3_factors[["Mkt-RF", "SMB", "HML"]]],
axis=1,
).dropna()
dates = combined.index.tolist()
if event_date not in combined.index:
pos = min(combined.index.searchsorted(event_date), len(dates) - 1)
else:
pos = dates.index(event_date)
est_s = max(0, pos + est_window[0])
est_e = max(0, pos + est_window[1])
est = combined.iloc[est_s:est_e]
X = sm.add_constant(est[["Mkt-RF", "SMB", "HML"]])
ols = sm.OLS(est["stock_excess"], X).fit()
return {
"alpha": ols.params["const"],
"b_mkt": ols.params["Mkt-RF"],
"b_smb": ols.params["SMB"],
"b_hml": ols.params["HML"],
"sigma": ols.resid.std(),
"r2": ols.rsquared,
}
7. Long-Run BHAR
def compute_bhar(
ret_series: pd.Series,
market_ret: pd.Series,
event_date: pd.Timestamp,
months: int = 36,
) -> float:
"""
Compute the buy-and-hold abnormal return (BHAR) over a post-event window.
BHAR = prod(1 + r_i,t) - prod(1 + r_m,t) over `months` calendar months.
Parameters
----------
ret_series : pd.Series
Stock daily log returns.
market_ret : pd.Series
Market daily log returns.
event_date : pd.Timestamp
Listing / event date.
months : int
Number of months for long-run window.
Returns
-------
float: BHAR in decimal form.
"""
combined = pd.concat([ret_series.rename("stock"), market_ret], axis=1).dropna()
end_date = event_date + pd.DateOffset(months=months)
window = combined.loc[event_date:end_date]
if len(window) < 20:
return np.nan
# Compounded gross returns (log to simple)
bhr_stock = np.exp(window["stock"].sum()) - 1
bhr_market = np.exp(window["market"].sum()) - 1
return bhr_stock - bhr_market
8. Event Study Plot
def plot_event_study_car(
car_means: pd.Series,
ci_low: pd.Series,
ci_high: pd.Series,
event_window: tuple[int, int],
title: str = "Cumulative Abnormal Returns",
) -> plt.Figure:
"""
Plot mean CAR with 95% confidence interval across the event window.
Parameters
----------
car_means : pd.Series
Mean CAR at each relative event day.
ci_low, ci_high : pd.Series
95% CI lower and upper bounds.
event_window : tuple
(start_day, end_day).
title : str
Chart title.
Returns
-------
matplotlib Figure.
"""
days = car_means.index
fig, ax = plt.subplots(figsize=(10, 5))
ax.plot(days, car_means * 100, color="steelblue", linewidth=2, label="Mean CAR")
ax.fill_between(days, ci_low * 100, ci_high * 100,
alpha=0.25, color="steelblue", label="95% CI")
ax.axvline(0, color="red", linestyle="--", linewidth=1.2, label="Event Day 0")
ax.axhline(0, color="black", linewidth=0.7)
ax.set_xlabel("Trading Days Relative to Event")
ax.set_ylabel("CAR (%)")
ax.set_title(title, fontsize=13, fontweight="bold")
ax.legend()
ax.set_xticks(range(event_window[0], event_window[1] + 1))
plt.tight_layout()
return fig
9. Example A — FDA Approval Announcement CAR [-1, +1]
import pandas as pd
import numpy as np
# ---- Event list: (ticker, announcement_date) -----------------------------------
events = [
("MRNA", "2020-12-18"),
("BNTX", "2021-08-23"),
("PFE", "2021-08-23"),
("NVAX", "2022-07-13"),
]
START_DATE = "2018-01-01"
END_DATE = "2023-06-30"
EVENT_WIN = (-1, 1) # tight window for FDA news
tickers = list({t for t, _ in events})
stock_rets, market_ret = download_returns(tickers, market_ticker="^GSPC",
start=START_DATE, end=END_DATE)
all_cars, all_tstats = [], []
for ticker, evt_date_str in events:
if ticker not in stock_rets.columns:
print(f"Skipping {ticker}: not in downloaded data.")
continue
evt_date = pd.Timestamp(evt_date_str)
ret_s = stock_rets[ticker]
try:
params = estimate_normal_returns(ret_s, market_ret, evt_date,
est_window=(EST_START, EST_END))
ar_series, car_series = compute_car(ret_s, market_ret, evt_date,
params, event_window=EVENT_WIN)
car_val = car_series.iloc[-1]
# Standardised t-stat for BMP
L = len(EVENT_WIN[0] - EVENT_WIN[0]) + (EVENT_WIN[1] - EVENT_WIN[0]) + 1
t_stat = car_val / (params["sigma"] * np.sqrt(L))
all_cars.append(car_val)
all_tstats.append(t_stat)
print(f"{ticker} ({evt_date_str}): "
f"CAR[-1,+1] = {car_val*100:.2f}%, "
f"alpha={params['alpha']:.5f}, beta={params['beta']:.3f}")
except Exception as exc:
print(f"{ticker}: error — {exc}")
if all_cars:
result = test_car_bmp(np.array(all_cars), np.array(all_tstats))
print("\n=== CAR Test Results ===")
for k, v in result.items():
print(f" {k}: {v}")
10. Example B — Long-Run BHAR for Post-IPO Performance (36 Months)
import pandas as pd
import numpy as np
# ---- Simulated IPO events (use real data from SDC Platinum or similar) ----------
ipo_events = [
("SNOW", "2020-09-16"),
("COIN", "2021-04-14"),
("RIVN", "2021-11-10"),
("UBER", "2019-05-10"),
("LYFT", "2019-03-29"),
]
START_DATE = "2019-01-01"
END_DATE = "2024-12-31"
MONTHS = 36
tickers = list({t for t, _ in ipo_events})
stock_rets, market_ret = download_returns(tickers, market_ticker="^GSPC",
start=START_DATE, end=END_DATE)
bhar_results = []
for ticker, ipo_date_str in ipo_events:
if ticker not in stock_rets.columns:
print(f"Skipping {ticker}: no data.")
continue
ipo_date = pd.Timestamp(ipo_date_str)
bhar = compute_bhar(stock_rets[ticker], market_ret, ipo_date, months=MONTHS)
bhar_results.append({"ticker": ticker, "ipo_date": ipo_date_str,
"bhar_36m": round(bhar * 100, 2) if not np.isnan(bhar) else np.nan})
print(f"{ticker} ({ipo_date_str}): {MONTHS}-month BHAR = {bhar*100:.2f}%"
if not np.isnan(bhar) else f"{ticker}: insufficient data")
bhar_df = pd.DataFrame(bhar_results)
print("\n=== Long-Run IPO BHAR Summary ===")
print(bhar_df.to_string(index=False))
mean_bhar = bhar_df["bhar_36m"].mean()
se_bhar = bhar_df["bhar_36m"].std() / np.sqrt(len(bhar_df))
t_stat = mean_bhar / se_bhar if se_bhar > 0 else np.nan
print(f"\nMean BHAR: {mean_bhar:.2f}%")
print(f"t-statistic: {t_stat:.3f}")
print("(Negative BHAR is typical for IPOs — long-run underperformance puzzle)")
# ---- Bar chart ------------------------------------------------------------------
fig, ax = plt.subplots(figsize=(9, 4))
colors = ["steelblue" if v >= 0 else "tomato" for v in bhar_df["bhar_36m"]]
ax.bar(bhar_df["ticker"], bhar_df["bhar_36m"], color=colors, edgecolor="white")
ax.axhline(0, color="black", linewidth=0.8)
ax.set_ylabel("36-Month BHAR (%)")
ax.set_title("Post-IPO Long-Run Abnormal Returns (36 months)", fontweight="bold")
plt.tight_layout()
plt.savefig("ipo_bhar_36m.png", dpi=150)
plt.show()
11. Tips and Common Pitfalls
- Estimation window contamination: Ensure the estimation window [-250, -11] does not overlap with other major announcements for the same firm. Use [-250, -31] for extra safety around quarterly earnings clusters.
- Non-synchronous trading: For thinly traded stocks, use weekly returns or the Scholes-Williams beta correction for the market model.
- Event-date misalignment: After-market announcements count as the next trading day (day +1). Always verify the announcement time (AMC vs BMO).
- Cross-sectional dependence: If events cluster in calendar time (e.g., industry shocks), individual AR are correlated. Use the calendar-time portfolio approach (Fama, 1998) as a robustness check.
- BHAR vs CAAR: BHAR compounds returns (multiplicative) while CAAR sums them (additive). BHAR better reflects investor wealth; CAAR is easier to test statistically. Use both and compare.
- Benchmark choice for BHAR: Common choices are the value-weighted market index, size-and-BM matched control firms, or the Fama-French 3-factor alpha.