# Event Study > Event study methodology in finance: estimate abnormal returns, CARs, BMP tests, Fama-French 3-factor normal returns, and long-run BHAR analysis using yfinance. - Skill: `xjtulyc/event-study` (Agent Skill) - Install (CLI): `npx skillmds@latest add xjtulyc/event-study` - Raw SKILL.md: https://api.skillmd.com/api/skills/xjtulyc/event-study/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: MIT - Author: xjtulyc (https://skillmd.com/u/xjtulyc) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/xjtulyc/event-study --- # 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 ```bash pip install yfinance pandas numpy scipy statsmodels matplotlib ``` ```python 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 ```python 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) ```python 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 ```python 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 ```python 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) ```python 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 ```python 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 ```python 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 ```python 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] ```python 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) ```python 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.