When researchers reach for Python

Python is the natural choice when the event study is one step in a larger data pipeline: scraping or querying prices, merging with deal or fundamentals data, and feeding results into a machine-learning or panel model. This tutorial builds the same estimator as the R tutorial so results match exactly; only the syntax differs.

Setup: pandas, numpy, statsmodels

import numpy as np
import pandas as pd
import statsmodels.api as sm
from scipy import stats

# panel: DataFrame[firm, date, price]
# market: DataFrame[date, mkt_price]
# events: DataFrame[firm, event_date]
EST_WIN = (-250, -11)   # estimation window in event time
EVT_WIN = (-5, 5)       # event window in event time

Step 1: Load prices, align trading days, compute returns

Compute simple returns $R_t = P_t/P_{t-1}-1$ per firm, attach the market return, and index each row in event time relative to the firm's event date.

panel = panel.sort_values(["firm", "date"]).copy()
panel["ret"] = panel.groupby("firm")["price"].pct_change()

market = market.sort_values("date").copy()
market["mkt"] = market["mkt_price"].pct_change()

df = (panel
      .merge(market[["date", "mkt"]], on="date", how="inner")
      .merge(events, on="firm", how="inner")
      .dropna(subset=["ret", "mkt"]))

# Event-time offset: 0 on the first trading day on/after the event date.
def add_event_time(g):
    g = g.sort_values("date").reset_index(drop=True)
    k = (g["date"] >= g["event_date"]).idxmax()
    g["rel_day"] = g.index - k
    return g

df = df.groupby("firm", group_keys=False).apply(add_event_time)

Step summary. Use groupby(firm).pct_change() for returns, merge the market return, and build an event-time index where rel_day = 0 is the event date.

Step 2: Fit the market model and extract alpha and beta

$$R_{i,t} = \alpha_i + \beta_i R_{m,t} + \varepsilon_{i,t}, \qquad t \in [T_0, T_1].$$

def fit_market_model(g):
    est = g[(g.rel_day >= EST_WIN[0]) & (g.rel_day = EST_WIN[1])]
    X = sm.add_constant(est["mkt"])
    res = sm.OLS(est["ret"], X).fit()
    M = len(est)
    return pd.Series({
        "alpha":   res.params["const"],
        "beta":    res.params["mkt"],
        "s_ar":    np.sqrt(res.ssr / (M - 2)),   # residual SD, M-2 dof
        "M":       M,
        "mkt_bar": est["mkt"].mean(),
        "mkt_ss":  ((est["mkt"] - est["mkt"].mean()) ** 2).sum(),
    })

params = df.groupby("firm").apply(fit_market_model).reset_index()

Step summary. Fit OLS(ret, const + mkt) per firm on the estimation window and keep alpha, beta, the residual standard deviation $S_{AR_i}=\sqrt{SSR/(M-2)}$, and $M_i$.

Step 3: Vectorised abnormal returns, CAR and CAAR

$$AR_{i,t} = R_{i,t} - (\hat\alpha_i + \hat\beta_i R_{m,t}), \quad CAR_i = \sum_{t} AR_{i,t}, \quad CAAR = \frac{1}{N}\sum_i CAR_i.$$

evt = (df[(df.rel_day >= EVT_WIN[0]) & (df.rel_day = EVT_WIN[1])]
       .merge(params, on="firm"))
evt["ar"] = evt["ret"] - (evt["alpha"] + evt["beta"] * evt["mkt"])

aar  = evt.groupby("rel_day")["ar"].mean()              # AAR path
car  = evt.groupby("firm")["ar"].sum().rename("car")    # CAR per firm
caar = car.mean()
N    = car.shape[0]

Step 4: Significance tests in Python

Cross-sectional t-test: $t = \sqrt{N}\,CAAR/S_{CAAR}$ with $S_{CAAR}^2=\frac{1}{N-1}\sum_i(CAR_i-CAAR)^2$.

# (a) Cross-sectional t-test.
s_caar = car.std(ddof=1)
t_cs   = np.sqrt(N) * caar / s_caar
p_cs   = 2 * stats.t.sf(abs(t_cs), df=N - 1)

Patell Z: standardise each AR by its forecast-error-adjusted SD, then aggregate. $S_{AR_{i,t}}^2 = S_{AR_i}^2\!\left(1+\frac{1}{M_i}+\frac{(R_{m,t}-\bar R_m)^2}{\sum(R_{m,s}-\bar R_m)^2}\right)$ and $z=\frac{1}{\sqrt N}\sum_i CSAR_i/S_{CSAR_i}$ with $S_{CSAR_i}^2=L_2\frac{M_i-2}{M_i-4}$.

# (b) Patell Z.
evt["fe_var"] = evt["s_ar"]**2 * (1 + 1/evt["M"]
                + (evt["mkt"] - evt["mkt_bar"])**2 / evt["mkt_ss"])
evt["sar"] = evt["ar"] / np.sqrt(evt["fe_var"])

g = evt.groupby("firm")
csar = g["sar"].sum()
L2   = g.size()
M    = g["M"].first()
var_cs = L2 * (M - 2) / (M - 4)            # L2 * (M-2)/(M-4)
z_i  = csar / np.sqrt(var_cs)
z_patell = z_i.sum() / np.sqrt(len(z_i))
p_patell = 2 * stats.norm.sf(abs(z_patell))

BMP (standardized cross-sectional) test: $t_{BMP}=\sqrt N\,\overline{SCAR}/S_{\overline{SCAR}}$ with $SCAR_i=CAR_i/S_{CAR_i}$, robust to event-induced volatility (Boehmer, Musumeci & Poulsen, 1991).

# (c) BMP test. Compute SCAR_i = CAR_i / S_CAR_i per firm, where S_CAR_i^2
# scales the residual variance to the event window with its own
# forecast-error correction (full expression on /significance-tests).
def scar_per_firm(sub):
    L2 = len(sub)
    M  = sub["M"].iloc[0]
    s  = sub["s_ar"].iloc[0]
    fe = ((sub["mkt"] - sub["mkt_bar"].iloc[0])**2).sum() / sub["mkt_ss"].iloc[0]
    s_car = np.sqrt(s**2 * (L2 + L2/M + fe))
    return sub["ar"].sum() / s_car

scar = evt.groupby("firm").apply(scar_per_firm)
t_bmp = np.sqrt(len(scar)) * scar.mean() / scar.std(ddof=1)
p_bmp = 2 * stats.t.sf(abs(t_bmp), df=len(scar) - 1)

print(f"CAAR={caar:.4f} | t_cs={t_cs:.2f} (p={p_cs:.3f}) | "
      f"Patell Z={z_patell:.2f} (p={p_patell:.3f}) | BMP t={t_bmp:.2f} (p={p_bmp:.3f})")

Step summary. The cross-sectional t-test gives a quick read; the Patell Z corrects for estimation error and unequal variances; the BMP test adds robustness to event-induced volatility.

Step 5: Plotting the CAAR path

import matplotlib.pyplot as plt
caar_path = aar.sort_index().cumsum()        # CAAR builds as cumulative AAR
ax = caar_path.plot(marker="o")
ax.axvline(0, ls="--", lw=1)                  # event day
ax.axhline(0, color="0.6", lw=0.8)
ax.set_xlabel("Event time (days)"); ax.set_ylabel("CAAR")
plt.tight_layout(); plt.show()

The CAAR path is the running sum of AAR across event time. A step at rel_day = 0 with a flat pre-event line is the textbook efficient-reaction pattern; a slope that begins before day 0 suggests information leakage.

No-code alternative: the free ARC calculator

The ARC calculator runs this same pipeline from a CSV upload. Choose the model on Expected-return models, the tests on Significance tests, upload, and download AR, CAR, CAAR and every statistic.

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