Long-Horizon Event Study

Definition

A long-horizon event study measures the buy-and-hold abnormal return (BHAR) of a sample of firms over 2–5 years following a corporate event (Initial Public Offering (IPO), seasoned equity offering, stock repurchase, merger, etc.) relative to a benchmark that captures expected returns. The goal is to test whether abnormal returns are zero under a given asset-pricing model, i.e., whether prices incorporate the event-related information immediately or with a long delay.

Key Ideas

Two statistical problems distinguish long-horizon from short-horizon event studies:
1. Non-normality: Compounding T monthly returns produces a right-skewed buy-and-hold distribution; the Student t-test is misspecified even asymptotically if skewness grows fast enough.
2. Cross-sectional dependence: Corporate events cluster in calendar time (IPO waves, merger waves). Firms overlapping in calendar time share unpriced industry factors, generating positive residual correlations. Conventional tests that assume independence are too narrow and over-reject.
Three biases in the conventional benchmark approach (Barber-Lyon 1997): new-listing bias (benchmark contains recently listed firms with abnormally low returns), rebalancing bias (benchmark assumes periodic rebalancing while event-firm returns are compounded without rebalancing), and skewness bias (right-skewed distribution implies the Student t-distribution's null has mean below zero).
Bootstrap approach (Ikenberry-Lakonishok-Vermaelen 1995): Replace each event firm with a characteristic-matched control and repeat 2,000 times. Fails because: (a) replacement firms may have systematically different residual SDs; (b) replacement firms are uncorrelated by construction while the original sample is not. Both biases make the bootstrap density too narrow.
Calendar-time portfolio (Fama 1998): Aggregates event firms into a portfolio by month; eliminating cross-sectional dependence. Disadvantage: time-varying factor loadings and portfolio composition complicate inference.
Bayesian predictive approach (Brav 2000): Fit a Seemingly Unrelated Regression (SUR) model per industry with Bayesian shrinkage priors on residual SDs and a common equicorrelation ρ; simulate the predictive distribution of the sample mean by compounding draws from the posterior predictive of single-period returns. The resulting null density correctly accounts for both non-normality and cross-correlation.

How It Works

Brav (2000) decomposes the N-firm SUR system:

$Y = F\iota + V, \quad V \sim \mathcal{N}(0, \Sigma), \quad \Sigma = SRS$

(Multivariate Normal, MVN)

where S is diagonal with firm-specific SDs σᵢ and R is an equicorrelation matrix with common ρ. Priors: log(σᵢ) ~ N(s̄, δ_σ) (lognormal, Empirical Bayes centered at industry grand mean); ρ ~ Uniform on the positive-definite support. Non-conjugate conditionals for ρ and σᵢ are sampled by Griddy-Gibbs. Given M posterior draws {Σⱼ}, simulate K vectors of monthly returns for each draw → compound into buy-and-hold returns → construct the predictive distribution of the industry-level sample mean → aggregate across industries.

Why It Matters

Inference in long-horizon studies is notoriously fragile to benchmark choice. The Brav approach provides a principled unified treatment of both statistical complications and shows that the popular bootstrap understates null distribution width by ~30% for IPO samples. Applied to 1,521 IPOs (1975–1984), the characteristic-based model (size and book-to-market matched portfolios) cannot be rejected while the Fama-French three-factor model is decisively rejected — the IPO factor loadings predict much higher returns than were realised.

Open Questions