1.7.5 Failure Modes & Real-World Practice

Basic Prerequisites: 04 · Statistical Testing.

---

1. Intuition & Practical Objective

Short-horizon event studies are, per Kothari–Warner, “relatively straightforward and trouble-free” and represent “the cleanest evidence we have on efficiency” (Fama 1991). But that reliability holds only if the design avoids a specific set of traps. This page names the traps precisely so a practitioner knows which assumption broke and how the failure shows up in the numbers. The objective is not cynicism - it is knowing exactly where an event study becomes unreliable so the design can be hardened.

The main failures, in one line each:

1. Event-window contamination - a second value-relevant event inside the window gets attributed to the event of interest.
2. Non-synchronous trading - thin stocks have OLS market-model $\beta$ that is biased and inconsistent (Brown–Warner 1985 §2.2).
3. Cross-sectional correlation / event-date clustering - inflates the t-stat by $\sqrt{1+(N-1)\rho }$.
4. Event-period variance increase - volatility rises around events, so estimation-window SEs understate it and the test over-rejects.
5. Long-horizon joint-test problem & low power - risk-adjustment error compounds; long-window inference is “treacherous.”

---

2. Mathematical Ground Truth & Derivations

Non-synchronous trading bias. When the security and the market index are measured over different intervals (a thin stock doesn’t trade every day), OLS estimates of the market-model $\beta$ are biased and inconsistent (Scholes–Williams 1977, p. 324; Dimson 1979, p. 197; Brown–Warner 1985 §2.2). With daily data the bias “can be severe.” The Scholes–Williams correction adds one-lagged and one-led market betas:

$${\hat{\beta }}_{SW}=\frac{{\hat{\beta }}_{-1}+{\hat{\beta }}_0+{\hat{\beta }}_{+1}}{1+2{\hat{\rho }}_m},$$

where ${\hat{\beta }}_0$ is the contemporaneous OLS beta, ${\hat{\beta }}_{-1},{\hat{\beta }}_{+1}$ are the betas from regressing the security’s return on the lagged and led market returns, and ${\hat{\rho }}_m$ is the market’s first-order autocorrelation.

Cross-correlation / event-date clustering. If the sample’s abnormal returns have average pairwise correlation ${\rho }_{ij}$, the SE of the cross-sectional mean is inflated by $\sqrt{1+(N-1){\rho }_{ij}}$ (Kothari–Warner eq. 10). Empirical average pairwise correlation in annual BHARs is ~0.02–0.03, so with 100 firms the test statistic is overstated by ~1.7×. The portfolio time-series approach (Brown–Warner 1985 eq. 5) already incorporates cross-sectional dependence by using the variability of the event-portfolio’s time series of returns. For long horizons, the calendar-time portfolio / Jensen-alpha method does the same.

Event-period variance increase. Events are often triggered by (or themselves cause) elevated uncertainty, so event-period return variability exceeds estimation-window variability (Beaver 1968; Patell & Wolfson 1979). Evaluating significance with historical SEs therefore overstates the statistical significance of event-window abnormal performance (Brown–Warner 1980, 1985; Collins & Dent 1984). A variance increase is indistinguishable from abnormal returns differing across sample securities - the two cannot be separated without auxiliary assumptions.

---

3. Computational Implementation - the failures in numbers

Stdlib only.

Experiment 1 - non-synchronous trading biases OLS beta. A stock trades only 60% of days; on non-trading days the observed return is 0. OLS beta is attenuated; Scholes–Williams corrects it toward the truth.

Thin trading drags OLS beta from the true $1.5$ down to $0.87$; the Scholes–Williams correction recovers $0.93$. An uncorrected market model would mis-state expected returns and hence abnormal returns for every thinly-traded firm in the sample.

Experiment 2 - event-period variance inflation of the t-stat. (Full code in 04.) When event-day variance doubles, a naive 5% test rejects the null 16.5% of the time instead of 5% - a directly misspecified significance test. The researcher’s “significant” CAR may just be the variance jump.

---

4. Failure Modes & First-Principles Breakdowns (numbered)

1. Event-window contamination. A same-window merger, earnings surprise, or regulatory change gets wholly attributed to the event of interest. There is no statistical fix - only a short window and careful sample screening (drop firms with other announcements in the window). This is the #1 practice error.
2. Non-synchronous trading. Thin stocks give biased OLS beta (Experiment 1). Use Scholes–Williams or Dimson lag/lead corrections, or restrict to liquid firms. The bias is severe precisely for the small, volatile firms where event effects are largest.
3. Cross-sectional dependence / clustering. Ignoring it inflates the t-stat by up to ~1.7× (KW eq. 10). The portfolio-time-series SE handles it at short horizons; calendar-time portfolios (Jensen alpha) handle it at long horizons. A clustered event (industry-wide regulation) is the worst case.
4. Event-period variance increase. Significance is overstated when estimation-window SEs are used and event-period volatility is higher. Adjust using the event-to-non-event variance ratio, or use nonparametric (rank) tests (Corrado 1989).
5. Long-horizon joint-test problem & low power. Over ≥1 year, risk-adjustment error compounds into economically large abnormal-return error, and the expected-return model choice drives the answer (Kothari–Warner §4.2; Fama 1998: “all models for expected returns are incomplete”). Combined with right skewness and cross-correlation of overlapping BHARs, long-window inference “requires extreme caution” (Kothari–Warner 1997).
6. Partial anticipation / endogenous event timing. If the market anticipates the event (CEO turnover after a crash, or a stock-split after good performance), part of the abnormal return shows up before day 0 and the event sample is non-random. Standard cross-sectional estimates can then be biased (Eckbo, Maksimovic & Williams 1990; Li & Prabhala 2007).

---

5. References

• Brown & Warner (1985), Using Daily Stock Returns, JFE 14(1)
• Kothari & Warner (2007), Econometrics of Event Studies, Handbook of Corporate Finance
• Kothari & Warner (1997), Measuring Long-Horizon Security Price Performance, JFE 43(3) - “extreme caution” on long-window inference; joint-test problem.
• Scholes & Williams (1977) and Dimson (1979)
• Corrado (1989), A Nonparametric Test for Abnormal Security-Price Performance in Event Studies, JFE 23(2)
• Mitchell & Stafford (2000), Managerial Decisions and Long-Term Stock Price Performance, J. Business 73(3)
• Lyon, Barber & Tsai (1999), Improved Methods for Tests of Long-Run Abnormal Stock Returns, J. Finance 54(1) - “the analysis of long-run abnormal returns is treacherous.”

---

6. Connected Graph Bridges

• Back: 04 · Statistical Testing · Index Hub
• Forward: 06 · Advanced Extensions (information content, PEAD - where these failures bite hardest)
• Sibling: Backtesting Hygiene · Statistical Arbitrage & Pairs (microstructure/illiquidity concerns)
• Base: Statistics & Inference · Econometrics & Time Series