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Event Studies and Causal Measurement in Finance / Abnormal-return measurement

CAR and BHAR

A one-day abnormal return is the announcement residual. The earnings design in this pathway uses a multi-day window, so the researcher has to add those residuals or compound the gross returns.

The sum is the cumulative abnormal return. The compounded gap versus a benchmark is the buy-and-hold abnormal return.

They answer different questions, and on long horizons the sum is a biased predictor of the compound gap. This note writes both, the two aggregation statistics J1J_1 and J2J_2, and the Dow day-0 averages MacKinlay reports.

It does not treat calendar overlap; that is overlapping events.
Learning objectives. By the end of this note you should be able to:
  • form CARi(τ1,τ2)CAR_i(\tau_1,\tau_2) and its large-L1L_1 variance;
  • distinguish J1J_1 from J2J_2 by the alternative each one favours;
  • compute a two-month BHAR from the Barber & Lyon return pair and see why the CAR differs;
  • name the new-listing, rebalancing, and skewness biases that attach to long-run reference-portfolio BHARs.

In this lesson

  1. Cumulative abnormal returns
  2. Averaging across announcements
  3. Buy-and-hold abnormal returns
  4. Audit on the running announcement

Before you start

The full lesson, with worked examples and exercise solutions, is for members.

Read the full lesson

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