Choosing a Benchmark for Buy-and-Hold Abnormal Returns

Summary

The document considers whether a broad market index can serve as the benchmark in a buy-and-hold abnormal return event study. It presents the calculation as the difference between an event asset’s compounded return and the compounded return of its benchmark over the same period. A familiar composite market index can be used for an individual security’s BHAR.

For an average across multiple event securities, the answer emphasizes applying the same benchmark consistently to each observation before aggregating the results. It also cites a research practice in which benchmark portfolios exclude the event firms while otherwise drawing from eligible firms assigned to size and book-to-market portfolios. The exchange is brief and does not settle which benchmark is suitable for every event or asset class; benchmark choice should reflect the research design and comparison being made.

Key ideas

• BHAR compares an asset’s compounded return with a benchmark’s compounded return over the event window.
• A broad composite market index can be used as an individual security’s benchmark.
• Use the same benchmark across observations when calculating an aggregate BHAR.
• Some research benchmarks exclude event firms and form portfolios based on size and book-to-market characteristics.

Tags

# BHAR Event Study - Index


# BHAR Event Study - Index












I want to perform a BHAR event study. For that, I subtract the compounded returns of a benchmark portfolio from the respective stock:

$$BHAR_{jt} = \prod_{t=T_t}^{T_2}{(1+R_{jt})- \prod_{t=T_t}^{T_2}{(1+R_{\text{RiskModel}})}}$$

Is my assumption right, that I can simply take any underlying index as the benchmark portfolio? E.g., when computing BHAR of US Corporates around a certain event, I can use the simple returns of the Dow Jones or S&P500 as benchmark?

## Answer by develarist (score 1)

https://quant.stackexchange.com/a/46130

Yes, a well-known composite index of the market can be used for $R_{riskmodel}$ in an individual buy-and-hold abnormal return ($BHAR_i$), but has to be used across all $BHAR_i$s in $\bar{BHAR}=\sum_{i=1}^N{w_i \times BHAR_i}$ to make sense.

Mitchell and Stafford (2000) said though that

> The benchmark portfolios exclude event firms, but otherwise they include all CRSP firms that can be assigned to a size-BE/ME portfolio.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.