# 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?

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.