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

I mean the RRiskModel...is that my index e.g. the S&P?

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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.

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