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?