A multivariate stochastic volatility model for S&P500 stocks panel in different industries

We estimate a multivariate stochastic volatility model for a panel of stock returns for a number of S&P 500 firms from different industries.  As in the case of a univariate model we use an efficient importance sampling (EIS) method to estimate the likelihood function of the given multivariate system that we analyze.  As opposed to univariate methods where each return is estimated separately for each firm, our results are based on joint estimation that can account for potential common error term interactions based on industry characteristics that cannot be detected by univariate methods. In our analysis we follow a similar methodology of Jun et al. (2009). Considering the joint behavior of the volatility for different stocks in the same industry, we allow for a single common industry factor and J stock-specific factors, where J is equal to the number of stocks in each industry. Hence in total for each industry we have J+1 factors for each industry. Each stock loads the common-industry factor by a factor loading and each idiosyncratic factor specific to itself with the factor loading parameter equal to 1. Our results reveal that there are important differences in the industry effects, something that suggests differential gains to portfolio allocations in the different industries that we examine.  There are differences due to idiosyncratic factors and the common industry factors that suggest that each industry requires a separate treatment in arriving at portfolio allocations. Therefore investors should treat their portfolio allocation differently based on the industry they are investing in.