A Simplified Approach to Modelling the Co-Movement of Asset Returns

This paper proposes a simplified multivariate GARCH model (the S-GARCH model) that involves the estimation of only univariate GARCH models, both for the individual return series and for the sum and difference of each pair of series. The covariance between each pair of return series is then imputed from these variance estimates. The model that we propose is considerably easier to estimate than existing multivariate GARCH models and does not suffer from the convergence problems that characterize many of these models. Moreover, the model can be easily extended to include more complex dynamics or alternative forms of the GARCH specification. We use the S-GARCH model to estimate the minimum-variance hedge ratio for the FTSE 100 index portfolio, hedged using index futures, and compare it to four of the most widely used multivariate GARCH models. Using both statistical and economic evaluation criteria, we find that the S-GARCH model performs at least as well as the other models that we consider, and in some cases better than them