Abstract
The authors propose a simplified multivariate GARCH (generalized autoregressive conditional heteroscedasticity) model (the SโGARCH model), which 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 proposed model 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. The SโGARCH model is used to estimate the minimumโvariance hedge ratio for the FTSE (Financial Times and the London Stock Exchange) 100 Index portfolio, hedged using index futures, and compared to four of the most widely used multivariate GARCH models. Using both statistical and economic evaluation criteria, it was found that the SโGARCH model performs at least as well as the other models that were considered, and in some cases it was better. ยฉ 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:575โ598, 2007