  We investigate a solution for the problems related to the application of
multivariate GARCH models to markets with a large number of stocks by
restricting the form of the conditional covariance matrix. The model is a
factor model and uses only six free GARCH parameters. One factor can be
interpreted as the market component, the remaining factors are equal. This
allow the analytical calculation of the inverse covariance matrix. The
time-dependence of the factors enables the determination of dynamical beta
coefficients. We compare the results from our model with the results of other
GARCH models for the daily returns from the S\&P500 market and find that they
are competitive. As applications we use the daily values of beta coefficients
to confirm a transition of the market in 2006. Furthermore we discuss the
relationship of our model with the leverage effect.
