For the last few weeks I studied GARCH with respect to individual assets. Now I want to combine assets and execute a multivariate (DCC) GARCH test. Let us say that I have a portfolio containing four assets. By using a software called G@RCH I obtained the conditional variance of the portfolio. Now I want to use this conditional variance of the portfolio to calculate the Value at Risk (abbreviated as VaR).
With univariate GARCH one could multiply the variance with the probability density function to obtain the Value at Risk. However, I’m not sure how I should perform this procedure for a multivariate GARCH!
I want to explain my thoughts and I hope someone can confirm or improve my way of thinking! I have a multivariate DCC student t-distribution GARCH which gives me the conditional variance for day t+1. Now I make an equally weighted portfolio times series from the individual returns (so 25%*asset1+25%*asset2+25%*asset3+25%*asset) to perform an univariate student t-distribution GARCH procedure to obtain the density function. Then I multiply this density function with the conditional variance to obtain the Value at Risk for the portfolio.
Is it correct to assume that the univariate GARCH distribution function will give me the correct density function as input for the Value at Risk formula?