ABSTRACT
One of the advantages of univariate models is their ease of estimation relative to more complex multivariate specifications. Univariate exponential moving averages (EWMAs) and generalized conditional heteroskedasticity (GARCH) models are therefore routinely used in the financial industry to estimate the VaR of portfolios of stocks over a given time horizon (see, for example, Bauwens et al., 2003). The univariate model, however, must be reestimated every time portfolio weights change. This can be a serious drawback if the portfolio contains large positions in financial instruments with nonlinear payoffs, payoffs that depend on the correlation structure of asset returns, and instruments that require time-consuming numerical procedures for their pricing. This problem does not arise, or it is considerably milder, if estimates of the full variance-covariance matrix are available. The elements of the latter can be directly used to compute the portfolio variance and hence VaR for any set of asset weights.
