This paper provides an analysis of asset allocation using univariate portfolio GARCH models from the Athens Stock Exchange. We use daily data for the period January 1997 to February 2005. Our analysis adopts the methodology due to Manganelli (2004) and we are able to recover from the univariate approach the multivariate dimension of the portfolio allocation problem. Manganelli (2004) suggests that such a dual problem can be solved with the application of a variance sensitivity analysis which considers the change in the portfolio variance induced by an infinitesimal change in the portfolio allocation. Our main findings are based on the estimation of the variance sensitivity for a portfolio of two assets and the way sensitivity has been changing over time and this has implications for risk management. In addition we compute the second derivative of the estimated variance with respect to portfolio weights and this gives an indication of the benefits arising from diversification at any given point of time.