Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of portfolios selection among a vast pool of assets, as demonstrated by Fan, Zhang, and Yu. The required high-dimensional volatility matrix can be estimated by using high-frequency financial data. This enables us to better adapt to the local volatilities and local correlations among a vast number of assets and to increase significantly the sample size for estimating the volatility matrix. This article studies the volatility matrix estimation using high-dimensional, high-frequency data from the perspective of portfolio selection. Specifically, we propose the use of pairwise-refresh time and all-refresh time methods based on the concept of refresh time proposed by Barndorff-Nielsen, Hansen, Lunde, and Shephard for the estimation of vast covariance matrix and compare their merits in the portfolio selection. We