When applying Value at Risk (VaR) procedures to specific positions or portfolios, we often focus on developing procedures only for the specific assets in the portfolio. However, since this small portfolio risk analysis ignores information from assets outside the target portfolio, there may be significant information loss. In this paper, we develop a dynamic process to incorporate the ignored information. We also study how to overcome the curse of dimensionality and discuss where and when benefits occur from a large number of assets, which is called the blessing of dimensionality. We find empirical support for the proposed method.​

JEL classification: C13, C14, C32, C55, C58, G32.
Key words and phrases: Value at Risk, blessing of dimensionality, curse of dimensionality high-dimensionality, principal component analysis, multivariate GARCH, factor model.​