Empirical Research on Relationships Between Marginal-VaR, Component-VaR and Incremental-VaR - Li, Kai (2013)
The aim of this dissertation is to investigate whether the relationships between Marginal-VaR, Component-VaR and Incremental-VaR demonstrated by Hallerbach (2002) are valid. Marginal-VaR, Component-VaR and Incremental-VaR contribute to portfolio managers to get more information on market risk of a portfolio and make better and faster investment decision-making in diverse financial market. The relationships between Marginal-VaR, Component-VaR and Incremental-VaR does not only provide intuitional and logical perspective when calculating Marginal-VaR, Component-VaR and Incremental-VaR to screen assets to lower overall potential loss, but also offers the ground when converting one of the three indicators to another in mathematics. Thus the precision of the relationships are important. Hallerbach (2002) demonstrates the relationship between Marginal-VaR and Component-VaR when “the portfolio operator is linear”. The study of this dissertation critical evaluated the relationship between Marginal-VaR and Component-VaR and confirms the relationship valid in a more general case even there are non-linear asset is included in the portfolio. Furthermore, Hallerbach (2002) demonstrates the relationship between Marginal-VaR and Incremental-VaR is valid in general case. However, the result of this dissertation shows the relationship is not valid when non-linear asset (option) in contained in the portfolio, and the option lead to the relationship not valid any more.