Sensitivity analysis of portfolio properties with budget constraints (Q548468)

Summary: We develop a framework for understanding how variations of portfolio properties are apportioned to changes in portfolio composition as trading is performed in the presence of budget constraints. Our approach is based on the concept of constrained derivative. It allows one to obtain the simultaneous sensitivity of portfolio properties w.r.t. assets groups for any choice of pivotal asset. Analytical expressions for the sensitivity of portfolio returns, variance, GARCH volatility and Value at Risk (VaR) are derived. A numerical exemplification is proposed with reference to the 30 assets of the Dow Jones Index.