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Suppose the risk measure R is VaR() for some . Let P1 and P2 be two portfolios whose returns have a joint normal distribution with

Suppose the risk measure R is VaR() for some . Let P1 and P2 be two portfolios whose returns have a joint normal distribution with means 1 and 2, standard deviations 1 and 2, and correlation . Suppose the initial investments are S1 and S2.

Show that R(P1+P2) R(P1)+R(P2)

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