Statement I is true - component VaR for individual assets in the portfolio add up to the total VaR for

the portfolio. This property makes component VaR extremely useful for risk disaggregation and

allocation.

Stateent II is incorrect, the incremental VaRs for the positions in a portfolio do not add up to the

portfolio VaR, in fact their sum would be greater.

Statement III is correct. Marginal VaR for an asset or position in the portfolio is by definition the

change in the VaR as a result of a $1 change in that position. Incremental VaR is the change in the VaR

for a portfolio from a new position added to the portfolio - and if that position is $1, it would be

identical to the marginal VaR.

Statement IV is correct, VaR is sub-additive due to the diversification effect. Adding up the VaRs for

all the positions in a portfolio will add up to more than the VaR for the portfolio as a whole (unless all

the positions are 100% correlated, which effectively would mean they are all identical securities

which means the portfolio has only one asset).

Statement V is in incorrect. As explained for Statement I above, component VaR adds up to the VaR

for the portfolio.