Which of the following are true:I.

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.