An investor holds a position that includes $100,000$$ invested in $10-$year US govern$-$

ment bond futures construct $($UGB$),$ and $100,000$$ invested in a US stock index futures

construct $($UXF$).$ Their annual volatilities are $5$ and $20$ percent, respectively with corre$-$

lation of $-0\mathrm{.}5.$ Assume that the returns are normally distributed. Confidence level is $5$

$\%.$

a$)$ Calculate VaR of the individuals and the portfolio.

b$)$ What is the marginal and component VaR of UGB and UXF

c$)$ What is the incremental VaR from setting UGB to zero