Consider an investor who holds a position that includes $500,000 invested in a 10-year Japanese government bond futures contract (YGB) and $500,000 invested in a Japanese stock index futures contract (YXF). Their annual volatilities are 6 and 18 percent respectively, with a correlation of -0.4. Assume that returns are normally distributed and VaR should be measured at 99 percent level.

a) What is the portfolio VaR?

b) What is the portfolio gain from diversification benefits?

c) What is the marginal and component VaR of YGB and YXF?

d) Which of the two assets is better to be removed if you want to reduce VaR?

e) What is the incremental VaR from setting YGB to zero?