Problem 5. Value-at-Risk (15 points) Value at Risk (VaR) is an attempt to provide a single number for senor management summarizing the total risk in...

Problem 5. Value-at-Risk (15 points)

Value at Risk (VaR) is an attempt to provide a single number for senor management summarizing the total risk in a portfolio of financial assets. It has become widely used by corporate treasurers and fund managers as well as by financial institutions.

A company currently has $5 million invested in commodity X and $3 million invested in commodity Y. The daily sigma of commodity X is 1 percent, the daily sigma of commodity Y is 1.5 percent, and the coefficient of correlation between returns from the two commodities is 0.7. What is the total investment's VaR for the next 10 days with a 99 percent confidence level?