You are a manager at Ventus LLC$,$ a producer of onshore wind farms. You are planning two large projects, one in Massachusetts and one in New York. While some companies have already committed to purchase energy from the wind farms, there is some risk that the projects will fail and generate a loss for the company. The CEO has asked you to give her your risk assessment of the two projects. You have to decide whether you want to pitch Based on historical data, you calculated the loss probabilities. Suppose that each of two projects has a $4\%$ chance of a loss of $$10$ million, a $2\%$ chance of a loss of $$1$ million, and a $94\%$ chance of a profit of $$1$ million. Since the two wind farms are located in two different US states, you can assume that they are independent of each other. Answer the following questions:

$1)$ What is the VaR for one of the projects when the confidence level is $95\%?$

Options:

a$.$ $$10$ million

b$.$$$1$ million

c$.$ $$400$ thousand

d$.$ $$20$ thousand

e$.$ $$420$ thousand

$2)$ What is the VaR for one of the projects when the confidence level is $99\%?$

Options:

a$.$$$10$ million

b$.$ $$1$ million

c$.$ $$400$ thousand

d$.$ $$20$ thousand

e$.$ $$420$ thousand

$3)$ What is the VaR for a portfolio consisting of the two projects when the confidence level is $95\%?$

Options:

a$.$ $$10$ million

b$.$ $$0$ million

c$.$ $$9$ million

d$.$ $$11$ million

e$.$ $$20$ million

f$.$ $$2$ million

$4)$ What is the VaR for a portfolio consisting of the two projects when the confidence level is $99\%?$

Options:

a$.$ $$10$ million

b$.$ $$0$ million

c$.$ $$9$ million

d$.$ $$11$ million

e$.$ $$20$ million

f$.$ $$2$ million

$5)$ Comparing the VaR for the individual projects versus the portfolio approach, which presents least risk to the CEO?

Options:

a$.$ The portfolio approach since the VaR is lower

b$.$ The individual project approach since VaR is higher

c$.$ Go with individual projects because VaR is always subadditive

d$.$ Depends on the chosen confidence level

e$.$ Not enough information to be able to calculate risk