I- (6 pts) Suppose you have some money to invest-for simplicity, $1-and are planning to put a fraction into a stock market mutual fund and the rest ( ), into a bond mutual fund. Suppose that a $1 invested in a stock fund yields after one year and a $1 invested in a bond fund yields . and are random variables with expected value of 9% and 6% respectively, and standard deviation of 5% and 3% respectively. The correlation between and is 0.70. If you place a fraction of your money in the stock fund and the rest ( ), in the bond fund then the return on your investment will be . The risk associated with your investment is measured by the standard deviation.

a. If you decide to invest 60% of your $1 in stock and the rest in bond, then what is the expected return of your investment? What is its associated risk?

b. What share of your $1 money should you invest in bond in order to expect a 8% return on your investment? For that same share i.e. invested in stock, what level of risk is associated with your investment?

c. What share of your $1 money should you invest in stock mutual fund in order for your investment risk to be 4%? (you can show your work using algebra, or calculus).