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 10% and 8% respectively, and standard deviation of 5% and 3% respectively. The correlation between and is 0.65. 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 9.4% return on your investment? For that same share i.e. invested in bond, what level of risk (in terms of standard deviation) 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).