Suppose you have some money to invest for simplicity, $1 and are planning to put a fraction w into a stock market mutual find and the rest, 1-w, into a bond mutual fund. Suppose that a $1 invested in a stock fund yeilds R_s after one year and a $1 invested in a bond fund yeilds R_b. R_s and R_b are random variables with expected value of 10% and 8% respectively, and standard deviation of 4% and 2% respectively. The correlation between R_s and R_b is 0.70. If you place a fraction w of your money in the stock fund and the rest, 1-w, in the bond fund then the return on your investment will be R = wR_s+(1-w)R_b. The risk associated wuth your investment is measured by the standard deviation.

a) If you decide to invest 40% of your $1 in stock and the rest in bond, then what is the expected return of your investment? What is the associated risk?

b) What share of your $1 money should you invest in bond in order to expect a 9.2% return on your investment? For that same share invested in bond, 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 3%.