1- (6 pts) Suppose you have some money to invest-for simplicity, $1-and are planning to put a fraction w into a stock market mutual fund and the rest (1-w), into a bond mutual fund. Suppose that a $1 invested in a stock fund yields R after one year and a $1 invested in a bond fund yields R. Rs and R are random variables with expected value of 10% and 8% respectively, and standard deviation of 4% and 2% respectively. The correlation between Rs and R, is 0.80. 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 + (1 -w)R, .The risk associated with 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 its associated risk? (2pts) 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 stock, what level of risk is associated with your investment? (2pts) C. What share of your $1 money should you invest in stock mutual fund in order for your investment risk to be 3%? (you can show your work using algebra, or calculus). (2pts)