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 yields Rs after one year and a $1 invested in a bond fund yields Rb. Rs and Rb are random variables with expected value of 9% and 6% respectively, and standard deviation of 5% and 3% respectively. The correlation between Rs and Rb 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 = wRs+(1-w)Rb. 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%?