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_s, after one year and a $1 invested in a bond fund yields 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 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?

(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%? (you can show your work using algebra, or calculus).

*Please explain it step-by-step, and please no reposted answers for the same question. Thank you!