4. Three friends each own portfolios consisting of a diversified stock index fund and short term risk-free Treasury bills. The risk-free rate of return is R_f = 4% and the stock market index fund has an expected return of R_mbar = 10% with a standard deviation of _m = 6%.

For each friend, find the portfolio weights for each investment (w_m and w_rf ), the expected portfolio rate of return, and the portfolio standard deviation of return.

a (12). Tanya has $50,000 to invest. She purchases $30,000 in stocks, and puts the rest into T-bills.

b. (12) Bruce has $25,000 to invest. He borrows an extra $20,000 from his broker at the risk-free rate, and puts all the funds into stocks.

c. (12) Camille has $9000 to invest. She puts all her funds in risk-free T-bills.

d. (14) Suppose after the friends invest, a recession occurs and the actual stock market return is -20%. What rate of return will each friend actually earn in this circumstance? Whose portfolio performed best?