Problem 5 (15 points, 5 points part (a), 10 points part (b)) Suppose there are two random assets where asset 1 has expected return u1- 8% and standard deviation 1-20% and asset 2 has expected return 2- 20% and standard deviation 2 = 25% and the correlation coefficient 1,2- 0.5. (a) Consider a portfolio of 30% in security 1 and the remaining amount in security 2. Compute the portfolio expected return and standard variance. Solution : portfolio mean is 16.4%, portfolio standard deviation 21.148% (b) Assets 1 and 2 are positively correlated so it seems like forming a portfolio of these assets is not a good idea. Would it ever be worthwhile to form a portfolio of assets 1 and 2 where positive amounts are invested in both assets? Justify your answer numerically Solution: yes, consider that for any positive investment in stock 1 up to and including 45% will result a portfolio of both stock 1 and stock with an expected return greater than 8% but with portfolio standard deviation less than 20%, so if your goal is to get at least 8% then it is worth while to invest in BOTH in the stated way since these portfolios are superior to just stock 1 which achieves 8% in expected return but has 20% standard deviation