Answer:
portfolio's standard deviation = 6.18%
Explanation:
we must first determine the expected returns for each stock:
stock A = (0.15 x 31%) + (0.6 x 16%) + (0.2 x -3%) + (0.05 x -11%) = 13.1%
stock B = (0.15 x 41%) + (0.6 x 12%) + (0.2 x -6%) + (0.05 x -16%) = 11.35%
stock C = (0.15 x 21%) + (0.6 x 10%) + (0.2 x -4%) + (0.05 x -8%) = 7.95%
then we must determine the variance of each stock's return:
stock A = {[0.15 x (31 - 13.1)²] + [0.6 x (16 - 13.1)²] + [0.2 x (-3- 13.1)²] + [0.05 x (-11 - 13.1)²]} / 4 = (48.0615 + 5.046 + 51.842 + 29.0405) / 4 = 33.4975
stock B = {[0.15 x (41 - 11.35)²] + [0.6 x (12 - 11.35)²] + [0.2 x (-6- 11.35)²] + [0.05 x (-16 - 11.35)²]} / 4 = (131.868375 + 0.2535 + 60.2045 + 37.401125) / 4 = 57.4219
stock C = {[0.15 x (21 - 7.95)²] + [0.6 x (10 - 7.95)²] + [0.2 x (-4- 7.95)²] + [0.05 x (-8 - 7.95)²]} / 4 = (25.545375 + 2.5215 + 28.5605 + 12.720125) / 4 = 17.3369
portfolio's variance = (0.3 x 33.4975) + (0.4 x 57.4219) + (0.3 x 17.3369) = 38.21908
portfolio's standard deviation = √38.21908 = 6.18%
