Question

Your portfolio is invested 30 percent each in Stocks A and C, and 40 percent in Stock B. What is the standard deviation of your portfolio given the following information?
Rate of Return if State Occurs
State of Economy Probability of State of Economy Stock A Stock B Stock C
Boom 0.15 0.31 0.41 0.21
Good 0.60 0.16 0.12 0.10
Poor 0.20 -0.03 -0.06 -0.04
Bust 0.05 -0.11 -0.16 -0.08

Answer 1

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%