Question

Consider the following information: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Recession 0.20 0.04 -0.23 Normal 0.70 0.08 0.14 Boom 0.10 0.14 0.35 Required: (a) Calculate the expected return for Stock A. (Do not round your intermediate calculations.) (b) Calculate the expected return for Stock B. (Do not round your intermediate calculations.) (c) Calculate the standard deviation for Stock A. (Do not round your intermediate calculations.) (d) Calculate the standard deviation for Stock B. (D

Answer 1

a). E(rA) = [Pi x Ri]

= [0.20 x 0.04] + [0.70 x 0.08] + [0.10 x 0.14] = 0.008 + 0.056 + 0.014 = 0.078, or 7.80%

b). E(rB) = [Pi x Ri]

= [0.20 x -0.23] + [0.70 x 0.14] + [0.10 x 0.35] = -0.046 + 0.098 + 0.035 = 0.087, or 8.70%

c). A = [{Pi x (E(r) - Ri)²}]^1/2

= [{0.20 x (0.078 - 0.04))²} + [{0.70 x (0.078 - 0.08)²} + [{0.10 x (0.078 - 0.14)²}]^1/2

= [0.0003 +0.000003+ 0.0004]^1/2 = [0.0007]^1/2 = 0.0260, or 2.60%

d). B = [{Pi x (E(r) - Ri)²}]^1/2

= [{0.20 x (0.087 - (-0.23))²} + [{0.70 x (0.087 - 0.14)²} + [{0.10 x (0.087 - 0.35)²}]^1/2

= [0.0201 + 0.0020 + 0.0069]^1/2 = [0.0290]^1/2 = 0.1702, or 17.02%