Question

Based on the following information, calculate the expected return and standard deviation for two stocks: State of the Economy Probability Rate of Return Stock A Rate of Return Stock B Recession .25 .05 -.19 Normal .50 .06 .14 Boom .25 .10

Answer 1

E(r) = [Pi x Ri]

E(rA) = [0.25 x 5%] + [0.50 x 6%] + [0.25 x 10%] = 1.25% + 3% + 2.5% = 6.75%

E(rB) = [0.25 x -19%] + [0.50 x 14%] + [0.25 x 0%] = -4.75% + 7% + 0% = 2.25%

(r) = [{Pi x (E(rP) - Ri)²}]^1/2

(rA) = [{0.25 x (6.75% - 5%)²} + {0.50 x (6.75% - 6%)²} + {0.25 x (6.75% - 10%)²}]^1/2

= [0.77%² + 0.28%² + 2.64%²]^1/2 = [3.6875%²]^1/2 = 1.92%

(rB) = [{0.25 x (2.25% + 19%)²} + {0.50 x (2.25% - 14%)²} + {0.25 x (2.25% - 0%)²}]^1/2

= [112.89%² + 69.03%² + 1.27%²]^1/2 = [183.19%²]^1/2 = 13.53%