Question

Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations. Prob. Economic Conditions Strong Normal Weak a. 21.71% 30% 40% 30% Return 40.0% 10.0% -16.0% O b. 25.18% O c. 17.59% O d. 22.58% O e. 24.75%

Answer 1

Expected Return = ∑i=1n​ [Probability_i * Return_i]

= [0.3 * 40%] + [0.4 * 10%] + [0.3 * (-16%)] = 12% + 4% - 4.8% = 11.20%

Portfolio's Standard Deviation = [∑i=1n​ {Probability_i * (Expected Return - Return_i)²}]^1/2

= [{0.30 * (11.2% - 40%)²} + {0.40 * (11.2% - 10%)²} + {0.30 * (11.2% + 16%)²}]^1/2

= [248.832%² + 0.576%² + 221.952%²]^1/2 = [471.36%²]^1/2 = 21.71%

Hence, Option "a" is correct.