Question

Problem 6-05 Expected Return: Discrete Distribution A stock's return has the following distribution: Demand for the Company's Products Probability of This Demand Occurring Rate of Return if This Demand Occurs (%) Weak 0.1 -30% Below average 0.2 -8 Average 0.4 15 Above average 0.2 35 Strong 0.1 75 1.0 Calculate the stock's expected return. Round your answer to two decimal places. % Calculate the standard deviation. Round your answer to two decimal places. %

Answer 1

E(r) = [Pi x Ri]

= [0.1 x -30%] + [0.2 x -8%] + [0.4 x 15%] + [0.2 x 35%] + [0.1 x 75%]

= -3% - 1.6% + 6% + 7% + 7.5% = 15.9%

(r) = [{Pi x (E(r) - Ri)²}]^1/2

= [{0.1 x (15.9% + 30%)²} + {0.2 x (15.9% + 8%)²} + {0.4 x (15.9% - 15%)²} + {0.2 x (15.9% - 35%)²} + {0.1 x (15.9% - 75%)²}]^1/2

= [210.68%² + 114.24%² + 0.32%² + 72.96%² + 349.28%²]^1/2 = [747.49%²]^1/2 = 27.34%