The returns on the common stock of Cool Toys are quite cyclical. In a boom economy, the stock is expected to return 23 percent in comparison to 14 percent in a normal economy and a negative 18 percent in a recessionary period. The probability of a recession is 18 percent while the probability of a boom is 22 percent. What is the standard deviation of the returns on this stock

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jepessoa jepessoa · Answer 1 · 2020-08-30T05:33:29+02:00

Answer:

13.71%

Explanation:

the expected returns on the stock:

normal economy = 0.14 x 0.6 = 0.084

boom economy = 0.23 x 0.22 = 0.0506

recessionary economy = -0.18 x 0.18 = -0.0324

expected return = 0.1022

the variance for each economic period:

normal economy = (0.14 - 0.1022)² = 0.00142884

boom economy = (0.23 - 0.1022)² = 0.01633284

recessionary economy = (-0.18 - 0.1022)² = 0.07963684

the variance of the stock's returns:

normal economy = 0.6 x 0.00142884 = 0.000857304

boom economy = 0.22 x 0.01633284 = 0.0035932248

recessionary economy = 0.18 x 0.07963684 = 0.014334631

variance of the stock's returns = 0.018785159

standard deviation of stock's returns = √0.018785159 = 0.137058964 = 13.71%