If the economy booms, Meyer&Co. stock will have a return of 18.5 percent. If the economy goes into a recession, the stock will have a lo

Question

If the economy booms, Meyer&Co. stock will have a return of 18.5 percent. If the economy goes into a recession, the stock will have a loss of 7.6 percent. The probability of a boom is 71 percent while the probability of a recession is 29 percent. What is the standard deviation of the returns on the stock?

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Madelyn 2 weeks 2021-09-11T02:21:21+00:00 1 Answer 0

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    2021-09-11T02:23:02+00:00

    Answer:

    11.84% approx.

    Step-by-step explanation:

    Expected return = Respective return × Respective probabilities

                               = (18.5 × 0.71) + (-7.6 × 0.29)

                               = 10.931%

    Probability          Return          Probability ×(Return – expected return)²

    0.71                         18.5               0.71×(18.5 – 10.931)² = 40.67573

    0.29                        -7.6               0.29×(-7.6 – 10.931)² = 99.585409

                                                                 Total                = 140.261139%

    SD=[\frac{\text{total probability(return-expected return)}^2}{\text{total probability}}]^{(\frac{1}{2})}

    = [\frac{140.261139^2}{140.261139}]^{\frac{1}{2} }

    = 11.84319 ≈ 11.84% approx.

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