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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?

Respuesta :

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%

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

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

= 11.84319 ≈ 11.84% approx.

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