The returns on the common stock of Maynard Cosmetic Specialties are quite cyclical. In a boom economy, the stock is expected to return 22 percent in comparison to 9 percent in a normal economy and a negative 14 percent in a recessionary period. The probability of a recession is 35 percent while the probability of a boom is 10 percent. What is the standard deviation of the returns on this stock?

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RenatoMattice RenatoMattice · Answer 1 · 2019-07-22T07:51:45+02:00

Answer: 12.51%

Explanation: Probability of normal = 100 - (35+10)=55%

Expected return = Respective return*Respective Probability

= (22*0.1)+(9*0.55)+(-14*0.35) = 2.25%

When

(a) Return = 22% , Probability = 0.1

[tex]\therefore Probability\times (Return-Expected Return)^2[/tex]

[tex]0.1\times(22-2.25)^2=39.006[/tex]

(b) Return = 9%, Probability = 0.55

[tex]\therefore Probability\times (Return-Expected Return)^2[/tex]

[tex]0.55\times(9-2.25)^2=25.05[/tex]

(b) Return = -14%, Probability = 0.35

[tex]\therefore Probability\times (Return-Expected Return)^2[/tex]

[tex]0.35\times(-14-2.25)^2=92.42[/tex]

Total=156.48%

[tex]Standard deviation= [Total Probability \times (Return-Expected Return)^{2}\div Total probability]^{1/2}[/tex]

Standard deviation = 12.51%