Question

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?

Answer 1

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

$\therefore Probability\times (Return-Expected Return)^2$

$0.1\times(22-2.25)^2=39.006$

(b) Return = 9%, Probability = 0.55

$\therefore Probability\times (Return-Expected Return)^2$

$0.55\times(9-2.25)^2=25.05$

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

$\therefore Probability\times (Return-Expected Return)^2$

$0.35\times(-14-2.25)^2=92.42$

Total=156.48%

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

Standard deviation = 12.51%