Question

# The rate of return on the common stock of a company is expected to be 13.75%...

The rate of return on the common stock of a company is expected to be 13.75% in a boom economy, 8.75% in a normal economy, and only 3.25% in a recessionary economy. The probabilities of these economic states are 31.0% for a boom, 48.0% for a normal economy, and 21.0% for a recession. What is the variance of the returns on the common stock of the company?

 0.001255 0.00129 0.001325 0.00136 0.001395

Expected return=Respective return*Respective probability

=(0.31*13.75)+(0.48*8.75)+(0.21*3.25)=9.145%

 probability Return probability*(Return-Expected Return)^2 0.31 13.75 0.31*(13.75-9.145)^2=6.57386775 0.48 8.75 0.48*(8.75-9.145)^2=0.074892 0.21 3.25 0.21*(3.25-9.145)^2=7.29771525 Total=13.946475%

Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)

=(13.946475)^(1/2)

=3.73%(Approx)

Variance=Standard deviation^2

=0.001395(Approx)

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