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 

0.001290 

0.001325 

0.001360 

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*(ReturnExpected Return)^2 
0.31  13.75  0.31*(13.759.145)^2=6.57386775 
0.48  8.75  0.48*(8.759.145)^2=0.074892 
0.21  3.25  0.21*(3.259.145)^2=7.29771525 
Total=13.946475% 
Standard deviation=[Total probability*(ReturnExpected Return)^2/Total probability]^(1/2)
=(13.946475)^(1/2)
=3.73%(Approx)
Variance=Standard deviation^2
=0.001395(Approx)
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