Question

Based on the following information, calculate the standard deviation of Stock A.

Round all intermediate calculations to 6 decimal places. State of the Economy Probability of State Occurring Return of Stock A if State Occurs Recession 0.20 0.03 Normal 0.50 0.08 Boom 0.30 0.12

a. 3.81% b. 8.20% c. 3.12% d. 9.76%

Answer 1

Expected return=respective return*Respective probability

=(0.2*3)+(0.5*8)+(0.3*12)=8.2%

probability	Return	probability(Return-Expected Return)^2
0.2	3	0.2*(3-8.2)^2=5.408
0.5	8	0.5*(8-8.2)^2=0.02
0.3	12	0.3*(12-8.2)^2=4.332
		Total=9.76%

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

=3.12%(Approx).