Question

A stock's return has the following distribution:

Calculate the standard deviation. Round your answer to two decimal places

Demand for the Company's Products	Probability of This Demand Occurring			Rate of Return if This Demand Occurs (%)
Weak		0.1		-25%
Below average		0.2		-5
Average		0.4		8
Above average		0.2		25
Strong		0.1		55
		1.0

Answer 1

Expected return=Respective return*Respective probability

=(0.1*-25)+(0.2*-5)+(0.4*8)+(0.2*25)+(0.1*55)

=10.2%

probability	Return	probability*(Return-Expected Return)^2
0.1	-25	0.1*(-25-10.2)^2=123.904
0.2	-5	0.2*(-5-10.2)^2=46.208
0.4	8	0.4*(8-10.2)^2=1.936
0.2	25	0.2*(25-10.2)^2=43.808
0.1	55	0.1*(55-10.2)^2=200.704
		Total=416.56%

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

=(416.56)^(1/2)

=20.41%(Approx)