Question

Expected Return: Discrete Distribution

A stock's return has the following distribution:

Demand for the Company's Products	Probability of This Demand Occurring			Rate of Return if This Demand Occurs (%)
Weak		0.1		-30	%
Below average		0.2		-10
Average		0.4		16
Above average		0.2		35
Strong		0.1		65
		1.0

Calculate the stock’s expected return and standard deviation. Do not round intermediate calculations. Round your answers to two decimal places.

Expected return:   %

Standard deviation:   %

Answer 1

Expected return=Respective return*Respective probability

=(0.1*-30)+(0.2*-10)+(0.4*16)+(0.2*35)+(0.1*65)

=14.9%

probability	Return	probability*(Return-Expected Return)^2
0.1	-30	0.1(-30-14.9)^2=201.601
0.2	-10	0.2*(-10-14.9)^2=124.002
0.4	16	0.4*(16-14.9)^2=0.484
0.2	35	0.2*(35-14.9)^2=80.802
0.1	65	0.1*(65-14.9)^2=251.001
		Total=657.89%

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

=25.65%(Approx).