Question

Expected Returns: Discrete Distribution

The market and Stock J have the following probability distributions:

Probability	rM	rJ
0.3	15%	22%
0.4	9	4
0.3	19	13

Calculate the expected rate of return for the market. Round your answer to two decimal places.
%

Calculate the expected rate of return for Stock J. Round your answer to two decimal places.
%

Calculate the standard deviation for the market. Do not round intermediate calculations. Round your answer to two decimal places.
%

Calculate the standard deviation for Stock J. Do not round intermediate calculations. Round your answer to two decimal places.

%

Answer 1

For the market:

Expected return=Respective return*Respective probability

=(0.3*15)+(0.4*9)+(0.3*19)=13.8%

probability	Return	probability*(Return-Expected return)^2
0.3	15	0.3*(15-13.8)^2=0.432
0.4	9	0.4*(9-13.8)^2=9.216
0.3	19	0.3*(19-13.8)^2=8.112
		Total=17.76%

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

which is equal to

=4.21%(Approx)

For the Stock J:

Expected return=Respective return*Respective probability

=(0.3*22)+(0.4*4)+(0.3*13)=12.1%

probability	Return	probability*(Return-Expected return)^2
0.3	22	0.3*(22-12.1)^2=29.403
0.4	4	0.4*(4-12.1)^2=26.244
0.3	13	0.3*(13-12.1)^2=0.243
		Total=55.89%

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

which is equal to

=7.48%(Approx)