Question

Consider the following information:

  

Rate of Return if State Occurs

  State of Economy

Probability of State of Economy

Stock A

Stock B

  Recession

0.10

0.03

-0.18

  Normal

0.50

0.08

0.16

  Boom

0.40

0.13

0.31

Required:

(a)	Calculate the expected return for Stock A. (Do not round your intermediate calculations.)
	(Click to select)9.50%7.52%11.22%9.70%8.63%

  

(b)	Calculate the expected return for Stock B. (Do not round your intermediate calculations.)
	(Click to select)18.60%9.67%20.53%17.67%19.34%

  

(c)	Calculate the standard deviation for Stock A. (Do not round your intermediate calculations.)
	(Click to select)3.20%2.26%3.36%3.04%3.33%

  

(d)	Calculate the standard deviation for Stock B. (Do not round your intermediate calculations.)
	(Click to select)14.10%9.97%15.81%13.40%14.67%

Answer 1

Expected return=Respective return*Respective probability

Expected return for A=(0.1*3)+(0.5*8)+(0.4*13)=9.50%

Probability	Return	Probability*(Return-Mean)^2
0.1	3	0.1*(3-9.5)^2=4.225
0.5	8	0.5*(8-9.5)^2=1.125
0.4	13	0.4*(13-9.5)^2=4.9
		Total=10.25%

Standard deviation for A=[Total Probability*(Return-Mean)^2/Total probability]^(1/2)

which is equal to

=3.20%(Approx).

Expected return for B=(0.1*-18)+(0.5*16)+(0.4*31)=18.60%

Probability	Return	Probability*(Return-Mean)^2
0.1	-18	0.1*(-18-18.6)^2=133.956
0.5	16	0.5*(16-18.6)^2=3.38
0.4	31	0.4*(31-18.6)^2=61.504
		Total=198.84%

Standard deviation for B=[Total Probability*(Return-Mean)^2/Total probability]^(1/2)

which is equal to

=14.10%(Approx)