Question

What is the expected return on this stock given the following information?

State of the Economy	Probability	E(R)
Boom	0.4	15	%
Recession	0.6	-20	%

Multiple Choice

-8.07 percent

-6.00 percent

-5.20 percent

-5.70 percent

-7.69 percent

A portfolio consists of the following securities. What is the portfolio weight of stock A?

Stock	#Shares	PPS
A	200	$	48
B	100	$	33
C	250	$	21

Multiple Choice

0.389

0.451

0.336

0.529

0.445

What is the variance of the expected returns on this stock?

State of the Economy	Probability	E(R)
Boom	0.35	18.00
Recession	0.65	8.00

Multiple Choice

50.03

22.75

18.75

48.97

31.53

An investor owns a security that is expected to return 10 percent in a booming economy and 3 percent in a normal economy. The overall expected return on the security is 5.45 percent. Given there are only two states of the economy, what is the probability that the economy will boom? Multiple Choice 45 percent 28 percent 35 percent 41 percent 33 percent

Answer 1

1.Expected return=Respective return*Respective probability

=(0.4*15)+(0.6*-20)

=(6%)(Negative).

2.

Total value of A=(200*48)=$9600

Total value of B=(100*33)=$3300

Total value of C=(250*21)=$5250

Total value =$18150
Hence portfolio weight of A=(9600/18150)

=0.529(Approx).

3.

Expected return=(0.35*18)+(0.65*8)

=11.5%

Probability	Return	Probability*(Return-Mean)^2
0.35	18	0.35*(18-11.5)^2=14.7875
0.65	8	0.65*(8-11.5)^2=7.9625
		Total=22.75%

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

=4.77(Approx)

Hence variance=Standard deviation^2

=22.75

4.

Let probability of boom=x

Hence probability of normal economy=(1-x)

Expected return=(10*x)+(3*(1-x)

5.45=10x+3-3x

(5.45-3)=7x

x=(2.45/7)

=35%