Question

Given the following information on a portfolio of Stock X and Stock Y, what is the portfolio standard deviation?

Probability of boom state = 30%

Probability of normal state = 70%

Expected return on X = 14.5%

Expected return on Y = 14%

Variance on X = 0.004725

Variance on Y = 0.0189

Portfolio weight on X = 50%

Portfolio weight on Y = 50%

Correlation between X and Y = -1

Answer #1

**3.44%**

**Working:**

a. | Standard deviation of X | = | Variance^(1/2) | ||||||||||||||||||||

= | 0.004725^(1/2) | ||||||||||||||||||||||

= | 0.0687 | ||||||||||||||||||||||

Standard deviation of Y | = | Variance^(1/2) | |||||||||||||||||||||

= | 0.0189^(1/2) | ||||||||||||||||||||||

= | 0.1375 | ||||||||||||||||||||||

b. | Portfolio standard deviation | = | (((Weight of X^2)*Variance of X)+((Weight of Y^2)*Variance of Y)+(2*Weight of X* Weight of Y *Standard deviation of X*Standard Deviation of Y*correlation between X and Y))^(1/2) | ||||||||||||||||||||

= | (((.50^2)*0.004725)+((0.50^2)*0.0189)+(2*0.50*0.50*0.0687*0.1375*-1))^(1/2) | ||||||||||||||||||||||

= | 3.44% |
||||||||||||||||||||||

A portfolio consists of 50% invested in Stock X and 50% invested
in Stock Y. We expect two probable states to occur in the future:
boom or normal. The probability of each state and the return of
each stock in each state are presented in the table below.
State
Probability of state
Return on Stock X
Return on Stock Y
Boom
30%
25%
35%
Normal
70%
10%
5%
What are the expected portfolio return and standard
deviation?
Select one:
a....

Portfolio P consists of Stock X and Stock Y. Stock X
weight is 70%. Stock X expected return is 14%, Stock Y expected
return is 10%. Stock X standard deviation of return is 3%, Stock Y
standard deviation of return is 1%. Correlation of Stock X and
Stock Y returns is -0.46. Expected portfolio P return
is:
6.91%
8.50%
12.80%
13.26%

You are given the following information about the stocks in a
two-stock portfolio
Stock
Return
Portfolio Weight
Standard Deviation
Blue Hotel Inc.
22%
45%
9%
Joys Food Inc.
25%
55%
11%
The correlation coefficient between the two stocks is 0.5.
Using the information above, calculate the following:
The expected return of the portfolio,
The variance of the portfolio,
The standard deviation of the portfolio.

Given the following information, what is the expected rate of
return and the standard deviation of a portfolio which is invested
30 percent in stock A, 20 percent in stock B, and 50 percent in
stock C?
State of Probability
of Rate
of Return if State
Occurs
Economy State
of Economy Stock
A Stock
B Stock
C
Boom .10
.22
.08
.18
..........................................Normal
.90 .08 .14 .07

Given the following information, calculate the expected return
and standard deviation for a portfolio that has 49 percent invested
in Stock A, 30 percent in Stock B, and the balance in Stock C.
(Do not round intermediate calculations. Enter your answers
as a percent rounded to 2 decimal places.)
Returns
State of
Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
.70
16
%
23
%
26
%
Bust
.30
8
0
−8

You decide to invest in a portfolio consisting of 23 percent
Stock X, 44 percent Stock Y, and the remainder in Stock Z. Based on
the following information, what is the standard deviation of your
portfolio?
State of Economy Probability of State of Economy Return if State
Occurs
Stock X Stock Y Stock Z
Normal 0.80 9.80% 3.20% 12.20%
Boom 0.20 17.10% 25.10% 16.60%

You decide to invest in a portfolio consisting of 13 percent
Stock X, 53 percent Stock Y, and the remainder in Stock Z. Based on
the following information, what is the standard deviation of your
portfolio?
State of Economy
Probability of State
Return if State Occurs
of Economy
Stock X
Stock Y
Stock Z
Normal
.77
10.80%
4.20%
13.20%
Boom
.23
18.10%
26.10%
17.60%

You decide to invest in a portfolio consisting of 21 percent
Stock X, 42 percent Stock Y, and the remainder in Stock Z. Based on
the following information, what is the standard deviation of your
portfolio?
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Probability of State
Return if State Occurs
of Economy
Stock X
Stock Y
Stock Z
Normal
.84
9.60%
3.00%
12.00%
Boom
.16
16.90%
24.90%
16.40%

Consider the following information on the expected return for
companies X and Y. Economy Probability X Y Boom 0.17 31% 12%
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(Round your final answers to 2 decimal places.) Company X Company Y
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(Round...

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
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