1. A portfolio consists of the following securities: Security Amount Invested St
ID: 2724921 • Letter: 1
Question
1. A portfolio consists of the following securities:
Security
Amount Invested
Std. Dev.
i
Beta
i
A
$250,000
15.50
1.45
B
$350,000
8.35
0.75
C
$200,000
21.22
1.85
D
$150,000
7.75
0.45
E
$50,000
13.75
1.25
What is the portfolio’s beta? Is the portfolio riskier than the market? Explain.
2. An investor’s portfolio two risky-asset portfolio is allocated as follows:
Asset Type
Amount Invested
Standard Deviation
Expected Return
Bonds
$45,000
15%
6.5%
Stocks
$55,000
22%
14.0%
The correlation coefficient between the two assets is zero ( b, s = 0). Based on this information, calculate the portfolio’s variance of returns (2p), standard deviation (p), and expected return E (Rp).
3. The realized returns for the common stock of Company X are given as follows:
2009
2010
2011
2012
2013
5.3%
15.5%
-35.0%
25.2%
12.7%
Based on this information calculate the stock’s average return, variance of returns, and standard deviation.
Security
Amount Invested
Std. Dev.
i
Beta
i
A
$250,000
15.50
1.45
B
$350,000
8.35
0.75
C
$200,000
21.22
1.85
D
$150,000
7.75
0.45
E
$50,000
13.75
1.25
Explanation / Answer
Solution:
Portfolio beta:
It is computed in a tabular form with formulas:
The portfolio is riskier to market as the portfolio beta is more than 1 .Higher the beat higher the risk of the portfolio
Solution2:
To compute the portfolio S.D = weight ^2 * variance ^2 + weight^2 * variance ^2 + 2* (0) because correlation is zero
= .45^2 *.00077^2 + .55^2 *.00063^2
= .00024
Solution 3:
S.d = SQRT variance / n-1
= SQRT (.0544)
S.D = .233
Thank you.
Security Amount Invested Std. Dev.i Beta
i Weights= invest/total investment Porfolio beta(weights* beta) A $250,000 15.5 1.45 0.25 0.3625 B $350,000 8.35 0.75 0.35 0.2625 C $200,000 21.22 1.85 0.2 0.37 D $150,000 7.75 0.45 0.15 0.0675 E $50,000 13.75 1.25 0.05 0.0625 $1,000,000 Porfolio beta 1.125
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