a. Based on the table above, construct an equal-weighted (50/50) portfolio of In
ID: 2619994 • Letter: A
Question
a. Based on the table above, construct an equal-weighted (50/50) portfolio of Investments B and C. What is the expected rate of return and standard deviation of the portfolio?
b. Now construct an equal-weighted (50/50) portfolio of Investments B and D. What is the expected rate of return and standard deviation of the portfolio?
Part A:
E(R) for BC portfolio: Note: format answer is 12.3%
SD for BC portfolio: Note: format answer is 1.2%
Part B:
E(R) for BD portfolio: Note: format answer is 12.3%
SD for BD portfolio: Note: format answer is 1.2%
conomic State Probability B C D Very poor 0.1 30% -25% 15% Poor 0.2 20% -5% 10% Average 0.4 10% 15% 0% Good 0.2 0% 35% 25% Very good 0.1 -10% 55% 35%Explanation / Answer
A
B
C=A*B
DEV=(B-10)
X=DEV^2
Y=X*A
Probability
Return of B in percentage
Probabity*Return
Deviation from expected
Deviation Squared
Deviation squared*Probability
0.1
30.00
3.00
20.00
400
40
0.2
20.00
4.00
10.00
100
20
0.4
10.00
4.00
-
-
-
0.2
-
-
(10.00)
100
20
0.1
(10.00)
(1.00)
(20.00)
400
40
SUM
10
SUM
120
VARIANCE
120
STANDARD DEVIATION
10.95445
(Square Root (Variance)
Expected Return of B=10%
Standard Deviation of return of B=10.95%
D
E
F=D*E
DEV=(E-15)
X=DEV^2
Y=X*A
Probability
Return of C in percentage
Probabity*Return
Deviation from expected
Deviation Squared
Deviation squared*Probability
0.1
(25.00)
(2.50)
(40.00)
1,600
160
0.2
(5.00)
(1.00)
(20.00)
400
80
0.4
15.00
6.00
-
-
-
0.2
35.00
7.00
20.00
400
80
0.1
55.00
5.50
40.00
1,600
160
SUM
15.00
SUM
480
VARIANCE
480
STANDARD DEVIATION
21.9089
(Square Root (Variance)
Expected Return of C=15%
Standard Deviation of return of C=21.91%
G
H
I=G*H
DEV=(H-12)
X=DEV^2
Y=X*A
Probability
Return of D
Probabity*Return
Deviation from expected
Deviation Squared
Deviation squared*Probability
0.1
15.00
1.50
3.00
9.00
0.90
0.2
10.00
2.00
(2.00)
4.00
0.80
0.4
-
-
(12.00)
144.00
57.60
0.2
25.00
5.00
13.00
169.00
33.80
0.1
35.00
3.50
23.00
529.00
52.90
SUM
12.00
SUM
146.00
VARIANCE
146
STANDARD DEVIATION
12.08305
(Square Root (Variance)
Expected Return of D=12%
Standard Deviation of return of D=12.08%
If w1, w2 , are weight in the portfolio for assets 1 and 2
Then,w1+w2=1
R1, R2 are the return of the assets 1and2
S1, S2 are the standard deviation of the assets 1, 2
Portfolio Return=w1R1+w2R2
PortfolioVariance=(w1^2)*(S1^2)+(w2^2)(S2^2)+2w1w2*Cov(1,2)
Cov(1,2)=Covariance of returns of asset1 and asset2
Portfolio Standard Deviation =Square root of Portfolio variance
a.PORTFOLIO OF B AND C
Return of assetB=Rb=10%%
Return of assetC=Rc=15%
Standard deviation of asset B=Sb=10.95%%
Standard deviation of asset C=Sc=21.91%
Correlation of asset Band C=0
Covariance(1,2)=0
wb=wc=0.5
Portfolio Return;
0.5*10+0.5*15=12.5%
Portfolio Variance=(0.5^2)*(10.95^2)+(0.5^2)*(21.91^2)=149.9877
Portfolio Standard Deviation=Square root of Variance=(149.9877^0.5)= 12.25%
b..PORTFOLIO OF B AND D
Return of assetB=Rb=10%
Return of assetD=Rd=12%
Standard deviation of asset B=Sb=10.95%
Standard deviation of asset D=Sd=12.08%
Correlation of asset Band C=0
Covariance(1,2)=0
wb=wd=0.5
Portfolio Return;
0.5*10+0.5*12=11%
Portfolio Variance=(0.5^2)*(10.95^2)+(0.5^2)*(12.08^2)=66.45723
Portfolio Standard Deviation=Square root of Variance=(66.45723^0.5)= 8.15%
ExpectedReturn(E(R)
Std Deviation
a) Portfolio of B and C
12.50%
12.25%
b) Portfolio of B and D
11%
8.15%
A
B
C=A*B
DEV=(B-10)
X=DEV^2
Y=X*A
Probability
Return of B in percentage
Probabity*Return
Deviation from expected
Deviation Squared
Deviation squared*Probability
0.1
30.00
3.00
20.00
400
40
0.2
20.00
4.00
10.00
100
20
0.4
10.00
4.00
-
-
-
0.2
-
-
(10.00)
100
20
0.1
(10.00)
(1.00)
(20.00)
400
40
SUM
10
SUM
120
VARIANCE
120
STANDARD DEVIATION
10.95445
(Square Root (Variance)
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