Use the information in the table below to answer the next seven multiple choice
ID: 2779426 • Letter: U
Question
Use the information in the table below to answer the next seven multiple choice questions. State of Nature Probability Return on A Return on B I 0.4 6% 11% II 0.2 9% 6% III 0.4 12% 15% The correlation between A and B is 0.35. The portfolio weight of A is 25%. The portfolio weight of B is 75%. 22.value:
The expected return in percent for investment A is 12.24% 7.74% 9.72% 9.00% 23.value:
The standard deviation of returns for investment A is 2.68% 2.82% 2.31% 3.33% 24.value:
The expected return in percent for investment B is 10.90% 11.60% 12.88% 14.73% 25.value:
The standard deviation of returns for investment B is 2.33% 3.59% 3.32% 4.52% 26.value:
The expected return in percent for a portfolio of 25% investment A and 75% investment B is 8.54% 14.89% 10.95% 12.15% 27.value:
The covariance between investment A and investment B is 4.06 3.12 3.84 2.93 28.value:
The return standard deviation for a portfolio of 25% investment A and 75% investment B is 3.64% 2.41% 3.02% 2.80%
Explanation / Answer
22.value:
The expected return in percent for investment A is 12.24% 7.74% 9.72% 9.00%
Answer:
The expected return of investment A = 0.4 x 6% + 0.2 x 9% + 0.4 x 12% = 9%
So the correct answer is 9%.
23.value:
The standard deviation of returns for investment A is 2.68% 2.82% 2.31% 3.33%
Answer:
Here Expected return, E(x), for A is = 9% as calculated above.
State
Probability
Return on A
Deviation= (x-E(x))
(x-E(x))2
Probability x (x-E(x))2
I
0.4
6%
-3%
0.09%
0.036%
II
0.2
9%
0%
0
0
III
0.4
12%
3%
0.09%
0.036%
Therefore standard for investment A is = Square root of (0.036+0 + 0.036)%
Or, required standard deviation = 0.0268 or 2.68%
24.value:
The expected return in percent for investment B is 10.90% 11.60% 12.88% 14.73%
Answer:
The expected return of investment B = 0.4 x 11% + 0.2 x 6% + 0.4 x 15% = 11.6%
So the correct answer is 11.6%.
25.value:
The standard deviation of returns for investment B is 2.33% 3.59% 3.32% 4.52%
Answer:
Here Expected return, E(x), for B is = 11.6% as calculated above.
State
Probability
Return on B
Deviation= (x-E(x))
(x-E(x))2
Probability x (x-E(x))2
I
0.4
11%
-0.6%
0.0036%
0.00144%
II
0.2
6%
-5.6%
0.3136%
0.06272%
III
0.4
15%
3.4%
0.1156%
0.04624%
Therefore standard for investment A is = Sq root of (0.00144+0.06272 + 0.04624)%
Or, required standard deviation = 0.03322 or 3.32%
26.value:
The expected return in percent for a portfolio of 25% investment A and 75% investment B is 8.54% 14.89% 10.95% 12.15%
Answer:
For calculating expected return we have to use this formula
Expected return = w1 x E(A) + w2 x E(B)
Here w1 = 25%
W2 = 75%
E(A) = 9%
E(B) = 11.6%
Therefore by using the formula we get:
Expected return on portfolio = 25% x 9% + 75% x 11.6% = 2.25% + 8.7% = 10.95% is the correct answer.
27.value:
The covariance between investment A and investment B is 4.06 3.12 3.84 2.93
Answer:
The covariance formula is:
Covariance = deviation on security A x deviation on security B x probability.
Therefore from the table:
State
Probability
=P
Return on A
Deviation=D1 = (x-E(x))
Return on B
Deviation=D2
=(x-E(x))
PxD1xD2
I
0.4
6%
-3%
11%
-0.6%
0.0072%
II
0.2
9%
0%
6%
-5.6%
0%
III
0.4
12%
3%
15%
3.4%
0.0408%
Therefore covariance = sum of 0.0072% and 0.0408%
Covariance = 0.048%
Therefore the correct answer is 4.8%
28.value:
The return standard deviation for a portfolio of 25% investment A and 75% investment B is 3.64% 2.41% 3.02% 2.80%
Answer:
The correlation between A and B is 0.35.
Now we can use this formula to calculate portfolio standard deviation:
Standard deviation = Sq Root (sA2*wA2 + sB2*wB2 + 2*sAsB wA wB Correl Coeff.
Standard deviation = Sq Root (2.682*25%2 + 3.322*75%2 + 2*2.28*3.32* 25%
75%* 0.35
= Sq Root (0.00003249 + 0.00062001 + 0.00028386)
= Sq Root (0.00093636)
Standard Deviation = 0.0302 or 3.02%
State
Probability
Return on A
Deviation= (x-E(x))
(x-E(x))2
Probability x (x-E(x))2
I
0.4
6%
-3%
0.09%
0.036%
II
0.2
9%
0%
0
0
III
0.4
12%
3%
0.09%
0.036%
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