Problem 1
Annual Expected Return = Rf + Risk PremiumA1*βA1 + Risk PremiumA2*βA2
Or 0.19 = 0.06 + Risk PremiumA1*1 + Risk PremiumA2*2
Or Risk PremiumA1*1 + Risk PremiumA2*2 = 0.13 ----------------------------(i)
Portfolio B:
Annual Expected Return = Rf + Risk PremiumA1*βA1 + Risk PremiumA2*βA2
Or 0.22 = 0.06 + Risk PremiumA1*2 + Risk PremiumA2*2
Or Risk PremiumA1*2 + Risk PremiumA2*2 = 0.16 ----------------------------(ii)
By equating both the equation, we get:
Risk Premium of F1 = 0.03 or 3%
Risk Premium of F2 = 0.05 or 5%
Portfolio using Factor 1:
Weight of resulting unit portfolio: |
|
Weight of Portfolio A |
60% |
Weight of Portfolio B |
0% |
Weight of Risk-free asset |
40% |
= (19%*60%)+(22%*0%)+(6%*40%)
= 13.80%
=(1*60%)+(2*0%)+(0*40%)
= 0.60
Portfolio using Factor 2:
Weight of resulting unit portfolio: |
|
Weight of Portfolio A |
0% |
Weight of Portfolio B |
70% |
Weight of Risk-free asset |
30% |
= (19%*0%)+(22%*70%)+(6%*30%)
= 17.20%
=(1*0%)+(2*70%)+(0*30%)
= 1.40
Required Return = Rf + Risk PremiumC1*βC1 + Risk PremiumC2*βC2
= 0.06 + (0.03*2) + (0.05*0)
= 0.06 + 0.06 + 0
= 0.12 or 12%
Annual expected return = 16%
Since, actual return is less than annual expected return, hence portfolio is overvalued.
Income = Return on combined portfolio -Return on Portfolio C
= 22% - 12% = 10%
Weight are given below (in both conditions):
Weight of Portfolio A : 0%
Weight of Portfolio B : 100%
Weight of Portfolio Risk free asset : 0%
Problem 2
A) |
Assets |
Expected Return |
SD |
Correlation with P |
Market beta |
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Stock A |
21% |
20% |
95% |
1.14 |
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Stock B |
34% |
40% |
80% |
3.20 |
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Portfolio P |
8% |
10% |
100% |
0.60 |
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T-Bill |
2% |
0% |
0% |
- |
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Here, |
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Rf = 2% |
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Portfolio P |
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By using CAPM, calculate Rm: |
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RR = Rf + (Rm - Rf)*β |
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8% = 2% + (Rm - 2%)*0.60 |
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Rm - 2% = 6%/0.60 |
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Rm - 2% = 10% |
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Rm = 12% |
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Standard Deviation of market portfolio: Systematic Risk of market = SD of portfolio P
|
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B) |
Expected Return of Stock A: |
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By using CAPM, calculate RR: |
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RR = Rf + (Rm - Rf)*β |
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RR = 2% + (12% - 2%)*1.90 |
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RR = 2% + 19% |
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RR = 21% |
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C) |
Market beta of Stock B: |
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Beta = (SD of Stock A/ SD Portfolio P)*Correlation between Stock B and Portfolio P |
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Beta = (40%/10%)*0.80 |
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Beta = 3.20 |
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D) |
Systematic Risk of Stock B = SD of portfolio*β |
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Systematic Risk of Stock B = 10%*3.20 |
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Systematic Risk of Stock B = 32% |
Problem 3
A) |
Fund |
Expected Return |
SD |
Beta |
(RRsec - Rf)/βsec |
Ranking |
Fund A |
8% |
20% |
0.50 |
0.12 |
1 |
|
Fund B |
18% |
60% |
2.00 |
0.08 |
3 |
|
Fund C |
16% |
40% |
1.50 |
0.09 |
2 |
|
T-bill |
2% |
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She should invest in Fund A. |
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B) |
Risk Aversion coefficient = 1.50 |
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Utility score of investment = Rf - 0.5*A*SD^2 |
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= 0.08 - 0.5*1.50*(0.20)2 |
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= 0.08 - 0.03 |
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= 0.05 or 5% |
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Now, to get the expected return of 5%, the proportion of Fund A in portfolio can be calculated as follows: |
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Expected return = (RR of Fund A)*(Weight of Fund A) + (RR of T-bill)*(Weight of T-bill) |
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Expected return = (0.08*Wa) + (0.02*Wt) |
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Expected return = (0.08*Wa) + (0.02*(1-Wa)) |
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0.05 = 0.08Wa + 0.02 - 0.02Wa |
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0.05 = 0.06Wa +0.02 |
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0.03 = 0.06Wa |
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Wa = 0.03/0.06 |
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Wa = 0.50 or 50% |
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Weight of this fund in his portfolio = 50% |
C)
Calculation of Portfolio Beta |
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Fund A |
0.33 |
0.5 |
0.165 |
Fund B |
0.33 |
2 |
0.66 |
Fund C |
0.33 |
1.5 |
0.495 |
1.32 |
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Calculation of Expected Return |
|||
Fund A |
0.33 |
0.08 |
0.0264 |
Fund B |
0.33 |
0.18 |
0.0594 |
Fund C |
0.33 |
0.16 |
0.0528 |
0.1386 |
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Basis |
Portfolio |
||
Alpha |
AR - RR |
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Calculation |
0.1386 - [0.02+(0.10-0.02)*1.32] |
||
|
0.013 |
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Remarks |
Under-priced |
||
Basis |
Portfolio |
||
Sharpe Ratio |
(RRport - Rf)/βport |
||
(13.86%-2%)/1.32 |
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0.08985 |
Problem 4
Variance of portfolio = + Covariance [Covariance = Beta of stock * Variance of Market]
= + 1*20*20
= 25+400
= 425
Standard deviation of portfolio =
= 20.62%
Earn back money you have spent on downloaded sample
To export a reference to this article please select a referencing stye below.
Urgent Homework (2021) . Retrive from http://www.urgenthomework.com/sample-homework/portfolio-solution
"." Urgent Homework ,2021, http://www.urgenthomework.com/sample-homework/portfolio-solution
Urgent Homework (2021) . Available from: http://www.urgenthomework.com/sample-homework/portfolio-solution
[Accessed 14/04/2021].
Urgent Homework . ''(Urgent Homework ,2021) http://www.urgenthomework.com/sample-homework/portfolio-solution accessed 14/04/2021.
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