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Problem 1

1. A) Portfolio A:

Portfolio B:

By equating both the equation, we get:

Risk Premium of F1 = 0.03 or 3%

Risk Premium of F2 = 0.05 or 5%

1. B) Construction of unit portfolio by using Factor 1:

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%
1. Expected Return: (Return on Portfolio A*Weight of Portfolio A)+ (Return on Portfolio B*Weight of Portfolio B)+ (Return on Portfolio Risk-free asset*Weight of Risk-free asset)

= (19%*60%)+(22%*0%)+(6%*40%)

= 13.80%

1. Portfolio beta = (Beta on Portfolio A*Weight of Portfolio A)+ (Beta on Portfolio A*Weight of Portfolio B)+ (Beta on Portfolio A*Weight of Risk-free asset)

=(1*60%)+(2*0%)+(0*40%)

= 0.60

1. C) Construction of unit portfolio by using Factor 2:

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%
• Expected Return: (Return on Portfolio A*Weight of Portfolio A)+ (Return on Portfolio B*Weight of Portfolio B)+ (Return on Portfolio Risk-free asset*Weight of Risk-free asset)

= (19%*0%)+(22%*70%)+(6%*30%)

= 17.20%

1. Portfolio beta = (Beta on Portfolio A*Weight of Portfolio A)+ (Beta on Portfolio A*Weight of Portfolio B)+ (Beta on Portfolio A*Weight of Risk-free asset)

=(1*0%)+(2*70%)+(0*30%)

= 1.40

1. D) Portfolio C:

= 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.

1. E) Since, the beta of portfolio C is 2 and return is 12% which is lower than the return of portfolio of A, B and risk-free asset i.e, it provides an expected return of 22% with same beta> hence, we should short sell the portfolio C to earn an income of 10% with no investment.

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

Stock A

21%

20%

95%

1.14

Stock B

34%

40%

80%

3.20

Portfolio P

8%

10%

100%

0.60

T-Bill

2%

0%

0%

-

Here,

Rf = 2%

Portfolio P

By using CAPM, calculate Rm:

RR = Rf + (Rm - Rf)*β

8% = 2% + (Rm - 2%)*0.60

Rm - 2% = 6%/0.60

Rm - 2% = 10%

Rm = 12%

Standard Deviation of market portfolio:

Systematic Risk of market = SD of portfolio P

 10% = (Beta of Portfolio P)*(SD of market) 10% = 0.60*SD of market SD of market = 10%/0.60 SD of market = 16.67%

B)

Expected Return of Stock A:

By using CAPM, calculate RR:

RR = Rf + (Rm - Rf)*β

RR = 2% + (12% - 2%)*1.90

RR  = 2% + 19%

RR = 21%

C)

Market beta of Stock B:

Beta = (SD of Stock A/ SD Portfolio P)*Correlation between Stock B and Portfolio P

Beta = (40%/10%)*0.80

Beta = 3.20

D)

Systematic Risk of Stock B = SD of portfolio*β

Systematic Risk of Stock B = 10%*3.20

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% She should invest in Fund A. B) Risk Aversion coefficient = 1.50 Utility score of investment = Rf - 0.5*A*SD^2 = 0.08 - 0.5*1.50*(0.20)2 = 0.08 - 0.03 = 0.05 or 5% Now, to get the expected return of 5%, the proportion of Fund A in portfolio can be calculated as follows: Expected return = (RR of Fund A)*(Weight of Fund A) + (RR of T-bill)*(Weight of T-bill) Expected return = (0.08*Wa) + (0.02*Wt) Expected return = (0.08*Wa) + (0.02*(1-Wa)) 0.05 = 0.08Wa + 0.02 - 0.02Wa 0.05 = 0.06Wa +0.02 0.03 = 0.06Wa Wa = 0.03/0.06 Wa = 0.50 or 50% Weight of this fund in his portfolio = 50%

C)

 Calculation of Portfolio Beta 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 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 Basis Portfolio Alpha AR - RR Calculation 0.1386 - [0.02+(0.10-0.02)*1.32] 0.013 Remarks Under-priced Basis Portfolio Sharpe Ratio (RRport - Rf)/βport (13.86%-2%)/1.32 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%   ## Cite This work.

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 17/10/2021].

Urgent Homework . ''(Urgent Homework ,2021) http://www.urgenthomework.com/sample-homework/portfolio-solution accessed 17/10/2021.

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