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Portfolio Solution

Problem 1

1. A) Portfolio A:

Annual Expected Return = R_f + Risk Premium_A1*β_{A1 +} Risk Premium_A2*β_A2

Or 0.19 = 0.06 + Risk Premium_A1*1 ₊ Risk Premium_A2*2

Or Risk Premium_A1*1 ₊ Risk Premium_A2*2 = 0.13 ----------------------------(i)

Portfolio B:

Annual Expected Return = R_f + Risk Premium_A1*β_{A1 +} Risk Premium_A2*β_A2

Or 0.22 = 0.06 + Risk Premium_A1*2 ₊ Risk Premium_A2*2

Or Risk Premium_A1*2 ₊ Risk Premium_A2*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%

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

Portfolio using Factor 1:

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:

• 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:

Required Return = R_f + Risk Premium_C1*β_{C1 +} Risk Premium_C2*β_C2

                           = 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

Problem 3

C)

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%

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