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Solutions+Problem+Set+10-1

# Solutions+Problem+Set+10-1 - E 120 Problem Set 10 Solutions...

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E 120 : Problem Set 10 Solutions - Fall 2010 Problem 1 In the Markowitz model, the minimum standard deviation for a desired expected return is given by the Capital Market Line. In this case, we have ρ = 0 . 10, r 0 = 0 . 05, ρ M = 0 . 15, and σ M = σ ( ρ M ) = 0 . 18. The equation of the Capital Market Line is given by ρ = r 0 + ρ M - r 0 σ M σ ( ρ ) = σ ( ρ ) = σ M ρ - r 0 ρ M - r 0 = 0 . 18 × 0 . 10 - 0 . 05 0 . 15 - 0 . 05 = 0 . 09 which is the minimum standard deviation you can achieve. Problem 2 In this case, we have ρ = 0 . 20, r 0 = 0 . 05, ρ M = 0 . 15, and σ M = σ ( ρ M ) = 0 . 18. Using the Capital Market Line, the minimum standard deviation that can be achieved is given by σ ( ρ ) = σ M ρ - r 0 ρ M - r 0 = 0 . 18 × 0 . 20 - 0 . 05 0 . 15 - 0 . 05 = 0 . 27 or 27% > 20% Hence, it is not possible to achieve an expected return of 20% and a standard deviation of 20% Problem 3 (a) We have r 0 = 0 . 04, ρ = 0 . 20 and r = 0 . 15 0 . 20 = ˜ ρ = ρ - r 0 = 0 . 16 and ˜ r = r - r 0 e = 0 . 11 0 . 16 Also, V = 0 . 01 0 0 0 . 0025 It follows that w ( ρ ) = ˜ ρ ˜ r T V - 1 ˜ r V - 1 ˜ r = 0 . 1537 0 . 8943 So the minimum variance portfolio with an expected return of 0 . 20 is given by w A = 0 . 1537, w B = 0 . 8943 and w 0 = 1 - e T w ( ρ ) = - 0 . 048. Hence, Jack should borrow \$1000 × 0 . 048 = \$48 from the bank, and invest \$1000 × 0 . 1537 = \$153 . 70 in Stock A and \$1000 × 0 . 8943 = \$894 . 30 in Stock B.

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Solutions+Problem+Set+10-1 - E 120 Problem Set 10 Solutions...

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