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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 ² σ ( ρ ) = σ ( ρ ) = σ M ± ρ - r 0 ρ M - r 0 ² = 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 ² = 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 = ³ 0 . 15 0 . 20 ´ = ˜ ρ = ρ - r 0 = 0 . 16 and ˜ r = r - r 0 e = ³ 0 . 11 0 . 16 ´ Also, V = ³ 0 . 01 0 0 0 . 0025 ´ It follows that w ( ρ ) = ± ˜ ρ ˜ r T V - 1 ˜ r ² V - 1 ˜ r = ³ 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/22/2010 for the course ENGIN 120 taught by Professor Ilan during the Fall '08 term at University of California, Berkeley.

Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online