Solutions+Problem+Set+9 - E 120 : Problem Set 9 Solutions -...

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

View Full Document Right Arrow Icon
E 120 : Problem Set 9 Solutions - Fall 2010 Problem 1 (a) Portfolio mean = E [ P ] = w 1 r 1 + w 2 r 2 = 0 . 2 × 0 . 05+0 . 8 × 0 . 2 = 0 . 17. Portfolio variance = V [ P ] = w 2 2 σ 2 2 = 0 . 8 2 × 0 . 15 2 = 0 . 0144. (b) Portfolio mean = E [ P ] = w 1 r 1 + w 2 r 2 = - 0 . 4 × 0 . 05 + 1 . 4 × 0 . 2 = 0 . 26. Portfolio variance = V [ P ] = w 2 2 σ 2 2 = 1 . 4 2 × 0 . 15 2 = 0 . 0441. Problem 2 In this case, the covariance matrix is given by V = ± 0 . 16 0 . 05 0 . 05 0 . 0625 ² . Hence, the portfolio variance is given by V ( P ) = x T V x = ³ x 1 x 2 ´ ± 0 . 16 0 . 05 0 . 05 0 . 0625 ²± x 1 x 2 ² = 0 . 16 x 2 1 + 0 . 1 x 1 x 2 + 0 . 0625 x 2 2 Using the constraint that x 2 = 1 - x 1 , we have V ( P )( x 1 ) = 0 . 16 x 2 1 + 0 . 1 x 1 (1 - x 1 ) + 0 . 0625(1 - x 1 ) 2 = 0 . 1225 x 2 1 - 0 . 025 x 1 + 0 . 0625 For V ( P )( x 1 ) to be minimized at x 1 , it is sufficient that V 0 ( P )( x 1 ) = 0 and V 00 ( P )( x 1 ) > 0, i.e. V 0 ( P )( x 1 ) = 0 . 245 x 1 - 0 . 025 = 0 = x 1 = 0 . 025 0 . 245 = 0 . 102 and V 00 ( P )( x 1 ) = 0 . 245
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 / 2

Solutions+Problem+Set+9 - E 120 : Problem Set 9 Solutions -...

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