{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

5.why_works - University of California Los Angeles...

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

View Full Document Right Arrow Icon
University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Portfolio expected return and risk Suppose a portfolio consists of n stocks. Let ¯ R i and σ 2 i the expected return and variance of stock i , i = 1 , 2 , · · · , n . Also, let σ ij the covariance between stocks i and j . Let x 1 , x 2 , · · · , x n the fractions of the investors wealth invested in each one of the n stocks ( n i =1 x i = 1). The resulting portfolio is x 1 R 1 + x 2 R 2 + · · · + x n R n and at time t it has return: R pt = x 1 R 1 t + x 2 R 2 t + · · · + x n R nt The expected return of this portfolio is given by: ¯ R p = x 1 ¯ R 1 + x 2 ¯ R 2 + · · · + x n ¯ R n = n X i =1 x i ¯ R i = x 0 ¯ R where, x 0 = ( x 1 , x 2 , · · · , x n ) , and ¯ R = ( ¯ R 1 , ¯ R 2 , · · · , ¯ R n ) And its risk (variance) by: σ 2 p = var ( x 1 R 1 + x 2 R 2 + · · · + x n R n ) = n X i =1 x 2 i σ 2 i + n X i =1 n X j 6 = i x i x j σ ij = n X i =1 n X j =1 x i x j σ ij Or in matrix form: σ 2 p = x 0 Σx where, Σ is the symmetric, positive definite n × n
Background image of page 1

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

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

{[ snackBarMessage ]}