5.why_works

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

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Unformatted text preview: 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 2 i the expected return and variance of stock i , i = 1 , 2 , ,n . Also, let 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 R where, x = ( x 1 ,x 2 , ,x n ) , and R = ( R 1 , R 2 , , R n ) And its risk (variance) by: 2 p = var ( x 1 R 1 + x 2 R 2 + + x n R n ) = n X i =1 x 2 i 2 i + n X i =1 n X j 6 = i x i x j ij = n X i =1 n X j =1 x i x j...
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This note was uploaded on 06/02/2011 for the course STATS 183 taught by Professor Nicolas during the Spring '11 term at UCLA.

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

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