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PS3_solution - UNIVERSITY OF NORTH CAROLINA KENAN-FLAGLER...

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1 U NIVERSITY OF N ORTH C AROLINA K ENAN -F LAGLER B USINESS S CHOOL BUSI 580: INVESTMENTS P ART I: P ORTFOLIO T HEORY AND A SSET P RICING Prof. Günter Strobl Spring 2010 Solution to Problem Set 3 A. The Arbitrage Pricing Theory 1. (a) In a two-factor economy, the expected return of any well-diversified portfolio is given by: ( ) 2 , p 2 1 , p 1 f p b b r r E λ λ + + = . Thus, in order to find the factor risk premia, we have to solve the following system of two equations in two unknowns: 2 1 4 . 3 2 . 1 % 5 % 1 . 13 λ λ × + × + = 2 1 6 . 2 6 . 2 % 5 % 4 . 15 λ λ × + × + = The solution to this set of equations is λ 1 = 2.5% (risk premium for factor F 1 ) and λ 2 = 1.5% (risk premium for factor F 2 ). (b) If the risk premium for F 1 increases from 2.5% to 2.75%, then the expected returns for portfolios X and Y are: ( ) % 4 . 13 % 5 . 1 4 . 3 % 75 . 2 2 . 1 % 5 r E X = × + × + = ( ) % 05 . 16 % 5 . 1 6 . 2 % 75 . 2 6 . 2 % 5 r E Y = × + × + =
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