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Lecture26-2004

# Lecture26-2004 - The Arbitrage Pricing Model Lecture XXVI A...

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The Arbitrage Pricing Model Lecture XXVI

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A Single Factor Model Abstracting away from the specific form of the CAPM model, we posit a single factor model written as In this model, the random return on an investment z i is a linear function of some random factor f i and an idiosyncratic term ε i . 1 K i i ik k i k z a b f ε = = + + % % %
( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 0 1 i k i j i k k l i i i k E E f E E f E f f E s S E f ε ε ε ε ε = = = = = = < = % % % % % % % % % %

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Abstracting away from the idiosyncratic risk If the b i s of two assets are the same, then the a i s must be the same for an arbitrage free model. Suppose we are interested in forming a portfolio of two assets with different b i s, b i b j , b i 0, b j 0 i i i i z a b f = + % %
( 29 ( 29 ( 29 ( 29 ( 29 1 i i j j i i j j j j i j j i j j z w a b f w a b f wa wb f a wa b f wb f w a a a w b b b f = + + - + = + + - + - � � = - + + - + � � Computing the mean and variance of this portfolio yields

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