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1 CHAPTER TWELVE ARBITRAGE PRICING THEORY

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2 FACTOR MODELS ARBITRAGE PRICING THEORY (APT) –is an equilibrium factor mode of security returns –Principle of Arbitrage the earning of riskless profit by taking advantage of differentiated pricing for the same physical asset or security –Arbitrage Portfolio requires no additional investor funds no factor sensitivity has positive expected returns

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3 FACTOR MODELS ARBITRAGE PRICING THEORY (APT) –Three Major Assumptions: capital markets are perfectly competitive investors always prefer more to less wealth price-generating process is a K factor model

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4 FACTOR MODELS MULTIPLE-FACTOR MODELS –FORMULA r i = a i + b i1 F 1 + b i2 F 2 +... + b iK F K + e i where r is the return on security i b is the coefficient of the factor F is the factor e is the error term

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5 FACTOR MODELS SECURITY PRICING FORMULA: r i = 0 + 1 b 1 + 2 b 2 +...+ K b K where r i = r RF +( 1 r RF b i1 2 r RF )b i2 + r RF b iK

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6 FACTOR MODELS where r is the return on security i is the risk free rate b is the factor e is the error term

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7 FACTOR MODELS hence –a stock’s expected return is equal to the risk free rate plus k risk premiums based on the stock’s sensitivities to the k factors

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