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ARBITRAGE PRICING THEORY

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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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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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FACTOR MODELS

• MULTIPLE-FACTOR MODELS– FORMULA

ri = ai + bi1 F1 + bi2 F2 +. . .

+ biKF K+ ei

where r is the return on security ib is the coefficient of the factorF is the factore is the error term

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FACTOR MODELS

• SECURITY PRICINGFORMULA:

ri = 0 + 1 b1 + 2 b2 +. . .+ KbK

where

ri = rRF +(1rRFbi12rRF)bi2+

rRFbiK

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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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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