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1. 1
CHAPTER TWELVE
ARBITRAGE PRICING
THEORY

2. 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

3. 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

4. 4
FACTOR MODELS
• MULTIPLE-FACTOR MODELS
– FORMULA
ri = ai + bi1 F1 + bi2 F2 +. . .
+ biKF K+ ei
where r is the return on security i
b is the coefficient of the factor
F is the factor
e is the error term

5. 5
FACTOR MODELS
• SECURITY PRICING
FORMULA:
ri = l0 + l1 b1 + l2 b2 +. . .+ lKbK
where
ri = rRF +(d1-rRF )bi1 + (d2- rRF)bi2+ . . .
+(d-rRF)biK

6. 6
FACTOR MODELS
where r is the return on security i
l0 is the risk free rate
b is the factor
e is the error term

7. 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