Arbitrage pricing theory (APT) is an equilibrium factor model of security returns based on the principle of arbitrage. It assumes capital markets are perfectly competitive, investors prefer more wealth, and prices are generated by a factor model. APT states that a security's expected return is equal to the risk-free rate plus risk premiums based on the security's sensitivity to multiple factors.

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