Arbitrage Pricing Theory
Arbitrage Pricing Theory (APT)
Based on the law of one price. Two items
that are the same cannot sell at different
prices
If they sell at a different price, arbitrage
will take place in which arbitrageurs buy
the good which is cheap and sell the one
which is higher priced till all prices for the
goods are equal
APT
 In APT, the assumption of investors utilizing a
mean-variance framework is replaced by an
assumption of the process of generating security
returns.
 APT requires that the returns on any stock be
linearly related to a set of indices.
 In APT, multiple factors have an impact on the
returns of an asset in contrast with CAPM model
that suggests that return is related to only one
factor, i.e., systematic risk
Factors that have an impact the returns of
all assets may include inflation, growth in
GNP, major political upheavals, or changes
in interest rates
ri = ai + bi1F1 + bi2F2 + …+bikFk + ei
Given these common factors, the bik terms
determine how each asset reacts to this
common factor.
 While all assets may be affected by growth in
GNP, the impact will differ.
 Which firms will be affected more by the growth
in GNP?
 The APT assumes that, in equilibrium, the return
on a zero-investment, zero-systematic risk
portfolio is zero, when the unique effects are
diversified away:
 E(ri) = 0 + 1bi1 + 2bi2 + … + kbik
Example of two stocks and two factor
model: