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Arbitrage Pricing Theory

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					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:

				
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