APT - Arbitrage Pricing Theory / Model

Arbitrage pricing theory (APT).
1. Assumptions
APT does not require assumptions about utility or the distribution of security returns. The APT relies on the following assumptions:
1. Returns are generated according to a linear factor model.
2. The number of assets is close to infinite.
3. Investors have homogenous expectations (same as CAPM)
4. Capital markets are perfect (i.e. perfect competition, no transactions costs [same as
CAPM])
The assumptions 1 and 2 are subject to criticism.

2. Definition and Equation
The APT offers an alternative to the CAPM. This theory was developed by Stephen Ross (1976-78).
The APT develops a model that doesn’t base on the returns on market as the CAPM did, it focuses on a number of macroeconomical factors and therefore we come to the multifactor regression:

ra = E(ra) + 1 F1+ 2 F2 + ... + k Fk + εa
where
ra = the stochastic rate of return on the asset
E(ra) = the expected rate of return on the asset
k = the sensitivity of the asset’s returns to the kth factor
Fk = the mean zero kth factor common to the returns of all assets under consideration
εa = a random, mean zero, disturbance term for the asset

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