Formulated by Ross(1976), the Arbitrage Pricing Theory(APT)offersa testable alternative to the capital market pricing model(CAPM). The main difference between CAPM and APT is that CAPM assumes that security rates of returns will be linearly related to a single common factor- the rate of return on the market portfolio. The APT is based on similar intuition but is much more general.
APT assumes that, in equilibrium, the return on an arbitrage portfolio (i.e. one with zero investment, and zero systematic risk) is zero. If this return is positive, then it would be eliminated immediately through the process of arbitrage trading to improve the expected returns. Ross (1976) demonstrated that when no further arbitrage opportunities exist, the expected return (E(Ri)) can be shown as follows:
E(Ri)=Rf + β1(R1-Rf)+β2(R2 -Rf)+--------+ βn(Rn-Rf)+έi
E(Ri) is the expected return on the security
Rf is the risk free rate
Βi is the sensitivity to changes in factor i
έi is a random error term.