The Arbitrage Pricing Theory, or APT, as it is usually called, is an empirical way to derive a CAPM-like security market line for well diversified portfolios.

The current price of the asset should be equal to the future price of the asset at the end of the expected period, discounted using the APT rate of return. If the price diverges, then the arbitrage mechanisms should eliminate the price divergence.

The APT requires three assumptions.

• (i) All asset returns follow a factor model
• (ii) There are sufficiently many assets to invest into such that asset specific risk can be diversified away
• (iii) Asset markets are arbitrage-free

Assumption (ii) implies that N is sufficiently large, so that it holds: $\sigma^2 \rightarrow 0$