# Arbitrage pricing theory

Arbitrage pricing theory (APT) is a valuation model. Compared to CAPM, it uses fewer assumptions but is harder to use.

The basis of arbitrage pricing theory is the idea that the price of a security is driven by a number of factors. These can be divided into two groups: macro factors, and company specific factors. The name of the theory comes from the fact that this division, together with the no arbitrage assumption can be used to derive the following formula:

r = rf + β1f1 + β2f2 + β3f3 + ⋅⋅⋅

where r is the expected return on the security,
rf is the risk free rate,
Each f is a separate factor and
each β is a measure of the relationship between the security price and that factor.

This is a recognisably similar formula to CAPM.

The difference between CAPM and arbitrage pricing theory is that CAPM has a single non-company factor and a single beta, whereas arbitrage pricing theory separates out non-company factors into as many as proves necessary. Each of these requires a separate beta. The beta of each factor is the sensitivity of the price of the security to that factor.

Arbitrage pricing theory does not rely on measuring the performance of the market. Instead, APT directly relates the price of the security to the fundamental factors driving it. The problem with this is that the theory in itself provides no indication of what these factors are, so they need to be empirically determined. Obvious factors include economic growth and interest rates. For companies in some sectors other factors are obviously relevant as well - such as consumer spending for retailers.

The potentially large number of factors means more betas to be calculated. There is also no guarantee that all the relevant factors have been identified. This added complexity is the reason arbitrage pricing theory is far less widely used than CAPM.