# Arbitrage Pricing Theory (APT)

Updated September 30, 2020

## What is Arbitrage Pricing Theory (APT)?

Arbitrage pricing theory (APT) is a well-known method of estimating the price of an asset. The theory assumes an asset's return is dependent on various macroeconomic, market and security-specific factors.

## How Does Arbitrage Pricing Theory (APT) Work?

APT is an alternative to the capital asset pricing model (CAPM). Stephen Ross developed the theory in 1976.

The APT formula is:

E(rj) = rf + bj1RP1 + bj2RP2 + bj3RP3 + bj4RP4 + ... + bjnRPn

where:
E(rj) = the asset's expected rate of return
rf = the risk-free rate
bj = the sensitivity of the asset's return to the particular factor
RP = the risk premium associated with the particular factor

The general idea behind APT is that two things can explain the expected return on a financial asset: 1) macroeconomic/security-specific influences and 2) the asset's sensitivity to those influences. This relationship takes the form of the linear regression formula above.

There are an infinite number of security-specific influences for any given security including inflation, production measures, investor confidence, exchange rates, market indices or changes in interest rates. It is up to the analyst to decide which influences are relevant to the asset being analyzed.

Once the analyst derives the asset's expected rate of return from the APT model, he or she can determine what the "correct" price of the asset should be by plugging the rate into a discounted cash flow model.

Note that APT can be applied to portfolios as well as individual securities. After all, a portfolio can have exposures and sensitivities to certain kinds of risk factors as well.

## Why Does Arbitrage Pricing Theory (APT) Matter?

The APT was a revolutionary model because it allows the user to adapt the model to the security being analyzed. And as with other pricing models, it helps the user decide whether a security is undervalued or overvalued and so he or she can profit from this information. APT is also very useful for building portfolios because it allows managers to test whether their portfolios are exposed to certain factors.

APT may be more customizable than CAPM, but it is also more difficult to apply because determining which factors influence a stock or portfolio takes a considerable amount of research. It can be virtually impossible to detect every influential factor much less determine how sensitive the security is to a particular factor. But getting "close enough" is often good enough; in fact studies find that four or five factors will usually explain most of a security's return: surprises in inflation, GNP, investor confidence and shifts in the yield curve.