Arbitrage Pricing Theory (APT)

The APT, or arbitrage pricing theory, provides a framework to assess market efficiency and detect arbitrage chances in financial markets.

What Is the Arbitrage Pricing Theory (APT)? 

The Arbitrage Pricing Theory (APT) is an extended model of the Capital Asset Pricing Model. It was developed in the 1980s and provides a framework for evaluating market efficiency and identifying arbitrage opportunities in financial markets. The theory is based on three main principles: risk, opportunity cost and equilibrium.

What Is Arbitrage?

Arbitrage is a trading technique that involves risk-free profit that can be earned by trading in two or more markets simultaneously. In many markets, arbitrage opportunities are rare because the markets are usually not identical, so it’s impossible to have the same opportunity in all the markets (unless you use some type of black box computer trading system). The arbitrage pricing theory (APT) is an economic theory that examines the relationship between asset prices and risk. It focuses on the idea that if two securities are priced differently, an investor can make a risk-free profit by buying one and selling the other.

Arbitrage Pricing Theory (APT) and Market Efficiency

The APT assumes that markets are efficient and that prices represent the best estimate of the true value of an asset. In other words, an asset’s price reflects all available information about the asset. If the price is different from what the APT predicts, then it’s possible that the information is not correctly reflected in the market price.

APT suggests that the expected return of an asset can be determined by the risk associated. Markets are efficient when arbitrage opportunities do not exist. The APT states that efficient markets should have the same rate of return on securities. It also states that the expected return on each security should be proportional to the risk associated with that security.

Mathematical Model for the Arbitrage Pricing Theory (APT)

The APT uses arbitrage to predict the expected return on each asset. It is calculated based on the risk associated with the asset using the following formula:

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Limitations of the Arbitrage Pricing Theory

The APT assumes that all investors are rational, all securities are efficiently priced, and the markets approach equilibrium. However, the assumption that all investors are rational is questionable since investors tend to make irrational investment decisions. 

The assumption that all securities are efficiently priced and the markets approach equilibrium are also questionable. While some financial markets are relatively efficient, others are not. Even in relatively efficient financial markets, arbitrage opportunities may exist. It is difficult to measure the convergence rate because the markets are constantly changing. The APT only predicts that the expected return on each asset should be proportional to the risk associated with that asset, not exactly equal.