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# Arbitrage Pricing Theory

## What is Arbitrage Price Theory?

In 1976, economics professor Steven Ross proposed an alternative risk modelling tool called Arbitrage Pricing Theory (APT). A multifactor model is a sort of model that assesses the linear relationship between a financial asset and numerous risk variables.

In its most basic form, the phrase arbitrage refers to the simultaneous purchase and sale of two securities to profit from a perceived anomalous price differential between the two assets. APT is a model that calculates expected returns based on several risk factors. Arbitrage Price Theory implies that there are no arbitrage opportunities available and that if there are, they will vanish soon owing to market participants’ trading behaviour.

## Example

ERiERz+EI-ERz* βn

where:

E(R)i​=Expected return on the asset

Rz​=Risk-free rate of return

βn=Sensitivity of the asset price to macroeconomic factor n

Ei=Risk premium associated with factor i​

For example, the following four factors have been identified as explaining a stock’s return. Its sensitivity to each factor and the risk premium associated with each have been calculated:

• Gross domestic product (GDP) growth: ß = 0.6, RP = 4%
• Inflation rate: ß = 0.8, RP = 2%
• Gold prices: ß = -0.7, RP = 5%
• Standard and Poor’s 500 index return: ß = 1.3, RP = 9%
• The risk-free rate is 3%

Using the APT formula, the expected return is calculated as

Expected return = 3% + (0.6 x 4%) + (0.8 x 2%) + (-0.7 x 5%) + (1.3 x 9%) = 15.2%

## Why is APT Important?

This idea assists investors and analysts in determining a correct multi-pricing structure and model for asset security based on a relationship between the asset’s expected returns and risk and provides a better estimate than the single factor models such as CAPM.

Owais Siddiqui