# Arbitrage pricing theory (APT)

Arbitrage Pricing Theory (APT) is a financial model used to determine the fair value of an asset, taking into account various macroeconomic factors that might influence its return.
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Updated: May 28, 2024

## 3 key takeaways

• APT is a multifactor model that assesses the fair value of an asset based on various economic factors.
• It differs from CAPM by considering multiple sources of risk rather than a single market risk factor.
• APT helps investors identify arbitrage opportunities by comparing the theoretical price to the market price of an asset.

## What is Arbitrage Pricing Theory (APT)?

Arbitrage Pricing Theory (APT) is an asset pricing model that aims to explain the return on an asset as a linear function of various macroeconomic factors. Unlike the Capital Asset Pricing Model (CAPM), which considers only market risk, APT includes multiple factors that might affect an asset’s return, such as inflation rates, interest rates, and GDP growth. The theory suggests that if an asset is mispriced, arbitrage opportunities will arise until the asset’s price aligns with its fair value.

## Importance of Arbitrage Pricing Theory

APT is important because it provides a more flexible and comprehensive approach to asset pricing compared to single-factor models like CAPM. By considering multiple sources of risk, APT offers a more accurate assessment of an asset’s expected return and helps investors better understand the factors driving price changes. This understanding can lead to more informed investment decisions and improved portfolio management.

## How Arbitrage Pricing Theory works

Factors identification: The first step in applying APT is to identify the relevant macroeconomic factors that influence the returns of a particular asset. These factors can vary depending on the asset and the economic environment.

Sensitivity estimation: Next, the sensitivity (or beta) of the asset to each identified factor is estimated. This measures how much the asset’s return is expected to change in response to changes in each factor.

Expected return calculation: The expected return of the asset is calculated as a linear combination of the risk-free rate and the sensitivities to each factor, multiplied by the risk premium associated with each factor.

Arbitrage opportunity identification: Investors compare the expected return derived from the APT model to the asset’s actual market return. If there is a significant discrepancy, it indicates a potential arbitrage opportunity, where investors can profit from the mispricing until the market corrects itself.

## Examples of Arbitrage Pricing Theory application

• Stock valuation: An investor uses APT to value a tech company’s stock, considering factors such as technological innovation rates, interest rates, and industry growth. By estimating the sensitivities to these factors and comparing the expected return to the current market price, the investor identifies a potential mispricing.
• Bond pricing: APT can be applied to bonds by incorporating factors such as interest rate changes, inflation expectations, and economic growth. This helps in assessing whether a bond is fairly priced and identifying arbitrage opportunities.

## Real-world application

Consider an investor analyzing a pharmaceutical company’s stock using APT. They identify key factors affecting the stock’s return, such as regulatory changes, healthcare spending, and R&D success rates. By estimating the stock’s sensitivities to these factors and calculating the expected return, the investor finds that the current market price is significantly lower than the theoretical price suggested by APT. Recognizing this as an arbitrage opportunity, the investor buys the stock, expecting the market price to adjust upwards, aligning with its fair value.

Understanding Arbitrage Pricing Theory is crucial for investors and financial analysts seeking to assess asset prices accurately and identify arbitrage opportunities. By considering multiple factors, APT provides a nuanced approach to understanding the dynamics of asset returns and market pricing.

Related topics you might want to learn about include the Capital Asset Pricing Model (CAPM), factor investing, and risk management. These areas provide further insights into asset pricing theories and investment strategies.

Sources & references
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Arti is a specialized AI Financial Assistant at Invezz, created to support the editorial team. He leverages both AI and the Invezz.com knowledge base, understands over 100,000... read more.