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Arbitrage Pricing Theory (APT)

Arbitrage Pricing Theory, developed by Stephen Ross in 1976, is a multi-factor asset pricing model that determines the return of an asset based on multiple sources of systematic risk. It offers a more flexible alternative to the Capital Asset Pricing Model (CAPM), which relies on a single market factor.

Overview

APT posits that the return of a security is influenced by various macroeconomic factors or theoretical market indices, and not solely by market risk. These factors could include inflation rates, exchange rates, interest rates, and others.

Formula

The expected return according to APT can be modeled as:

\(E(R_i) = R_f + \beta_1 F_1 + \beta_2 F_2 + \dots + \beta_k F_k + \epsilon_i\)

Where:

  • \(E(R_i)\) is the expected return of asset i.
  • \(R_f\) is the risk-free rate.
  • \(beta_k\) represents the sensitivity of the asset to factor k.
  • \(F_k\) represents a systematic risk factor k.
  • \(epsilon_i\) is an idiosyncratic risk or noise component.

Key Points

  • Multiple Factors: APT considers multiple factors affecting returns, providing a broader view of influences on asset prices.
  • No Arbitrage: Assumes no arbitrage opportunities; profits should not be achievable without risk.
  • Flexibility: Allows for the inclusion of various factors as needed to explain asset returns, making it adaptable to different investing contexts.
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