Arbitrage pricing theory

Arbitrage pricing theory models expected asset returns as compensation for exposure to multiple systematic risk factors. It derives this relationship from the assumption that competitive markets contain no persistent arbitrage opportunities.

Factor model: A statistical or economic model that explains outcomes through exposure to a set of common variables. APT expresses each asset’s return as factor exposures plus an asset-specific component.
Capital asset pricing model: An asset-pricing model linking expected returns to exposure to the market portfolio’s systematic risk. CAPM uses one market factor, while APT permits several systematic factors.
Law of one price: The principle that identical claims with identical payoffs should have the same price in an arbitrage-free market. APT extends this pricing intuition across diversified portfolios with different factor exposures.
Macroeconomic factor models: Asset-pricing models that use economic variables such as inflation or interest rates as common return factors. They operationalize APT by choosing observable macroeconomic sources of systematic risk.
Factor zoo: The large collection of proposed variables reported to explain differences in average asset returns. APT does not determine how many factors to include, intensifying model-selection concerns.
Systematic risk: Risk arising from market-wide forces that cannot be eliminated by holding a diversified portfolio. APT prices exposures to shared risks rather than risks unique to individual assets.
Fama–French three-factor model: An empirical asset-pricing model using market, size, and value factors to explain stock returns. It specifies three factors explicitly, unlike APT’s general, unspecified factor set.
Portfolio theory: The study of how investment risk and return depend on combining assets into portfolios. APT’s argument concerns portfolios as well as individual assets.
Statistical factor models: Models that extract common return factors from asset data using statistical techniques. They estimate shared return drivers without requiring APT’s factors to have economic labels.
Factor replication: The effort to verify whether reported return factors persist across samples, markets, and methods. APT’s empirical usefulness depends on whether estimated factor premia replicate.

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