Arbitrage Pricing Theory and Multi-Factor Models › Arbitrage Pricing Theory and Multi-Factor Models

In the previous chapter, we explored the Capital Asset Pricing Model, which elegantly explains expected returns through a single factor: the market portfolio. While CAPM provides powerful insights, it relies on strong assumptions and reduces all systematic risk to one dimension. Real markets, however, are influenced by multiple sources of risk: interest rate changes, inflation surprises, oil price shocks, and shifts in investor sentiment toward different types of stocks.

Arbitrage Pricing Theory (APT), developed by Stephen Ross in 1976, offers a more flexible framework. Rather than prescribing a single source of systematic risk, APT allows for multiple factors to drive returns. The theory rests on a simple but powerful idea: in well-functioning markets, arbitrage opportunities cannot persist. This no-arbitrage condition, combined with a factor structure for returns, yields pricing relationships similar to CAPM but with greater generality.

This chapter develops the APT framework from first principles, then explores its practical implementation through multi-factor models. We'll examine the famous Fama-French factors that have transformed empirical finance, learn to estimate factor exposures through regression, and build working factor models. By the end, you'll understand both the theoretical foundations and practical applications of factor-based investing.