ARBITRAGE PRICING THEORY
One of the fundamental problems in finance is to explain the cross-section differences in asset expected returns. Specifically, what factors can explain the observed differences. Those factors that systematically affect the differences in expected returns are therefore the risks that investors are compensated for. Hence, the term factors is interchangeabley with the term risk factors.
The Arbitrage Pricing Theory (APT), formulated by Stephen Ross,58 posits that expected returns of assets are linearly related to K systematic factors and the exposure to these factors is measured by factor betas; that is,
where βik is the beta or risk exposure on the k-th factor, and γk is the factor risk premium, for k = 1, 2, …, K.
Technically, the APT assumes a K-factor model for the return-generating process, that is, the asset returns are influenced by K factors in the economy via linear regression equations,
where 
are the systematic factors that affect all the asset returns on the left- hand side, i = 1, 2, …, N; and 
is the asset specific risk. Note that ...
are the systematic factors that affect all the asset returns on the left- hand side, i = 1, 2, …, N; and is the asset specific risk. Note that ...Get The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
