Explain arbitrage pricing theory (APT), the assumptions it rests on, and how it connects to multifactor models

Arbitrage pricing theory says an asset's expected return is linear in its sensitivities to a set of systematic factors: r = risk-free rate + the sum of each factor sensitivity times that factor's risk premium. It rests on three assumptions: returns are generated by a factor model; investors can form well-diversified portfolios in which asset-specific risk disappears; and no arbitrage opportunities persist among such portfolios. Unlike the CAPM, it needs no assumptions about utility or a market portfolio and allows several factors, but it does not say what the factors are or how many there should be. Multifactor models, whether macroeconomic, fundamental or statistical, supply them. The trap is thinking APT requires investors to hold the market portfolio.