What is a multi-factor model, and how could one test such models against the CAPM?

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The CAPM is a one- factor asset- pricing model- it assumes that stocks’ returns are determined by returns on the market plus random factors that affect individual stocks. However, some analysts and professionals argue that multi-factor models describe investor behavior better than the CAPM. What is a multi-factor model, and how could one test such models against the CAPM? (Note: Multi-factor models have been tested to see if they work better than the pure CAPM, but the results have been inconclusive.)

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