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Consider a factor model like Fama and French (1993). Total risk has two components, systematic risk and idiosyncratic risk. Idiosyncratic risk can be diversified while systematic risk cannot. Systematic risk is the risk that amounts to the priced risk factors of the model.

My question is: when can the risk of a factor be diversified? Can there be a priced and a diversifiable risk factor? Does this implies that investors hold not diversified portfolios?

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