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FRM Part I · FRM Exam Part I · The Arbitrage Pricing Theory and Multifactor Models of Risk and Return

Under the Arbitrage Pricing Theory, which statement best explains why only systematic factor risk earns a risk premium in a well-diversified portfolio?

Idiosyncratic risk is diversified away in a large portfolio at no cost, so the market offers no compensation for bearing it. Only exposure to systematic factors, which cannot be diversified, earns a risk premium under APT.

  1. AIdiosyncratic risk is eliminated by diversification, so investors cannot earn a premium for bearing itCorrect
  2. BIdiosyncratic risk is always smaller than factor risk for every individual security
  3. CInvestors in APT are assumed to be risk neutral toward firm-specific events
  4. DFactor risk can be diversified away by holding many securities from the same industry

Explanation

In a well-diversified portfolio, firm-specific risks average out and their variance approaches zero as the number of holdings grows. Because investors can remove this risk at no cost, the market does not pay for it. Factor risk cannot be diversified away, so it carries a premium.

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