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

Under a two-factor APT, the risk-free rate is 2%, the risk premium on factor 1 is 4% and on factor 2 is 3%. A well-diversified portfolio has betas of 0.8 on factor 1 and 1.5 on factor 2. What is its expected return?

The expected return is the risk-free rate plus each beta times its factor premium: 2% plus 3.2% plus 4.5%, which equals 9.7%. Leaving out the risk-free rate would give 7.7%, which is wrong.

  1. A9.7%Correct
  2. B7.7%
  3. C5.9%
  4. D9.2%

Explanation

E(R) = 2% + 0.8×4% + 1.5×3% = 2% + 3.2% + 4.5% = 9.7%. Omitting the risk-free rate gives 7.7%. Using only factor 1 gives 5.2%, and adding the betas to the premiums mistakenly gives other values.

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