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

A portfolio manager uses a two-factor model in which the expected return on a stock is the risk-free rate plus the sum of each factor beta multiplied by that factor's risk premium. The risk-free rate is 3%. Factor 1 has a premium of 5% and factor 2 has a premium of 2%. The stock has betas of 1.2 on factor 1 and 0.5 on factor 2. What is the stock's expected return?

The expected return is 10%. Add the risk-free rate of 3% to the factor 1 contribution of 6% (1.2 times 5%) and the factor 2 contribution of 1% (0.5 times 2%). Leaving out the risk-free rate would wrongly give 7%.

  1. A10.0%Correct
  2. B9.0%
  3. C7.0%
  4. D11.0%

Explanation

Expected return = 3% + 1.2×5% + 0.5×2% = 3% + 6% + 1% = 10%. Omitting the risk-free rate gives 7%. Using only the first factor gives 9%.

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