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

A stock has a three-factor model with risk-free rate 2%, market beta 1.10, SMB beta 0.50 and HML beta -0.20. Expected factor premiums are: market excess return 6%, SMB 2%, HML 4%. What is the stock's expected return?

The expected return is 8.8%. Add the risk-free rate of 2% to each beta times its factor premium: 6.6% from the market, 1.0% from SMB, and minus 0.8% from HML. The negative HML beta reduces the expected return.

  1. A8.8%
  2. B9.4%Correct
  3. C10.6%
  4. D7.6%

Explanation

Expected return = 2% + 1.10(6%) + 0.50(2%) + (-0.20)(4%) = 2 + 6.6 + 1.0 - 0.8 = 8.8%. Check: 6.6+1.0=7.6, minus 0.8 = 6.8, plus 2 = 8.8%. The option 9.4% would be wrong, so the key must be recomputed: the correct value is 8.8%.

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