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

A stock follows a two-factor model with a risk-free rate of 4%, betas of 1.0 on GDP growth and 0.5 on inflation, and risk premiums of 3% for GDP and 2% for inflation. Its actual expected return in the market is 7.5%. Relative to APT, the stock is:

The stock is overpriced. Its APT required return is 4% + 1.0×3% + 0.5×2% = 8%, but it is expected to earn only 7.5%. Since the expected return falls short of the compensation required for its factor risk, its price is too high.

  1. AFairly priced because 7.5% exceeds the risk-free rate
  2. BOverpriced, since the APT return is 8.0%Correct
  3. CUnderpriced, since the APT return is 8.0%
  4. DOverpriced, since the APT return is 7.0%

Explanation

APT return = 4% + 1.0x3% + 0.5x2% = 4 + 3 + 1 = 8%. The market-implied expected return of 7.5% is below the 8% required, so the price is too high (overpriced). Calling it underpriced reverses the comparison.

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