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

A well-diversified portfolio has factor betas of 0.8 on factor 1 and 1.5 on factor 2. Risk-free rate is 2%. Factor risk premiums are 4% and 3%. The portfolio currently has an expected return of 11%. Using APT, which action exploits the mispricing, and what is the mispricing size?

APT required return is 9.7%, from 2% plus 0.8×4% plus 1.5×3%. The portfolio's 11% expected return exceeds this by 1.3%, so it is underpriced. An arbitrageur buys it and shorts a portfolio with the same factor betas, locking in a 1.3% riskless gain.

  1. ARequired return is 9.7%; buy the portfolio, financed by shorting a factor-matched portfolio, for a 1.3% gainCorrect
  2. BRequired return is 9.7%; short the portfolio and buy a factor-matched portfolio, for a 1.3% gain
  3. CRequired return is 7.7%; buy the portfolio, financed by a factor-matched short position, for a 3.3% gain
  4. DRequired return is 10.2%; buy the portfolio financed by a factor-matched short, for a 0.8% gain

Explanation

Required return = 2% + 0.8×4% + 1.5×3% = 2% + 3.2% + 4.5% = 9.7%. The portfolio offers 11%, so it is underpriced by 1.3%. Buy it and short a replicating combination with identical betas to lock in 1.3%. Option 3 omits the risk-free rate incorrectly in sums.

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