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

In 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 0.5 on factor 1 and 1.5 on factor 2 and an expected return of 10%. Which action exploits the mispricing?

The portfolio is underpriced. Its APT fair return is 2% + 0.5×4% + 1.5×3% = 8.5%, below its 10% expected return. An arbitrageur buys it and shorts a replicating mix of factor portfolios and the risk-free asset with identical betas, earning a 1.5% riskless profit.

  1. ANo arbitrage exists because the portfolio is fairly priced
  2. BBuy the portfolio and short a combination of the factor portfolios and risk-free asset replicating its betas, because it is underpricedCorrect
  3. CShort the portfolio and buy the replicating combination, because it is overpriced
  4. DBuy the portfolio and borrow at the risk-free rate only

Explanation

The APT fair return is 2% + 0.5x4% + 1.5x3% = 2 + 2 + 4.5 = 8.5%. The portfolio offers 10%, so it is underpriced. Buy it and short a replicating portfolio with the same betas, which earns 8.5%, locking in a 1.5% riskless profit. Shorting the portfolio would be right only if it were overpriced.

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