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

Two well-diversified portfolios, A and B, are exposed to one factor. Portfolio A has beta 0.5 and expected return 8%. Portfolio B has beta 1.5 and expected return 14%. The risk-free rate is 2%. Portfolio C, also well diversified with beta 1.0, offers expected return 10%. Which strategy captures an arbitrage profit and what is its size per unit invested?

The 50/50 mix of A and B has beta 1.0 and a return of 11%, while C with the same beta returns only 10%. Buy the mix, short C, and earn a riskless 1.0% per unit invested.

  1. ABuy C, short a 50/50 mix of A and B; profit 1.0%Correct
  2. BShort C, buy a 50/50 mix of A and B; profit 1.0%
  3. CBuy C, short a 50/50 mix of A and B; profit 2.0%
  4. DNo arbitrage exists because C lies between A and B

Explanation

A 50/50 mix of A and B has beta 0.5×0.5+0.5×1.5 = 1.0 and return 0.5×8%+0.5×14% = 11%. C has the same beta but returns only 10%, so C is overpriced relative to the mix. Therefore short C, buy the mix, and earn 1.0%. Rechecking: the key direction is short C and buy the mix, so option 2 is correct.

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