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CA Final · Advanced Financial Management · Portfolio Management

Under a single-factor APT, the risk-free rate is 7%. Portfolio A has factor sensitivity 1.0 and expected return 12%. Portfolio B has factor sensitivity 2.0 and expected return 16%. Both are well diversified. Which arbitrage action exploits the mispricing?

Short Portfolio B and buy the replicating mix of A and the risk-free asset. A offers a 5% premium per unit of sensitivity, so beta 2.0 should return 17% (2 x 12% minus 7% borrowing), but B yields only 16%. This gives a riskless 1% gain.

  1. AShort Portfolio B and invest in a combination of Portfolio A and the risk-free asset replicating beta 2.0, as B is overpricedCorrect
  2. BBuy Portfolio B and short a mix of Portfolio A and risk-free asset, as B is underpriced
  3. CBuy Portfolio A and short the risk-free asset, as A is underpriced
  4. DNo arbitrage exists because both portfolios lie on the same line

Explanation

A's premium per unit of factor sensitivity is (12-7)/1 = 5%. So a beta of 2.0 should earn 7 + 2 x 5 = 17%, but B earns only 16%. B is overpriced. Replicate beta 2 by investing 2 times in A and borrowing 1 at 7%: return = 2 x 12 - 7 = 17%. Short B (16%) and buy this mix (17%) to earn a riskless 1%. Buying B would be the wrong direction.

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