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

A long-short manager is long a $80 million stock portfolio with market beta 1.25 and expected return 11.0%. The risk-free rate is 3%, and the expected market return is 9%. The manager shorts index futures to make the portfolio market neutral, with the futures priced fairly so they earn the market's expected excess return over the risk-free rate. Treating the position as fully funded, what is the expected return of the hedged portfolio, as a percentage of $80 million?

The hedged portfolio's expected return is 3.5%. CAPM gives a required return of 10.5%, so alpha is 0.5%. Removing market exposure with fairly priced futures leaves the risk-free rate of 3% plus that 0.5% alpha.

  1. A3.5%Correct
  2. B6.5%
  3. C2.0%
  4. D5.0%

Explanation

Required return under CAPM = 3% + 1.25 x 6% = 10.5%, so alpha = 11.0% - 10.5% = 0.5%. Hedged portfolio earns the risk-free rate plus alpha: 3% + 0.5% = 3.5%. Option 6.5% wrongly uses 11% - 3% + ... mistaken beta handling; 2.0% subtracts alpha wrongly.

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