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

A manager runs a USD 100 million long-only portfolio with betas of 1.10 to the market factor and 0.40 to a value factor. The portfolio's alpha is 2% per year with residual volatility 4%. The manager sells market futures and a value-factor swap to remove both exposures, assuming factor betas are exact and hedges are costless. Factor risk premia are 5% for the market and 3% for value, ignoring the risk-free rate. The portfolio's expected return before hedging is 8.7% (alpha plus factor premia). What are the hedged position's expected return and the dollar notional of the market hedge?

The hedged position's expected return is 2.0%, with a short market hedge of USD 110 million. Removing both factor exposures strips out the 5.5% and 1.2% risk premia from the 8.7% total, leaving alpha, and the market notional equals beta 1.10 times USD 100 million.

  1. AExpected return 2.0%; market hedge short USD 110 millionCorrect
  2. BExpected return 8.7%; market hedge short USD 110 million
  3. CExpected return 2.0%; market hedge short USD 40 million
  4. DExpected return 6.7%; market hedge short USD 110 million

Explanation

Check: 2 + 1.10x5 + 0.40x3 = 2 + 5.5 + 1.2 = 8.7%. Hedging removes the factor premia, leaving alpha of 2.0%. The market hedge notional is 1.10 x 100 = USD 110 million short. The 40 million figure is the value-factor notional, and 6.7% removes only the market premium wrongly sized.

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