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

A portfolio manager holds a $50 million equity portfolio whose returns are explained by a single-factor model with a market factor beta of 1.20. The manager wants to remove all exposure to the market factor using index futures positions. What position is required, in terms of notional value of the index futures?

The manager should short $60 million of index futures. The hedge notional equals the portfolio value times its factor beta, 1.20 times $50 million, and the position is short to offset the portfolio's positive market exposure, leaving no net market factor sensitivity.

  1. AShort $60 millionCorrect
  2. BShort $50 million
  3. CLong $60 million
  4. DShort $41.7 million

Explanation

To neutralize factor exposure, the hedge notional equals beta times portfolio value: 1.20 x $50 million = $60 million, and the position must be short to offset the positive exposure. Short $50 million ignores beta. Long adds exposure. $41.7 million divides by beta instead of multiplying.

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