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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 USD 50 million equity portfolio whose returns are explained by a single-factor model with the market index as the factor. The portfolio's estimated beta is 1.20. The manager wants to eliminate the market factor exposure using index futures positions. Which position is required in terms of market value of index exposure?

The manager should short USD 60 million of index futures. A beta-neutral hedge requires a notional equal to beta times portfolio value, 1.20 times USD 50 million, and the position must be short to offset the long market exposure.

  1. AShort USD 60 million of index futuresCorrect
  2. BShort USD 50 million of index futures
  3. CLong USD 60 million of index futures
  4. DShort USD 41.7 million of index futures

Explanation

To neutralize the factor exposure the hedge notional must equal beta times portfolio value: 1.20 x 50 = USD 60 million, taken short. Short USD 50 million ignores beta and leaves residual exposure of 0.20 x 50 = USD 10 million. USD 41.7 million wrongly divides 50 by 1.2.

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