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FRM Part I · FRM Exam Part I · Pricing Financial Forwards and Futures

A manager holds a USD 20 million equity portfolio with beta 0.90 and wants to raise beta to 1.50 for the next two months using index futures priced at 2,000 with a multiplier of USD 100 per point (contract value USD 200,000). What position is required?

Buy 60 contracts. Raising beta from 0.90 to 1.50 adds 0.60 of market exposure, and 0.60 x USD 20 million / USD 200,000 per contract equals 60. The sign is positive because beta is being increased, which requires long futures.

  1. ABuy 60 contractsCorrect
  2. BBuy 90 contracts
  3. CSell 60 contracts
  4. DBuy 30 contracts

Explanation

Contracts = (target beta - current beta) x portfolio value / contract value = (1.50 - 0.90) x 20,000,000 / 200,000 = 0.60 x 100 = 60. Positive, so buy. Buying 90 uses the full target beta of 0.90 difference error (0.9 x 100), and selling 60 reverses the sign.

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