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FRM Part I · FRM Exam Part I · Using Futures for Hedging

A portfolio manager holds a diversified equity portfolio worth $50 million with a beta of 1.2 relative to an index. The manager wants to reduce the portfolio beta to zero using index futures. The index futures price is 2,000 and the contract multiplier is $250. How many contracts should be traded?

The manager should sell 120 contracts. Each contract is worth $500,000 (2,000 x 250), and eliminating a beta of 1.2 on $50 million requires futures notional of 1.2 x $50 million = $60 million, which is 120 contracts, sold short.

  1. ASell 100 contracts
  2. BSell 120 contractsCorrect
  3. CBuy 120 contracts
  4. DSell 83 contracts

Explanation

Contract value = 2,000 x 250 = $500,000. Contracts to go to beta zero = 1.2 x 50,000,000 / 500,000 = 120, and the manager must sell since the position is long equities. Selling 100 ignores the beta. Buying has the wrong direction. Selling 83 divides by beta instead of multiplying.

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