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FRM Part I · FRM Exam Part I · Futures Markets

A USD 20 million portfolio has a beta of 1.5 and is fully hedged to a beta of zero with index futures. Over the hedge period the index rises 4%, and the portfolio rises 5%. The futures position was sized exactly at beta x portfolio value, and the futures price change equals the index change. Ignoring the risk-free rate, dividends and basis, what is the approximate net gain or loss on the combined position?

The combined position loses about USD 200,000. The portfolio gains 5% of USD 20 million, which is USD 1.0 million, while the short futures position of USD 30 million loses 4%, or USD 1.2 million. The portfolio returned less than its beta implied, so the hedge leaves a net loss.

  1. ALoss of USD 200,000Correct
  2. BGain of USD 200,000
  3. CGain of USD 1,000,000
  4. DLoss of USD 1,200,000

Explanation

Portfolio gain = 5% x 20,000,000 = USD 1,000,000. Futures notional = 1.5 x 20,000,000 = USD 30 million, short, so loss = 4% x 30,000,000 = USD 1,200,000. Net = 1,000,000 - 1,200,000 = a loss of USD 200,000. The portfolio outperformed what beta predicted (6% would be expected from 1.5 x 4%, so alpha is negative at -1%), producing the residual loss. Reporting only the portfolio gain ignores the futures loss.

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