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

An investor owns a $20 million portfolio with beta 1.5 and hedges fully with short index futures. Over the period the index falls 4%, the risk-free rate is negligible, and the portfolio's alpha is zero. Ignoring basis and margin effects, which is the approximate combined result of the hedged position?

The net result is approximately zero. The portfolio loses about 6% (beta 1.5 x 4%), or $1.2 million, while the short futures on $30 million of notional gain 4%, or $1.2 million. The gain offsets the loss when alpha and basis are ignored.

  1. AA loss of about $1.2 million
  2. BA gain of about $1.2 million
  3. CApproximately zeroCorrect
  4. DA loss of about $0.8 million

Explanation

The portfolio falls about 1.5 x 4% = 6%, or $1.2 million. The short futures with notional 1.5 x $20m = $30m gain 4% = $1.2 million. The net is about zero. A loss of $1.2m ignores the hedge, and $0.8m would come from using beta 1 on the portfolio.

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