FRM Part II · FRM Exam Part II · VaR Mapping
A manager holds $6 million of stock A (beta 1.5) and $4 million of stock B (beta 0.5). She wants to cut the portfolio beta to 0.5 by selling index futures. The index level is 2,000 and the futures multiplier is $250 per index point. How many futures contracts should she sell?
The portfolio beta is 1.1, giving $11 million of index exposure. Cutting beta to 0.5 leaves $5 million, so $6 million must be hedged. Each contract has notional $500,000 (2,000 times $250), so she must sell 12 contracts.
- A22
- B10
- C6
- D12Correct
Explanation
Portfolio beta = (6×1.5 + 4×0.5)/10 = 1.1, so index exposure is $11m. Target exposure is $5m, so reduce by $6m. Contract notional = 2,000 × 250 = $500,000, so 6m/500k = 12 contracts. Selling 22 would fully hedge to beta zero; 10 ignores the actual beta of 1.1.
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