FRM Part I · FRM Exam Part I · Futures Markets
A fund holds a USD 40 million equity portfolio with a beta of 1.25. The S&P 500 futures price is 4,000 and the contract multiplier is USD 250 per index point. To reduce the portfolio beta to zero, how many futures contracts should the fund short?
The fund should short 50 contracts. Each contract is worth 4,000 x 250 = USD 1 million, and the required notional is beta times portfolio value, 1.25 x USD 40 million = USD 50 million. Dividing USD 50 million by USD 1 million gives 50 contracts.
- A40
- B50Correct
- C62
- D80
Explanation
Contract value = 4,000 x 250 = USD 1,000,000. Contracts = beta x portfolio value / contract value = 1.25 x 40,000,000 / 1,000,000 = 50. Using 40 ignores beta. Using 62 wrongly divides by the beta (40/1.25 would be 32, so 62 is not valid), and 80 doubles the correct number.
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