FRM Mock Test Q15

d2syh
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FRM Mock Test Q15

A fund manager has a portfolio worth \$10 million with a beta of 1.0. The manager is concerned about the performance of the market over the next 2 months and plans to use 3-month futures contracts on the Nasdaq to hedge the risk. The current level of index is \$800, one contract is on 500 times the index, the risk free rate is 4% per annum, and the dividend yield on the index is 4% per annum. The current 3-month futures price is 750. What is the expected value of the hedger’s position over the next two months?

[Explanation]
Here, value of the futures contracts = 500 * 800 = \$400000
So complete hedge requires 1.0 * 10,000,000 / 400000 = 25 contracts need to be shorted thus minimising the risk.
Since the current 3-month future price turns out be 750. The gain in the short futures position is given by,
40 * (800 – 750) * 500 = \$1,000,000

To calculate the short futures position, why is "40" being used instead of 25 contracts?

Thanks...

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