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?

Choose one answer.

a. $9,980,000

b. $10,860,000

c. $9,085,000

d. $10,475,000

The correct answer is $10,475,000.

[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

But loss on the index is 50/800 = -6.25%.

The index pays a dividend of 4% per annum, or 1% per 3-months. So investor would earn -5.25% in the 3-month period. Also, risk-free interest rate is approximately 1% per 3-months.

So, Expected return on the portfolio during 2-months when the 3-months return on the index is -5.25% is given by,

1 + [1 * (-5.25 – 1)] = -5.25%

Therefore, expected value of the portfolio at the end of 2-months is given by,

10,000,000 * 0.9475 = $9,475,000

So the expected value of the hedger position is given by,

$9,475,000 + $1,000,000 = $10,475,000

Could you explain why we are using "40" for the gain in futures position? How do we get the value 0.9475?

Thanks

Choose one answer.

a. $9,980,000

b. $10,860,000

c. $9,085,000

d. $10,475,000

The correct answer is $10,475,000.

[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

But loss on the index is 50/800 = -6.25%.

The index pays a dividend of 4% per annum, or 1% per 3-months. So investor would earn -5.25% in the 3-month period. Also, risk-free interest rate is approximately 1% per 3-months.

So, Expected return on the portfolio during 2-months when the 3-months return on the index is -5.25% is given by,

1 + [1 * (-5.25 – 1)] = -5.25%

Therefore, expected value of the portfolio at the end of 2-months is given by,

10,000,000 * 0.9475 = $9,475,000

So the expected value of the hedger position is given by,

$9,475,000 + $1,000,000 = $10,475,000

Could you explain why we are using "40" for the gain in futures position? How do we get the value 0.9475?

Thanks

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