2.1 Slide 8

An investor enters into a short position in a gold futures contract at 294.20 USD. Each futures contract controls 100 troy ounces. The initial margin is USD 3,200, and the maintenance margin is USD 2,900. At the end of the first day, the futures price drops to 286.6 USD. What is the profit or loss at the end of the first trading day?

Solution. We consider to chose number B. USD 760

An investor has short the gold futures contract, he will benefit only if price falls.

In this case price has decreased, so he will have earn: \[\text{Earn} =(294.20-286.6)\times 100=760\]

2.2 Slide 11

The below table shows the results of nine days’ trading in two identical long futures contracts on VN30 index. Unit of prices is 1000 (VND). Complete the table and find the overall gain or loss over the nine days’ trading in the four contracts.

Solution.

Consider a long future contract:

• The margin ratio is (15,000/103,502)*100 = 14.4925%
• Maintenance ratio: (12,000/15,000)*100 = 80%
• The overall gain of the nine days’ trading in the two contract is 1, 2,926,000 ∗ 2 = 5,852,000 (VND)
• The rate of return is 2,926/15,000 = 19.51% in 9 trading days.

2.3 Slide 16

It is \(1^{\textrm{st}}\) of July. A company knows it will have to buy 1000 metric tons of gas oil on \(1^{\textrm{st}}\) of October. The spot price per metric ton on \(1^{\textrm{st}}\) of July is $214.65. A long October futures contract in gas oil is priced at $219.70 per metric ton. The size of each futures contract is 100 metric tons.

1. What is the number of futures contracts bought for perfect hedging?
2. How much money should the company pay to buy 1000 metric tons of gas on \(1^{\textrm{st}}\) October?

Solution.

1. The number of futures contracts bought for perfect hedging is: 1000/100=10 contracts
2. On 1 October, again there are two possibilities (all prices are per metric ton).

• The spot price on 1 October is greater than or equal to $219.70. Suppose the spot price is $220.50.

Since, at maturity, the spot price and the futures price converge, the futures price on this day will be close to $220.50. The futures contracts are to buy the gas oil for $219.70, so by closing out its futures contracts, the company will make a profit of (approx) $(220.50 − 219.70). The company will pay $220.50 for the gas oil. Hence, the company will be paying $220.50 − $(220.50 − 219.70) = $219.70 per metric ton, as hoped for.

• The spot price on 1 October is less than $219.70.

Suppose the spot price is $218.30. By closing out the futures contracts, the company loses (approx) $(219.70 − 218.30). In the purchase, the company pays out $218.30. So in total, the company pays out (approximately) $218.30 + $(219.70 − 218.30) = $219.70.

So, money should the company pay to buy 1000 metric tons of gas on \(1^{\textrm{st}}\) October is: 219.7 \(\times\) 1000=$219700

3.1 Problem 5

On 7 September, Martin enters three long futures contracts in corn with December delivery. One contract is to buy 5000 bushels of corn and today the price of a December futures contract in corn is 268 cents per bushel. Initial margin is set at $1300 per contract. Maintenance margin is 75% of the initial margin. The futures price on successive days is:

Martin closes out the contract at the close of trading on Day 7. Complete the table. What is Martin’s overall gain or loss?

Solution

Therefore, the overall gain or loss incurred from the future contract is at -$1,650

3.2 Problem 6

The details of 9 days’ trading in a long futures contract are shown. There is something wrong with this table. What is it?

Solution

On Day 6,the margin account balance should be $21600.The calculation performs a margin call when the margin account falls below the level of the initial margin. A margin call should be made when the margin account falls below the maintenance margin

3.3 Problem 7

The details of 8 days’ trading in a short futures contract are shown. Prices are in pounds. Complete the table. What was the overall gain or loss over the 8 days of trading?

Solution:

Any amount below the maintenance margin would result in a margin call. The margin call would be the difference between the Initial Margin and the current margin shortfall. For the future prices provided on daily basis, there is a need to determine the contract value that would be the product of the number of contracts, contract size, and future price applied on daily basis. Compute the contract value on day 1: \[\text{Contract Value} =\text{Number of contract}\times\text{Contract Size}\times\text{Future Size} \\=4.78\times 5\times 10,000=239,000\] Compute the contract value on day 2,3,4, …,8 similarly

Compute the overall gain or loss as shown below: \[Overall gain=14,000+7,000+-5,500+-6,000+-9,500+-9,000+-10,000\\=-19,000\]

As per the above table above, the individual would get margin calls for the day ending 7 and day 8 as the margin account went to -4,000 and -5,000 which is below the maintenance margin of £3,750 as prescribed by the broker before facilitating the futures contract. Therefore, the overall gain or loss from strategy is at -19,000.

3.4 Problem 8

The results of 8 days’ trading in a long futures contract are shown. Prices are in dollars. Complete the table. Find the overall gain or loss over the 8 days.

Solution:

Overall gain $840 per contract or $2520 on the three contracts.

3.5 Problem 9

The figures from 7 days’ trading in a short futures contract can be seen. Prices are in pounds. Complete the table. What was the overall gain or loss over the 7 days’ trading?

Solution:

Overall gain £1700 per contract or £5100 on the three contracts.