32.a.1 Define Long Hedge

Let's break down the explanation of a long hedge point by point:

1. **Definition of Long Hedge**: A long hedge is a risk management strategy used by hedgers (investors or traders) to protect against potential losses from an existing short position in an asset.

2. **Short Position**: A short position is taken by selling an asset that the trader does not currently own, with the expectation that its price will decrease in the future. The trader aims to buy it back later at a lower price to make a profit.

3. **Objective of Long Hedge**: The main goal of a long hedge is to offset or mitigate the potential losses from the short position. It does this by creating a counteracting long futures position that benefits from an increase in the price of the underlying asset.

4. **Buying Futures Contract**: To execute a long hedge, the hedger buys a futures contract. A futures contract is an agreement to buy or sell an asset at a predetermined price on a specific date in the future.

5. **Futures Contract and Underlying Asset**: The futures contract used in the long hedge is based on the same underlying asset that the hedger has shorted. For example, let's say the trader has taken a short position in 100 shares of Company X.

6. **Expectation of Price Increase**: The hedger enters into the long futures position because they anticipate that the price of the asset (in this case, shares of Company X) will rise in the future.

7. **Compensation for Short Position Loss**: If the price of the shorted asset indeed increases, the trader would face losses in the short position. However, the gain from the long futures position will help compensate for these losses.

Let's illustrate this with a numerical example:

**Scenario**: A trader shorts 100 shares of Company X at $50 per share, expecting the price to decrease. However, they are concerned that the price might rise in the future, leading to losses in their short position. To protect against this, they decide to enter into a long hedge.

1. **Initial Short Position**: Short 100 shares of Company X at $50 per share.

2. **Buying Futures Contract**: The trader buys a futures contract for 100 shares of Company X, with a delivery date one month from now, at $55 per share. This means they are agreeing to buy 100 shares of Company X at $55 each, regardless of the market price at that time.

3. **Expectation**: The trader anticipates that the price of Company X shares will increase in the next month.

**Possible Scenarios after One Month**:

A. **Price Decreases**: If the price of Company X shares decreases to $40 per share, the short position gains $10 per share (the initial price of $50 minus the current price of $40).

   - Short Position: $10 gain per share * 100 shares = $1,000 gain.

   - Long Futures Position: The futures contract is not exercised since the market price is below the contract price ($40 < $55). The trader incurs a loss of $0, as they are not obligated to buy the shares at a higher price.

Overall, the trader gains $1,000 from the short position and incurs no loss from the long futures position, resulting in a net gain of $1,000.

B. **Price Increases**: If the price of Company X shares increases to $60 per share, the short position incurs a loss of $10 per share (the current price of $60 minus the initial price of $50).

   - Short Position: $10 loss per share * 100 shares = $1,000 loss.

   - Long Futures Position: The futures contract is exercised, and the trader buys 100 shares of Company X at the pre-agreed price of $55 per share. Since the current market price is $60, they gain $5 per share.

   Net gain from the long futures position: $5 gain per share * 100 shares = $500 gain.

Overall, the trader's loss from the short position is offset by the gain from the long futures position, resulting in a net loss of $500 (i.e., $1,000 - $500).

In this example, the long hedge helped the trader limit their potential losses from the short position by taking advantage of a long futures position that benefits from an increase in the asset's price.

Example: Assume an investor will need to buy 75,000 pounds of copper in three months. The current spot price is $2.80/pound. In order to hedge this entire position, the investor will buy three-month futures contracts priced at $3.50. Compute the payment on the overall position assuming the spot price at time of delivery is either $3.00 or $4.25. Suppose each futures contract represents 25,000 pounds of copper.

Sure, let's break down the calculation of the overall payment on the long hedge in both scenarios:

**Scenario 1: Spot Price at Delivery is $3.00/pound**

1. **Spot Price**: The investor needs to buy 75,000 pounds of copper at the spot price of $3.00 per pound. - Total Cost = 75,000 pounds * $3.00/pound = $225,000 2. **Futures Contracts**: The investor hedges the position by buying three-month futures contracts at a price of $3.50 per pound. Each futures contract represents 25,000 pounds of copper. - Number of Contracts Required = Total Pounds to Buy / Pounds per Contract = 75,000 pounds / 25,000 pounds per contract = 3 contracts 3. **Loss from Long Futures Position**: The spot price at delivery is $3.00, which is lower than the futures contract price of $3.50. - Loss per Contract = Futures Contract Price - Spot Price at Delivery = $3.50 - $3.00 = $0.50/pound - Total Loss from 3 Contracts = 3 contracts * $0.50/pound * 25,000 pounds per contract = $37,500 4. **Overall Payment**: To calculate the overall payment, we add the spot price cost to the loss from the long futures position. - Overall Payment = Total Cost + Loss from Long Futures Position = $225,000 + $37,500 = $262,500 **Scenario 2: Spot Price at Delivery is $4.25/pound** 1. **Spot Price**: The investor needs to buy 75,000 pounds of copper at the spot price of $4.25 per pound. - Total Cost = 75,000 pounds * $4.25/pound = $318,750 2. **Futures Contracts**: The investor hedges the position by buying three-month futures contracts at a price of $3.50 per pound. Each futures contract represents 25,000 pounds of copper. - Number of Contracts Required = Total Pounds to Buy / Pounds per Contract = 75,000 pounds / 25,000 pounds per contract = 3 contracts 3. **Gain from Long Futures Position**: The spot price at delivery is $4.25, which is higher than the futures contract price of $3.50. - Gain per Contract = Spot Price at Delivery - Futures Contract Price = $4.25 - $3.50 = $0.75/pound - Total Gain from 3 Contracts = 3 contracts * $0.75/pound * 25,000 pounds per contract = $56,250 4. **Overall Payment**: To calculate the overall payment, we subtract the gain from the long futures position from the spot price cost. - Overall Payment = Total Cost - Gain from Long Futures Position = $318,750 - $56,250 = $262,500 **Explanation**:

In both scenarios, the overall payment comes out to be $262,500. This is because the gain or loss from the long futures position offsets the difference between the spot price at delivery and the futures contract price. When the spot price at delivery is lower than the futures contract price, the investor incurs a loss on the futures position, but this loss is compensated by the lower cost of purchasing copper at the spot price. Similarly, when the spot price at delivery is higher than the futures contract price, the investor gains from the futures position, but this gain is offset by the higher cost of purchasing copper at the spot price. This ability to mitigate risk and lock in a known cost is one of the primary benefits of using hedging strategies like the long hedge.

Sure! Here are some multiple-choice questions related to hedging and long hedges, along with their possible answers:

**Question 1**: What is the purpose of a long hedge in financial markets?

A) To speculate on the price movement of an asset.

B) To protect against potential losses from an existing short position.

C) To increase potential gains from an existing long position.

D) To minimize transaction costs in the futures market.

**Answer**: B) To protect against potential losses from an existing short position.

**Question 2**: Which of the following best describes a short position in financial markets?

A) Buying an asset with the expectation of price appreciation.

B) Selling an asset with the expectation of price appreciation.

C) Buying an asset with the expectation of price depreciation.

D) Selling an asset with the expectation of price depreciation.

**Answer**: D) Selling an asset with the expectation of price depreciation.

**Question 3**: A trader shorts 1,000 shares of Company Y at $60 per share. To hedge against a potential increase in the stock's price, the trader buys 5 futures contracts of Company Y, with each contract representing 200 shares. If the stock's price rises from $60 to $70, what is the net effect of the hedge?

A) The trader incurs a loss on the short position, but the gain from the futures position offsets the loss.

B) The trader incurs a loss on the short position, and there is no gain from the futures position.

C) The trader makes a profit on the short position, but the loss from the futures position offsets the profit.

D) The trader makes a profit on the short position, and there is also a gain from the futures position.

**Answer**: A) The trader incurs a loss on the short position, but the gain from the futures position offsets the loss.

**Question 4**: An investor plans to buy 50,000 barrels of crude oil in six months. The current spot price is $70 per barrel. To hedge this position, the investor buys six-month futures contracts at $75 per barrel. Each contract represents 1,000 barrels. If the spot price at delivery is $80 per barrel, what is the net effect of the hedge?

A) The investor gains from the futures position, but the loss from the spot price increase offsets the gain.

B) The investor incurs a loss on the futures position, but the gain from the spot price increase offsets the loss.

C) The investor incurs a loss on both the futures position and the spot price increase.

D) The investor gains from both the futures position and the spot price increase.

**Answer**: B) The investor incurs a loss on the futures position, but the gain from the spot price increase offsets the loss.

**Question 5**: In a long hedge, an investor buys a futures contract to protect against:

A) A decrease in the value of the underlying asset.

B) An increase in the value of the underlying asset.

C) A decrease in the futures contract price.

D) An increase in the futures contract price.

**Answer**: B) An increase in the value of the underlying asset.