Sure, let's break down the explanation pointwise and include a numerical example to illustrate each concept:
1. Spot Price: The spot price, also known as the cash price, is the current market price of a commodity or financial asset for immediate settlement or delivery. It represents the cost of buying or selling the asset at that specific moment in time.
Example: Let's consider gold. If the spot price of gold is $1,800 per ounce, it means that you can buy or sell one ounce of gold for $1,800 in the current market.
2. Futures Price: The futures price is the price at which a contract is traded today for the delivery of the commodity or asset at some predetermined future date, known as the maturity date. Futures contracts are standardized agreements that specify the quantity and quality of the asset to be delivered.
Example: Suppose there is a gold futures contract with a maturity date one month from now. The futures price for this contract is $1,820 per ounce.
3. Basis: The basis is the difference between the spot price and the futures price of the same commodity or asset. It represents the cost or premium associated with holding the asset in the futures market instead of the spot market until the contract's maturity date.
Example: Using the examples above, the basis would be calculated as follows:
Basis = Spot price - Futures price
Basis = $1,800 - $1,820
Basis = -$20
In this example, the basis is negative, indicating that the futures price is $20 less than the spot price. This situation is known as "backwardation."
4. Convergence of Basis: As the maturity date of the futures contract approaches, the basis tends to converge toward zero. This means that the difference between the spot price and the futures price diminishes over time.
Example: Let's assume that as the maturity date gets closer, the futures price for the gold contract changes to $1,810 per ounce.
Updated Basis = Spot price - New Futures price
Updated Basis = $1,800 - $1,810
Updated Basis = -$10
As the maturity date nears, the basis has reduced from -$20 to -$10, getting closer to zero. This phenomenon is known as the "convergence of basis."
5. Arbitrage at Contract Expiration: At the contract's expiration, the spot price and the futures price must be equal. This is because the futures price, which was agreed upon earlier, has become the current market price for immediate delivery (since it is now the maturity date).
Example: On the expiration date of the gold futures contract, the spot price of gold is $1,810 per ounce. To ensure that there is no arbitrage opportunity, the futures price must also be $1,810 per ounce.
If, for some reason, the futures price were higher or lower than the spot price at expiration, market participants could exploit the price difference through arbitrage. They would buy the asset at the lower-priced market and sell it at the higher-priced market, making a risk-free profit until the prices equalize.
In summary, the relationship between spot and futures prices, as well as the basis, is essential for understanding the dynamics of the futures market and how prices adjust over time until contract expiration. Arbitrage ensures that these prices are in line with each other at the contract's maturity, removing any potential opportunities for riskless profit.
Let's go through the arbitrage process step by step with numerical examples to demonstrate why the futures price must equal the spot price at expiration:
1. Spot Price of Silver: $4.65
2. Futures Price: $4.70
- In this scenario, the futures price is higher than the spot price. To take advantage of this price difference, an arbitrage opportunity exists.
- Arbitrage Process:
- Step 1: Buy Silver at Spot Price ($4.65)
- Step 2: Sell Futures Contract at Futures Price ($4.70)
- Step 3: Deliver the Silver under the Contract at $4.70
- Profit from Arbitrage:
- Profit = Futures Price - Spot Price
- Profit = $4.70 - $4.65 = $0.05
3. Futures Price: $4.61
- In this scenario, the futures price is lower than the spot price. Once again, an arbitrage opportunity exists.
- Arbitrage Process:
- Step 1: Buy Futures Contract at Futures Price ($4.61)
- Step 2: Take Delivery of the Silver by Paying the Futures Price ($4.61)
- Step 3: Sell the Silver at Spot Price ($4.65)
- Profit from Arbitrage:
- Profit = Spot Price - Futures Price
- Profit = $4.65 - $4.61 = $0.04
In both cases, we can see that an arbitrage opportunity arises, and traders can make a riskless profit by exploiting the price difference between the spot and futures prices. The key point is that these arbitrage opportunities exist because the futures contract has a specific expiration date. If the futures price deviates from the spot price, traders can buy or sell the commodity at a favorable price in the present and lock in a profit by offsetting their position in the futures market.
To prevent these arbitrage opportunities and bring stability to the market, the futures price at the maturity of the contract must be equal to the spot price. At expiration, the spot price must converge to the futures price, ensuring that there are no risk-free profits to be made through arbitrage.
The concept of convergence is crucial in futures markets, where traders actively adjust their positions as the maturity date approaches. This ensures that the futures price aligns with the spot price at the time of contract expiration. Arbitrage opportunities, like the ones presented in the examples, help drive the prices together and maintain market efficiency.
Sure! Here are some multiple-choice questions related to the concept of futures prices, spot prices, and arbitrage:
Question 1:
What is the basis in a futures contract?
A) The difference between the spot price and the futures price.
B) The price for immediate delivery.
C) The difference between the futures price and the contract expiration date.
D) The price for delivery at some future point in time.
Answer: A) The difference between the spot price and the futures price.
Question 2:
Why does the basis converge toward zero as the maturity date of a futures contract nears?
A) To create arbitrage opportunities.
B) To encourage speculative trading.
C) To eliminate the need for delivery of the underlying asset.
D) To align the futures price with the spot price at contract expiration.
Answer: D) To align the futures price with the spot price at contract expiration.
Question 3:
Suppose the current spot price of gold is $1,500 per ounce, and the futures price for a contract expiring in one month is $1,520. What arbitrage opportunity exists, if any?
A) No arbitrage opportunity exists.
B) An arbitrage opportunity to profit $20 per ounce exists.
C) An arbitrage opportunity to profit $2 per ounce exists.
D) An arbitrage opportunity to profit $200 per ounce exists.
Answer: B) An arbitrage opportunity to profit $20 per ounce exists.
Question 4:
If the futures price for a commodity is higher than the spot price, what should traders do to take advantage of the situation?
A) Buy the commodity at the spot price and sell the futures contract.
B) Buy the futures contract and take delivery of the commodity at the futures price.
C) Buy the futures contract and sell the commodity at the spot price.
D) Buy the commodity at the spot price and deliver it under the futures contract.
Answer: A) Buy the commodity at the spot price and sell the futures contract.
Question 5:
Why must the futures price equal the spot price at contract expiration?
A) To encourage speculative trading.
B) To maintain market volatility.
C) To create arbitrage opportunities for traders.
D) To prevent riskless profits through arbitrage.
Answer: D) To prevent riskless profits through arbitrage.
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