🔎 Introduction to Futures

Like with options, we can think of profit and loss both “per share” and “per contract.” However, because Futures contract can be for things other than shares of stock, I’ll refer to these versions as:

1. Per contract
2. Per unit

First we’ll discuss P/L per unit of the underlying asset.

P/L per unit when you buy a contract

If you buy a futures contract to purchase 5000 pounds of soybeans for $1.50 per pound, and the actual price when the contract expires is $1.60, then you are getting a discount of $0.10 per pound. Mathematically:

Per-unit P/L when buy contract = $1.60 - $1.50 = Market Price - Contract Price = $0.10
To calculate your total (per contract) profit, you just multiply the per-unit profit by 5000 pounds. It’s just like with options.

You can use the same calculate for when you are losing money. For example, if the actual price of soybeans is $1.45 when the contract expires, then you are overpaying by $0.05 per pound. We write this loss as:

Per-unit P/L = $1.45 - $1.50 = Market Price - Contract Price = -$0.05 (A negative number indicates a loss.)

Sometimes, I will write this as:

Per-unit P/L = Δ Contract Price This way is a helpful way of thinking about it if you sell to close your contract (and this is what the majority of futures traders will do.

For example, suppose that you buy a futures contract to purchase 5000 pounds of soybeans for $1.50 pound and the price rise all of the way up to $1.66 per pound. If you sell your contract back to close your position out at $1.66 per pound, then you have bought the contract at $1.50 and sold it at $1.66, so your profit is equal to the change in the contract price:

Per-unit P/L = Δ Contract Price = New Contract Price - Old Contract Price

Note that you can also use this formula for index options (or any other sort of option). Suppose you purchase an e-mini future on the S&P 500 at 4000 points. Suppose it expires in 4 months. Then, a week later, you sell that contract at a futures price of 4100 points. Your P/L per point will be:

Per-unit P/L = Δ Contract Price = New - Old = 4100 points - 4000 point = 100 points. This might be hard to interpret per point, so let’s think of it per-contract. An E-Mini S&P contract has a contract-size of $50 per point, so your total profits will be $50 per-point * 100 points = $5,000.

Per contract profit

As we saw with the examples above, the per-contract profit is just the “per-unit profit” multiplied by the contract size.

Per-contract profit = per-unit profit × contract size

If you buy the contract, this is:

• per-contract P/L = Δ contract price × contract size
  • (if you sell to close out your position)
  • Δ contract price = new price - old price
• per-contract P/L = (market price - contract price) × contract size
  • (if you hold to expiration)

If you sell the contract, this is:

per-contract P/L = - Δ contract price × contract size

(if you sell to close out your position) Δ contract price = new price - old price

• per-contract P/L = - (market price - contract price) × contract size
  • (if you hold the contract to expiration and must actually take delivery of the good)

Summary

ΔContractPrice = NewPrice - OldPrice = FuturesPrice - MarketPrice

(If you buy or sell a contract and it expires later, then the price that you purchased the contract at is the FuturesPrice. The Market Price is the market cost of that commodity today.)

Buy the contract: P/L = ΔContractPrice * ContractSize

If you buy the contract, you want ΔContractPrice to be positive and large, so it’s a bet on an increase in the contract price.

Sell the contract: P/L = -ΔContractPrice * ContractSize

For an index future, you just use point values on the index as the prices.

Examples

✏️ Suppose that you bought the E-Mini S&P Contract at 4100. When your futures contract expires, the S&P is at 4150. What is your P/L?
✔ContractSize for an e-mini is $50/point Buy the contract: P/L = ΔContractPrice * ContractSize = (4150-4100)*$50 = $2500

✏️ Suppose you sold a soybean contract at $11 and then closed out your position by buying it back at $12. The ContractSize is 5000 bushels. What is your P/L?
✔ Sell the contract: P/L = -ΔContractPrice * ContractSize = -($12 - $11) * 5000 = -$5000.00