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Formulas for this lecture can be found in my online formula sheet and paper formula sheet.

A futures contract is essentially an exchange of promises. A buyer of a futures contract promises to take delivery of (ie buy) a specified amount of a commodity (like wheat, gold, or soybeans) when the contract expires; a seller of a futures contract promises to make delivery of (sell) a specified amount of a commodity when the contract expires.

Formulas used in section:

Section titled β€œFormulas used in section:”

If the futures price falls by $2 per bushel from $5 to $3, then Ξ”ContractPrice=βˆ’$2\Delta ContractPrice = -\$2

Buy the contract:

P/L=Ξ”ContractPriceΓ—ContractSizeP/L = \Delta ContractPrice \times ContractSize

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

Sell the contract:

P/L=βˆ’Ξ”ContractPriceΓ—ContractSizeP/L = -\Delta ContractPrice \times ContractSize

ContractSizeContractSize = 5000 bushels wheat (for example)
ContractSizeContractSize = $50 per point of S&P 500 (e-mini)

ValueOfContract=ContractPriceΓ—ContractSizeValue Of Contract = ContractPrice \times ContractSize

If Bob the buyer buys a wheat contract at a contract price of $4.50 and then the contract price rises to $4.70, what is his P/L? What would his P/L be if he had sold the contract instead?

βœ” Click here to view answer

Buy the contract:

Profit=Ξ”ContractPriceΓ—ContractSize=($4.70βˆ’$4.50)Γ—5000=$1000 \begin{aligned} Profit &= \Delta ContractPrice \times ContractSize \\ &= (\$4.70-\$4.50)\times 5000 \\ &=\$1000 \end{aligned}

Sell the contract:

Profit=βˆ’Ξ”ContractPriceΓ—ContractSize=βˆ’($4.70βˆ’$4.50)Γ—5000=βˆ’$1000 \begin{aligned} Profit &= -\Delta ContractPrice \times ContractSize \\ &= -(\$4.70-\$4.50)\times 5000 \\ &= -\$1000 \end{aligned}

If Bob the buyer buys an e-mini S&P 500 contract at a contract price of 3725 and the S&P rises to 3798, what is his P/L? What would his P/L be if he had sold the contract instead?

βœ” Click here to view answer

I sometimes use the same shortcut formulas I used above. However, let’s start by doing it the way that Bruce does it in the slides:
   Seller: Owes buyer $50 Γ— Index value = $50 * 3798 = $189900

   Buyer: Owes seller $50 Γ— initial contract value = $50 * 3725 = $186250
Bob the Buyer pays $186250 and receives $189900.

Therefore, his profit is:
  profit = $189900 - $186250 = $3650
The seller’s profit will be the opposite of this.

Sometimes, I find it faster to do index problems like Bruce demonstrated for wheat contracts. You’ll get the same answer!

Buy the contract:

Profit=Ξ”ContractPriceΓ—ContractSize=(3798βˆ’3725)Γ—$50/point=(3798βˆ’3725)Γ—$50=$3650 \begin{aligned} Profit &= \Delta ContractPrice \times ContractSize \\ &= (3798 - 3725)\times \$50/point \\ &= (3798-3725)\times \$50 \\ &= \$3650 \end{aligned}

Sold the contract:

Profit=βˆ’Ξ”ContractPriceΓ—ContractSize=(3798βˆ’3725)Γ—$50/point=βˆ’(3798βˆ’3725)Γ—$50=βˆ’$3650\begin{aligned} Profit &= - \Delta ContractPrice \times ContractSize \\ &= (3798 - 3725)\times \$50/point \\ &= -(3798-3725)\times \$50 \\ &= -\$3650 \end{aligned}

Buying the contract is a bet that the price will go up. Therefore, it is β€œbullish.”
Selling the contract is a bet that the price will go down. It is β€œbearish.”

Initial margin is the amount that the buyer or seller of a futures contract must have on deposit with their broker in order to buy or sell the futures contract.

Maintenance margin is the amount that triggers a β€œmargin call.” Every day, a buyer or seller’s profit or loss from a trade is added to, or subtracted from, respectively, their brokerage account balance. If they are losing money, and their account balance falls below the maintenance margin level, they are required to deposit sufficient funds to bring their account balance back up to the required initial margin.

Suppose you purchase a S&P 500 stock index future at 4,155.17. Suppose this contract has an initial margin requirement of 15% of the contract value. Also suppose that it has a maintenance margin requirement of $20,000. If the stock index drops to $3800, will you get a margin call? Assume that the contract size is $50 per index point of the S&P 500.

βœ” Click here to view answer

First, we must figure out what the initial margin is in dollars.

Contractβ€…β€ŠValue=$50Γ—4155.17=$207,758.50Initialβ€…β€Šmargin=ContractValueΓ—15%=$207,758.50Γ—15%=$31,163.78\begin{aligned} Contract\; Value &= \$50\times 4155.17 \\ &= \$207,758.50 \\ \\ Initial\; margin &= Contract Value \times 15\% \\ &= \$207,758.50\times 15\% \\ &= \$31,163.78 \end{aligned}

Suppose the contract drops to 3800 points. How much money have you lost?
   Note: I’m using the shortcut formulas that we used in the second β€œBob the Buyer” question.

P/L=Ξ”ContractPriceΓ—ContractSize=(3800βˆ’4155.17)Γ—$50=βˆ’$17,758.50\begin{aligned} P/L &= \Delta ContractPrice \times ContractSize \\ &= (3800 - 4155.17)\times \$50 \\ &= -\$17,758.50 \\ \end{aligned}

Your account started off with $31,163.78 in it, but you lost -$17,758.50 already, leaving only:

$31,163.78βˆ’$17,758.50=$13,405.28\$31,163.78 - \$17,758.50 = \$13,405.28

Because this is less than your maintenance margin, you will get a margin call. You will need to deposit enough money in your account to lift the account balance up to the current initial margin amount.

Stretch question:

Continuing on the previous question… At what value of the S&P 500 would you first get a margin call?

βœ” Click here to view answer

As we saw above, the initial margin is $31,163.78 and the maintenance margin is $20K. You get a margin call when the value of your margin account drops to $20K, so you get a margin call when you have lost:

$31,163.78βˆ’$20,000=$11,163.78\$31,163.78 - \$20,000 = \$11,163.78

This is because, when you’ve lost $11,163.78, you only have $20,000 left in your margin account. Having that little money in your account is precisely what triggers the margin call.

We need to find the value of the S&P 500 which will cause your P/L to be -$11,163.78, precipitating a margin call. We can use algebra for this. All that we have to do is to substitute the numbers we have into our main P/L shortcut formula: P/L = \Delta ContractPrice * ContractSize, because we bought the contract.

Plug and chug: (help)
  1. Equation:
    P/L=Ξ”ContractPriceΓ—ContractSizeP/L = \Delta ContractPrice \times ContractSize
  2. Plug:πŸ”Œ
    βˆ’$11,163.78=Ξ”ContractPriceΓ—$50-\$11,163.78 = \Delta ContractPrice \times \$50
  3. Solve: πŸš‚
    We divide both sides by $50 to get:
    βˆ’$11,163.78/$50=Ξ”ContractPriceΞ”ContractPrice=βˆ’$11,163.78/$50=βˆ’223.28-\$11,163.78/\$50 = \Delta ContractPrice \\ \Delta ContractPrice = -\$11,163.78/\$50=-223.28
  4. Reflect: 🧠
    If the contract goes down by 223.28 points, you will get a margin call. If the contract starts at 4,155.17 and drops by 223.38, then it will end up at 4,155.17-223.38=3,931.79.

We can double check our work, checking to see how much will be in our margin account if the contract drops to 3,931.79

P/L=Ξ”ContractPriceΓ—ContractSize=(3,931.79βˆ’4,155.17)Γ—50=βˆ’11,169.0 \begin{aligned} P/L &= \Delta ContractPrice \times ContractSize \\ &= (3,931.79 - 4,155.17) \times 50 \\ &= -11,169.0 \end{aligned}

We have a little rounding error because my calculations weren’t super exact, but that is approximately correct! We would have $31,163.78 - 11,169.0 = $19,994.78 in our account and would get a margin call.