Author’s note: This document is primarily written for the investing@ group at Google. This is published on the open web, but much of the content will have a bias toward what that group tends to care about.

Disclaimer

On investing@, there are many discussions that involve futures. Errors are frequent about the basic mechanics of futures. I am writing this post to clear up some misconceptions. There are of course many documents like this floating around on the web, but this is mine, and I hope it will be more clear than other documents.

The author of this document is not a hedge fund manager or certified financial advisor; I am a software engineer. Nothing in this document will tell you how to make easy money. This document is mostly about the mechanics of the futures market.

Futures, Forwards, and the no-arb rule

TL;DR, and motivation

The main purpose of futures markets for a retail trader is that it gives us access to interest rates that are only available to large banks. Euro-denominated loans with negative interest rates are the norm for banks, but rarely directly available to retail traders. Via the futures markets and the law of no-arbitrage, retail traders can effectively borrow Euros at negative interest rates or even lock in Euros at negative interests for up to a decade.

We will start the discussion with currency futures. Currency futures are not especially popular trading tools, and I don’t think most retail investors should touch them. With that said, let’s discuss them anyway because it introduces two key concepts: the concept of a forwards price, and the rule of “No arbitrage”. For the purpose of this discussion, we will use the Euro as an example, though everything discussed applies to all financial futures.

How much is a Euro delivered in 3 months’ time worth today?

As the name suggests, futures are about the future. If you go long (buy) a Euro future for June 2021 at $1.11 per Euro and hold to expiration, then on the right day in June 2021, you will be given a pile of Euro, and you will pay $1.11 per Euro. This is not an option; both sides have the obligation to make this happen.

If the Euro is over $1.11 on that day, you will have turned a profit. Even if you don’t want the Euro, you can sell the Euro for a profit.

If the Euro is under $1.11 on that day, you will have lost money. Even if you do want the Euro, you could have simply brought the Euro for less money.

You are a trader at a major bank. What is the correct price for a Euro delivered in 3 month’s time?

All you need to answer this question is the following: interest rate in dollars, the interest rate in Euro, and the current spot price of the Euro. Imagine the following set of transactions:

Going long the Euro future. (So someone will deliver you a bunch of Euro at the pre-agreed upon price at a pre-agreed upon date in the future.)

Note that this can be broken into two parts, with the quantity known in advance

Someone will give you a bunch of Euro at a future date.
You will have to give them a bunch of dollars at that same future date.

Taking a loan in Euro. You pay some interest based on Euro rates. Convert the Euro to dollars.
Deposit the dollars you got. You get some interest based on dollar rates.
Wait until the day arrives. Use the dollars in step 3 to pay your dollar obligations to your counterparty. Use the Euro from the transaction to pay off your loans (step 2).

Based on the interest rates and the current spot price, you can figure out the fair price for the future. The formula is this:
Forward Price = Spot Price + Euro interest rates - dollar interest rates

Note that as of May 2021, Euro interest rates are negative, but dollar interest rates are positive, so the forward price is always lower than the spot price.

You also discovered a way to perform arbitrage. Based on the rules from above, if the future price ever differed from the fair price, you now have a way to make absolutely riskless money by performing the set of trades above. Free money.

There is of course more than a single bank in the world that likes free money. Therefore, banks will buy and sell Euro futures until the price hits the fair price precisely.

The no-arbitrage rule

The no-arbitrage rule states that it is never possible to construct a set of trades such that you will end up with a profit no matter what happens. There is one caveat in the rule:

The rule is enforced by humans and machines built by humans. As such, someone needs to be arbitraging to keep the prices in line. Circa 2021, this is pretty much all done by high-frequency trading firms. When prices diverge, the first group to notice and trades to bring prices back in line wins. The odds of a retail trader finding a violation of this rule is therefore vanishingly small, thanks to humans being slow.

Convertibility

For the no-arb rule, convertibility is important. GOOG and GOOGL represent the same underlying company, but there is no mechanism to convert shares of one to the other. Therefore, it is impossible to perform arbitrage between GOOG and GOOGL: you noticed that the prices diverged, so you short one and buy the other. Problem is, there are no reason why the prices can’t keep diverging. Arbitraging between GOOG and GOOGL requires the ability to remain solvent until the markets become rational, which is difficult. For our example of Euro futures above, arbitraging between them only requires the ability to remain solvent until the 3rd Friday of June 2021, which is much easier.
Corollary to no-arbitrage rule: Turning the futures into normal transactions

In the Euro example, we had a formula to calculate how much Euro future should cost very accurately. If the actual market price was anything different, a bank would be able to step in and arbitrage.

Assuming the no-arbitrage rule, then, we can assume the following property to hold:

Going long on Euro futures + borrowing Euro + lending dollars + converting Euro to Dollars = 0

Therefore, we can derive the following property:

Going short on Euro futures = borrowing Euro + lending dollars + converting Euro to Dollars

Remember, in the math above, the borrowing and lending uses rates that are available to banks. Thanks to the no-arbitrage rule, retail effectively gets the same interest rates as the banks, as long as there is the right futures contract.

Futures mechanics

So far, we have discussed holding futures to expiration. Which is something that people generally don’t do. One important mechanic of futures is all contracts are against the exchange. That is, if you and I trade on the opposite side of a futures contract, the actual rights and obligations in the future to actually deliver are against the exchange, not against each other. This means that it is possible to get out of a contract by simply taking the opposite direction.

For example, if you were to go long on the Euro future at $1.11, and the next day, the Euro future goes to $1.10, you can go short on the Euro at $1.10. The two will cancel out. But because the position moved against you, you will have to pay $0.01 per Euro to the exchange.

Mark to market, daily settlement, and margin

This leads us into an important part of future mechanics: each day, all open positions are “marked-to-market”, and “daily settlement” occurs where the exchange pays you if the position moves in your favor, and you pay the exchange if the market is against you.

To make this work, futures have a concept of margin, which is money that both sides need to deposit with the exchange. Each day, as the positions are marked to market, money is taken from the margin of the losing side and given to the winning side. If the margin falls below the minimum margin set by the exchange, the exchange will liquidate the position in a margin call.

The margin on most futures is not large. This generally allows for very high leverage.

Other financial futures

Based on the example of Euro futures we can extend the math and logic to other financial futures.

For example,:
Long S&P 500 futures contract = Buying SPY+ borrowing the money to buy SPY
Long Nasdaq futures contract = Buying QQQ + borrowing the money to buy QQQ
Long treasury futures contract = Buying treasury bonds + borrowing the money to buy the bond.

Non financial futures

This simplistic logic works for financial futures, but breaks down for non-financial futures. There are many reasons for this, but the simplest is storing and moving SPY shares is free, but storing and moving mountains of oil is not. The most famous oil futures contract, WTI, requires delivery of oil to a specific spot in Cushing, OK. There are arbitrage desks at banks and funds that keep track of oil costs in various parts of the world, transportation costs, and storage costs, but the costs are very difficult to reason about. Non-financial futures carry the danger where the investor thinks that they are betting on the price of oil, but they are accidentally betting on the repair timetable of a pipeline that moves oil to Cushing, OK.

Zero Sum Game?

There are those who say that futures are a zero-sum game and therefore carry no expected value for either side. This is true to some extent; for every long, there needs to be a short. However, as discussed above, the prices for the S&P 500 futures are set by the arbitrage against the underlying index. The outcome of buying the futures has to be the same as buying the underlying stocks of the S&P 500 while borrowing money at money market rates. Whether there is a positive expected value in buying the stocks in the S&P 500 is up to the reader, but the expected value does not change just because the stocks are bought indirectly via the futures.

A special note on the S&P 500 futures

On the Chicago Mercantile Exchange (CME), the S&P 500 futures trade with the ticker of /ES. The formula for /ES that satisfy the no-arb rule is:

Futures price = Spot price - dividends + interest.

We will be discussing /ES and options on /ES on a upcoming options section.

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