TL;DR: We can expect trading in bitcoin futures to be very speculative, and unlikely to tame the volatility we have seen in the underlying.

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In ye olde world of traditional finance, there is a formula that tells you what the “fair value” price of the future should be. If you want to understand how the futures market works, you need to understand this formula.

For example, speculators use the formula to help them make trading decisions. If the market price of the future is higher than the fair value, profit-minded traders will sell the future. They expect the price to fall back to its fair value. When it does, they will close their position and book a tidy profit.

Simple!

The futures-pricing formula isn't complicated (there are much worse formulae in finance!) but before I assault you with letters and symbols, let’s develop some intuition.

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Imagine you are an oil producer. You dig wells, pump oil, and sell it to refineries. You know that a year from now you’ll have 1 million barrels of oil that you’ll be wanting to sell.

You could wait a year to sell it for whatever the price of oil happens to be on the day, but that’s quite risky. Who knows what dastardly schemes OPEC or the Russians (or even Uncle Sam!) could get up to in the meantime.

Instead, you’ll go to the futures market today and sell some oil futures. Specifically, you’ll sell 1,000 (each oil future is for 1,000 barrels) 12-month oil futures.

Sell! Sell! Sell!

But at what price? Well, that depends on a few things.

The most important variable is today’s price. Ceteris paribus, the higher the price of oil today, the higher the price of the futures contract. The length of the contract is another important variable, but we'll come back to that later.

One of the practical matters with selling oil futures is that they have physical delivery i.e. you will actually be sending someone 1 million barrels of oil. In the meantime, you’ll have to store the oil, and that’s expensive. If the buyer bought 1 million barrels oil in the spot market he’d have to pay storage costs, but since he’s buying in the future, he doesn’t.

At least, not directly.

Those storage costs are a business cost for you like any other. The price you sell you product should be higher than your costs. You’ll pass the cost on to the buyer by adding it the price of the future.

Cost of Carry

If there are costs to holding an asset until the futures contract matures, it stands to reason that there are also benefits. To demonstrate this, consider a future on a Treasury Bond.

Let’s say you own the Treasury and for whatever reason, you know that you’ll have to sell it a year from now. Again, you go the futures market and sell a 12-month future.

What should the futures price be?

The price of a Bond is the present value of the Bond’s coupon payments plus the present value of the principal that will be returned at the Bond’s maturity.

Although you have agreed to sell the Bond, you still hold it until the future delivery date. As the holder of the Bond so you will receive the coupon payments for the next year. The buyer of the Bond won’t receive them, so he won’t be willing to pay for them.

Whatever the price of the Bond today, the futures price should be lower by the present value of the coupon payments occurring between now and futures expiry.

The same logic holds for futures on dividend-paying equities. Some people are surprised when they first see an equity future trading below the spot equity price. If equities go up over time, how can the future price be lower? There must be easy money to be made!

Sadly not :( The difference is often due to dividends.

Dividends and coupon payments aren’t the only benefits. Some assets offer a “convenience yield” to the holder. For example the holder of a Treasury Bond can use the Bond as collateral for borrowing and other financial transactions. Another example is that as the holder of the underlying asset, you could sell it in the spot market if price changes make it profitable to do so¹. (Of course you would also need to offset your short futures position.)

The point of these two examples is to show you that the fair value of the future will account for all the costs and benefits of holding the asset between the time the futures contract is agreed and the time it matures. We call this the “cost of carry”.

When we price the future we start with the spot price then adjust for the cost of carry. The buyer of the future doesn’t receive the benefits so he takes them away from the spot price. On the other hand, he doesn’t pay for the costs of holding the asset, so they must be added on.

Future = Spot + Costs - Benefits

The Time Value Of Money

There’s one more factor we need to consider – interest rates.

All the cashflows that occur during the life of the contract (storage costs, coupons, dividends, etc) must be discounted back to the present. We do this because a dollar today isn’t the same as a dollar a year from now (as the crypto community are only too eager to point out!). You can watch [this video on the time value of money] (https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/present-value/v/time-value-of-money) if you want to know more.

This is why the time to maturity is such an important factor. A longer duration futures contract has more storage costs, more dividends, and more convenience yield. Time has a magnifying effect on the other variables.

Our Formula

Finally, we have our formula²

F = Se^(r+c-d-y)T

The fair value of a future (F) that mature T years in the future is equal to the spot price of the asset (S) plus storage costs (c) minus any dividends or coupons accruing to the asset holder in that time (d) minus the convenience yield (y) all discounted back to the present at interest rate r.

So What About Our Bitcoin Futures?

Storage costs are minimal. Whether you’re an individual storing your BTC on a Trezor, or a hedge fund using a Faraday Cage, storage costs as a percentage of total value is insignificant, and unlikely to affect trading decisions.

Bitcoin doesn’t produce any dividends or coupons so we can ignore Q. And no, forks don’t count as dividends. The contract is cash-settled, so no one is delivering / receiving any bitcoin. No bitcoin means no airdrops when the chain forks.

As for the convenience yield, well, ask yourself, what do you do with your bitcoin? You can’t consume it. You can buy stuff with it, but not many do. You could trade with it in the meantime (but I hope you don’t!). Realistically, would you do anything other than hodl?

There is however, one characteristic of bitcoin that is quite “convenient”: price appreciation. Holding bitcoin over any time period tends to be very profitable. This factor, combined with the limitations of arbitrage I mentioned in my previous post, will be the most significant in determining the price of bitcoin futures. Even if there were storage costs and dividends, the expected price appreciation would probably drown them out.

My conclusion: We can expect trading in bitcoin futures to be very speculative, and unlikely to tame the volatility we have seen in the underlying.

Footnotes

1 A simpler example is to think of a car. You can use it whenever you want. It saves you paying for taxis or public transport, and it’s probably quicker too. It’s fun to drive, and maybe it even looks good in your driveway! Whatever the case, it’s not easy to put a monetary value on these benefits, so the convenience yield can’t be calculated directly. It is usually implied based on the price of the future and the other inputs.

2 We use the exponential function to discount the cashflows back to the present. This allows us to use “continuous compounding”, which is common in finance. Again, I’ll leave it to Kahn Academy to explain.