## Interest rates in bull and bear cycles

Being aware of the interest rates at which traders can borrow and lend their USD or BTC is crucial as it can tell you a lot about the market sentiment and, possibly, let you make riskless profits with arbitrage.

In bull markets, there’s usually a high demand to go long with leverage, which causes interest rates for the quote currency, which is the USD in the BTC/USD pair, to rise rapidly, as people are willing to pay more interest to borrow and go long. Those who lend their USD stand to make riskless profits but are giving up on the possibility to make much more significant gains with the upside movement of BTC.

In the bitcoin futures markets, if the demand to go long is high, the contracts will be trading at a premium to the spot/index market. This premium is playing the same role as interest rates in the spot market since those who go long at a premium are overpaying this amount to those who accept another side of the contract and go short against them (similar to how those who hold USD and lend it are short on BTC).

The opposite happens in the bear market. With a lot of market participants willing to go short, interest rates for borrowing the base currency (BTC in BTC/USD pair) to sell it short goes up, and the lending rates for the quote currency go down (since fewer people willing to borrow to go long).

## Connecting futures prices and interest rates together

Market mechanics described above create an interconnection between the spot price, futures price and interest rates. Let’s take a look at a simplified example to understand how all these variables connected.

### Example №1 (without lending BTC)

Suppose the price of one BTC is $10,000 while the futures expiring precisely in one year are at $12,500 (the premium is $2,500, or 25% above the spot). If you could borrow $10,000 for one year with anything less than 25% annual interest, you can make a riskless profit (all fees, transactions costs etc. are neglected for the sake of simplicity).

The process would be next:

- Borrow $10,000 at, let’s say, 10% annual (anything less than 25%)
- Buy 1 BTC for $10,000 at the spot market
- Sell 1 BTC with a futures contract at $12,500
- Wait one year until the contract expires
- Get your $12,500 after contract expiry
- Repay $11,000 borrowed at the start
- Pocket what’s left, $12,500 – $11,000 = $1,500

It doesn’t matter where the price of bitcoin will be in one year since you already sold your one bitcoin forward in one year for $12,500, and your payment on the loan is known too.

This simplified example shows you, how lending fees for the quote currency connected with the futures price. The higher the futures price away from the spot market, and the less the interest to borrow quote currency, the more profit you can make.

Fair futures price, in this example, would mean that there’s no discrepancy between interest rate and the premium, so there’s no opportunity to make a riskless profit (e.g. premium % is equal to interest %).

However, futures price and quote currency interest rates are not all pieces to the puzzle. Don’t forget that there are interest rates for borrowing the base currency too, which is the BTC in our example.

If you can lend your BTC while fixing your selling price with a futures contract expiring in one year, you can make a profit even if the interest for borrowing USD is the same as the premium. Let’s expand our previous example a bit.

### Example №2 (with lending BTC)

Suppose the spot price is still at $10,000 BTC/USD and the futures are at $12,500 (same premium of 25% or $2,500). The cost to borrow USD, however, is now 25% per year, so it’s at par with the premium. Also, assume that interest to borrow bitcoin is 10% per year.

The steps to make a riskless profit:

- Borrow $10,000 at 25% per year
- Buy 1 BTC for $10,000 at the spot
- Lend 1 BTC for one year at 10%
- Secure the selling price of 1.1 BTC at $12,500 with the futures contract
- Wait one year, get $13,750 for selling 1.1 BTC at $12,500 (1 BTC + 10%)
- Repay your loan with $12,500 and pocket the rest
- $13,750 – $12,500 = $1,250

Hopefully, these examples give you an idea, how all four variables (quote currency interest, base currency interest, spot price, futures price) are interconnected with each other.

The critical concept to understand is that the premium/discount at which futures are trading should match the interest rates of the quote and base currencies in percentages. If there are discrepancies, then there should be arbitrage possibilities and the market forces will move the premium/discount towards interest rates for base and quote.

## Interest rate parity

In the equilibrium situation, the difference between the futures price and the spot price should correspond to the difference between the quote currency and the base currency interest rates, a case known as the interest rate parity in finance.

F / S = Q / B

F – futures price; S – spot price; Q – quote currency interest; B – base currency interest

Note: Quote and Base interest expressed as 1 + %. For example 25% interest would be expressed as 1.25, since to apply interest increase to a sum we would just multiply it by 1.25 (examle: $100,000 at 25% would mean $100,000 * 1.25 = $125,000)

From this equation, we can derive a fair value of a futures contract if we know the interest rates of BTC and USD and the spot price.

F = S (Q / B)

### Fair futures price example

Spot price: $10,000

USD rate: 25% (same as 1.25)

BTC rate: 10% (same as 1.1)

Fair futures price = $10,000 ( 1.25 / 1.1) = $11,363

We can see that there’s arbitrage opportunity since the futures price is higher than the fair price we derived using interest rates. To exploit this situation we would do the same steps we did in the second example explained earlier: borrow USD at 25% –> buy BTC at $10,000 –> lend BTC at 10% –> sell future at $12,500.

The real market is much more complicated, but these simple examples should give you a basic understanding of how interest rates affect the futures price.

## Conclusion

Interest rates play a crucial role when it comes to the futures market. The interest rates for the base and quote currencies directly affect the futures price. The arbitrageurs capitalise on the discrepancies between interest rates and futures premium or discount by borrowing one currency at a lower rate than the difference between future and spot. Constant race to make riskless profit pushes the futures prices towards equilibrium with the interest rates (interest rate and the premium/discount of a future are at par).

Hi,

would you clarify why lending BCT at 25% in the Fair futures price example?

Formula:

borrow USD at 25% –> buy BTC at $10,000 –> lend BTC at 25% ( 10% instead??) –> sell future at $12,500

Cheers

I’m sorry that was a typo, it’s 10%. Thank you