Introduction

In crypto, perpetual instruments (usually called perps) are the most common kind of future contract. Traditional dated futures have an expiration date, at which the related parties agree to exchange the underlying asset (e.g. BTC in a BTC-USDT future) at the entry price.

Instead, perps have no expiration. They are only related to the underlying via a funding mechanism. When the perpetual price is above the underlying price, traders holding a long position pay a funding fee to those holding opposite short positions. If the perp price is below spot, “shorts pay longs” (as they say).

Arbitrage

How does funding work? Why would that make the perp price (which is independent) roughly track the spot price? Essentially, arbitrage. When the price deviates, arbitrageurs can make an easy profit and drive the price back.

Let’s explore an example of cash-and-carry trading, a kind of arbitrage we can do when the perp trades above spot (which is quite common in mainstream cryptos such as BTC and ETH).

Cash-and-Carry Trading Example

Let’s say we’re trading BTC/USDT, and current prices are:

• Spot: 100k
• Perp: 101k

So, we’ll:

1. Spot: Buy 1BTC @ 100k
2. Perp: Short 1BTC @ 101k

Liquidations aside, this strategy has a constant payoff. Let’s define:

• Underlying price $u$
• Spot entry price $u_s=100k$
• Perp entry price $u_p=101k$
• Position size $q=1$

The spot payoff is:

$$ V_s(u)=q(u-u_s) $$

The perp short is the opposite:

$$ V_p(u)=q(u_p-u) $$

Thus the total payoff:

$$ V(u)=V_s(u)+V_p(u)=q(u-u_s+u_p-u)=q(u_p-u_s)=1\cdot(101k-100k)=1k $$

Execution

Now, we’ll only be able to cash that in if the perp price goes back down to the spot. However, since we’re shorting, we’ll be earning funding fees. Thus, the trade will proceed like this, generally:

1. Whilst the perp trades above spot, we earn funding fees (usually around 10% APR).
2. Once the perp price goes down (it generally does every so often), we’ll exit both positions and lock in the profit.

Summary

We’ve introduced perpetual instruments (perps), their funding mechanism, and the arbitrage that makes them work:

1. Perps are only tied to the underlying via funding. When price is above spot, longs pay shorts, and viceversa.
2. Carry trading allows arbitrageurs to make a profit from a perp-spot price deviation, and with that help the perpetual price track the spot.