Understanding How AMMs Work

As the name implies, automated market makers, or AMMs, are programs that automate the creation of a market for a specific pair (or sometimes more) of assets. AMMs take care of matching buy orders on one side of the market with the sell orders on the other side of the market using a decentralized application instead of relying on a third party.

Let’s go back to the example of Alice, Bob, and basic market making, when Alice is trading Bob’s asset A for asset B, they’ll often need Charlie to meet them in the middle in order to complete the transaction and close the bid-ask price gap (the gap between the price that Alice is willing to buy for and what Bob is willing to sell for). Unless Charlie steps in to resolve the trade, both Alice and Bob will continue to wait for another party who’s willing to make the deal on each of their respective terms.

AMMs allow anybody to be Charlie. All the individual has to do is deposit however much of asset A and asset B  they’re willing to provide to the market, and the AMM takes care of the rest.

When a crypto market maker works with an AMM, their assets go into a liquidity pool along with the assets of any other crypto market maker who wants to provide more of assets A and B. Then, when Alice and Bob want to trade, the AMM uses a formula that determines how much asset A can be traded for a given amount of asset B at every moment.

This formula varies depending on the preferences of a particular exchange. Some of the most popular formulas include:

• Constant product
• Constant sum
• Constant mean

Each of these has its nuances, but the function remains the same: they allow the AMM to set prices mathematically so the market can be automated.

Uniswap, for example, uses a constant product formula:

A x B = C

All this means is that the AMM is making sure that the amount of A times the amount of B  in the pool is always equal to a constant number C. This is how it automatically determines at what price to buy or sell the assets. When there’s less of A in the pool, it charges more for B, and vice versa.

Read more: Comparing v3 AMMs 

Let’s go through what this looks like in a typical trading situation, taking the constant product formula as an example.

As a crypto market maker, you provide an equal value of both asset A and asset B to a liquidity pool. Let’s say they’re worth the same, and you deposit 10 of each. The product of 10 A and 10 B is 100.

Now, let’s say Bob wants some of asset A and is willing to give up some more of asset B. He tells the AMM how much of A he wants to get. The AMM calculates how much B Bob must provide in order for the trade to keep the total value of A in the pool times the total value of B equal to 100. For example, if he wants to purchase 3 of A, he must provide ~4.286 of B. Every unit of A that Bob gets decreases its supply in the liquidity pool, making A worth more regarding B. Simple supply and demand.

After the trade is made, the AMM automatically rebalances the price of A in terms of B one more time, so the next purchase also maintains a total liquidity of 100. If someone else comes along, they’ll find that the price of 1 A is “another step” higher than the price Bob got for his last unit of B.

To be exact, they’ll find that the price of the next unit of A will cost 6.666 B.

(*Play around with these values in a constant product simulator. You’ll find that the greater the amount of total liquidity provided, the less dramatic the price changes between assets A and B become. This is called market depth, and it is an essential part of crypto market makers’ role in reducing volatility.)