Automated Market Makers
AMMs democratized cryptocurrency trading by doing away with order books and institutional market makers.
MARKETS
Markets facilitate trade in a society by connecting the sellers to the buyers. Trading of goods, services, or information (assets collectively) happens in a purpose-built marketplace. For instance, a local community might have a farmers’ market to trade locally produced vegetables and fruits. Whilst a stock market like New York Stock Exchange (NYSE) allows global participants to trade in stocks. A traditional market comprises buyers, sellers, brokers-dealers, and market makers.
Let’s look at the fundamentals first.
Buyer: A person or an organization buying, planning to buy, or agrees to buy assets.
Seller: A person or an organization selling, planning to sell, or agrees to sell assets.
Broker-Dealer: A person or an organization buying and/or selling on behalf of its customers or for their own. The person/organization acts as a broker (or agent) when executing orders on behalf of the client and acts as a dealer (or principal) when trades for their own account.
Bid: Buyers make a bid, specifying the price they will pay and the quantity required.
Ask: Sellers offer an ask price, specifying the price they will sell and the quantity available.
Bid-Ask Spread: The difference between the Ask and the Bid. For example, if the sellers’ ask is $55 and the buyers’ bid is $53, the bid-ask spread is $2. The bid-ask spread determines the market liquidity. For heavily traded assets, the bid-ask spread will be tighter (narrow). However, for assets with little demand or sparsely traded, the bid-ask spread may be high or even unknown.
Liquidity: Refers to how easily and quickly assets are bought or sold without affecting the asset's price. If there is a high volume of trade, the bid-ask spread should be narrow for the asset traded. Therefore, liquid. Contrarily, when there is a wide (or unknown) bid-ask spread, then the asset is illiquid.
Market Maker: Market makers (MM) help keep the market functioning by actively buying and selling assets. MMs can be an individual or an organization providing liquidity to the market by transacting on both sides of the market (buy and sell). For example, the MM might offer a Bid for $20/stock and Ask for $20.05/stock. Market makers earn a profit through the bid-ask spread and carry a risk of price variations during Buy-Hold-Sell cycle. The common type of market maker are the brokerage houses.
Slippage: Slippage results from a change in bid-ask spread. There is a time delay between the trade request and execution in the market. During this time, if the bid-ask spread changes, then slippage occurs.
Order Book: Most modern financial markets are order-driven (buy-sell) markets. At the heart of the trade is an order book; an electronic register of the list of buy and sell orders. A typical order book has three parts – buy orders, sell orders, and order history. The order book helps improve market transparency, help traders make informed decisions, and identifies participants and price of a trade.
Exchange: Exchange is a market where trading is conducted. For example, New York Stock Exchange (NYSE), London Stock Exchange (LSE), or the Cryptocurrency exchanges like Saddle, Binance, Coinbase, or Uniswap.
CRYPTOCURRENCY EXCHANGES
A cryptocurrency exchange is a marketplace for trading cryptocurrencies. Broadly, two types of cryptocurrency exchanges exist:
Centralized Exchanges (CEX): A cryptocurrency exchange owned and governed by a 3rd party. E.g., Binance, Coinbase, and Bitfinex.
The DEX ecosystem is nascent and maturing. Despite few shortcomings, compared to CEX, decentralized exchanges grew in popularity. The allure of removing middlemen, lower fees, and decentralization pushed the adoption of DEX.
Order Book Challenges
In the illustration below, the seller's Ask is $20.50 and the buyer's Bids are not closer to the Ask. This results in a liquidity challenge. Market makers, therefore, step in to keep the market functioning by actively buying and selling assets - i.e., transacting on both sides to keep the market functioning. The market makers carry the risk of a price variation during Buy-Hold-Sell cycle.
The main issue is related to high slippages and volatility due to low volumes of trade. The absence of market makers round the clock further constrained the liquidity. Automated Market Makers (AMM), therefore, emerged as a solution to the order book challenge.
AUTOMATED MARKET MAKER (AMM)
Permissionless: Unlike traditional exchanges, permission-less networks require no permission to join and interact with the blockchain network. Permission-less AMMs allow anyone with an internet connection to become a part of the market to trade.
Liquidity Pools: Instead of an order book, AMMs use liquidity pools to facilitate trade. Liquidity pool, a smart contract, is a fund of tokens (or coins). In AMMs, traders interact with the smart contracts, to enable liquidity and price discovery. Because of the permissionless nature, AMMs allow anyone to provide liquidity to the liquidity pool. The liquidity pool smart contract holds two or more tokens and allows anyone to deposit and withdraw funds from them, but only according to specific mathematical rules.
Liquidity Providers: Liquidity providers contribute assets (cryptocurrency tokens and coins) to liquidity pools. In exchange for providing the tokens, the LPs normally earn a fee. Now, when a trade executes on an AMM, the trade executes against the liquidity pool. This eliminates the need for an order book and for the buyer and seller to be present at that moment in time.
Impermanent Loss: Though the AMM model offers better stability and returns, there is a risk of impermanent loss – a temporary loss experienced by liquidity providers because of volatility in the liquidity pool assets. In simple terms, if the liquidity provider had held onto the asset, without providing it as a liquidity to the pool, the individuals would have had more money/value. But impermanent loss is a temporary situation as the AMMs regulate the price closer to market, eventually.
AMM SWAP ALGORITHMS
Having understood what AMMs are, let’s now deconstruct them. You can think of an AMM as a friendly and obedient market maker bot, always willing to quote a price, no matter the time of the day or day of the week.
Constant Product Formula
Constant product formula is probably the simplest and the earliest algorithm to come into the market. Uniswap popularized the mathematical formula:
x * y = k
where x is the amount of Token#1 in the liquidity pool, y is the amount of Token#2 in the liquidity pool, and k is a fixed constant.
Let’s look at a few critical aspects from the example below. An ETH-USDT liquidity pool is set-up with 100 ETH and 300,000 USDT, provided by the liquidity providers. As the pool is set-up, the initial conditions are:
USDT: ETH PRICE
USDT Liquidity
ETH Liquidity
Constant Product
3000 : 1
300,000
100
30,000,000
Initial price
x
y
k
When a trader wants to swap the tokens in the pool, the formula will try to achieve the constant product equilibrium. For example, if a trader wants to swap USDT for 1 ETH, then to maintain a constant product of 30,000,000 the price quoted for USDT will be 3,030.30 (a premium of 1% over the initial setup price) and the liquid pool composition after the swap will be:
USDT: ETH PRICE
USDT Liquidity
ETH Liquidity
Constant Product
3030.30 : 1
303,030.30
99
30,000,000
1% premium
x
y
k
Likewise, if a trader wants to swap USDT for 5 ETH, the price quoted by the algorithm will be 3,157.89 (a premium of 5.3% over the initial setup price) and the liquid pool composition after the swap will be:
USDT: ETH PRICE
USDT Liquidity
ETH Liquidity
Constant Product
3157.89 : 1
315,789.47
95
30,000,000
5.26% premium
x
y
k
Uniswap first implemented the constant product formula and Balancer refined it with a generalized formula. But there is a challenge.
The constant product formula determines the price when someone trades against the liquidity pool. As we see from the chart below, we calculate the price as a ratio of the tokens in the pool. The pricing curve has a hyperbola when plotted against two tokens. When someone withdraws, say Token#1, the proportionate Token#2 to be deposited, to maintain the constant product, varies.
Constant Sum Formula
To address the slippage issue, AMMs explored the constant sum formula as an option. Constant sum formula solves for the equation:
x + y = k
where x is the amount of Token#1 in the liquidity pool, y is the amount of Token#2 in the liquidity pool, and k is a fixed constant.
While the constant sum formula solves the slippage problem, it provides only fixed liquidity. For markets to function well, they need a constant supply of liquidity and hence this model didn’t suit the purpose well.
Stableswap Algorithm
The innovation into AMMs mathematical formula continued to find a solution to the slippage (constant product formula) and fixed liquidity (constant sum formula) problems. Hybrid mathematical models, combining the best of many models, rose to prominence. One such model is the Stableswap algorithm.
Constant Sum: When the liquidity pool portfolio is balanced, the algorithm functions as a Constant Sum formula; x + y = k. You can observe the StableSwap blue line staying close to the Constant Sum red line, and the price is stable.
Constant Product: As the liquidity pool portfolio becomes imbalanced, the StableSwap algorithm functions as a Constant Product formula; x * y = k. You can observe the StableSwap blue line now resembling the Constant Product purple line, and the price becoming expensive.
PEGGED-VALUE ASSETS
USDT: A stablecoin pegged 1:1 to the USD fiat currency as the underlying asset.
DAI: A stablecoin soft pegged to the USD algorithmically.
FRAX: A fractional-algorithmic stablecoin that is partially backed by collateral and partially stabilized algorithmically.
wBTC: An ERC20 token backed 1:1 by the actual Bitcoin.
alETH: An ERC20 token, but backed 4:1 by ETH.
Dynamic Pegs
The Constant Product formula does not update the price of the tokens in the pool with the market movement. The Stableswap formula motivates swaps around price ratio 1.0, well suited for stablecoins. Dynamic pegs are the next evolution of AMMs.
Dynamic pegs will bring the benefits of Stableswaps to cryptocurrency assets which aren’t pegged to another asset. By using an automatic price change mechanism, the algorithm will move the price based on real-time profit margin calculations, to adjust for slippages. Thus, benefiting both the traders and the AMMs.
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