Learning from DeFi: Would Automated  
Market Makers  Improve Equity Trading?

Katya Malinova and Andreas Park

Agenda

• Very brief overview of Automated Market Makers
  • function
  • difference crypto-trading to traditional markets
  • difference DeFi to CeFi trading
• Research question: what if we used AMMs for equities?
  • theory: liquidity provision & demand
  • data: implementation & trading costs

Why did we write this paper?

1. Current U.S. mindset: everything crypto-related is evil
    
2. GG/S.E.C.: "We made up a new market institution that is so awesome that it'll save (retail) investors $1.5B per year"

Some Motivation

• Blockchain: borderless general purpose value and resource management tool

Basic Idea

• DeFi: financial applications that run on blockchains

• \(\Rightarrow\) brought new ideas and tools

Trading Infrastructure

Application: decentralized trading with automated market makers

New institutions!

• passive "shared" liquidity provision
• new pricing function

Key Components

Automated Market Makers

Basics of Liquidity Provision

• Basic idea of liquidity provision: earn more on balanced flow than what you lose on price movement
  
  \[\text{fee income}+\text{what I sold it for}-\text{value of net position} \ge 0 \]

Some simple general economics:

• for fixed volume
  • earn more when fees are higher
  • \(\to\) more willing to provide liquidity
• for fixed change in the fundamental
  • lose more when trade imbalance is larger

What we do in the paper?

• Liquidity providers share
  • risk
  • fee income
• Fix:
  • the pricing rule
  • "dumb" volume
  • distribution/volatility of fundamental
• For what level of liquidity do liquidity providers break even?
  • What would liquidity demanders pay?
• \(\Rightarrow\) Liquidity provider net benefit = welfare improvement

Liquidity Provider Decision

Sidebar: we can quantify how much a PASSIVE LP loses when the price moves by \(R\)

The Decision of the Liquidity Demander

• Wants to trade some quantity.
   
• Is better off with AMM relative to traditional market if
  
  \[\text{bid-ask spread}\ge\text{AMM price impact} +\text{AMM fee}.\]

• two opposing forces for \(F\nearrow\)
  • more liquidity provision
    \(\to\) lower price impact
  • more fees to pay
• Finding: There is an optimal fee!

Model Summary

• Have: equilibrium choice for liquidity provision.
   
• Measure: benefit for liquidity demanders to use AMM.
   
• Know: fee that maximizes liquidity demander benefit (\(\not=0\))
   
• Next: Calibrate to stock markets
  • Optimal fees?
  • Feasible?
  • Empirical benefits?

How we think of the Implementation of an AMM for our Empirical Analysis

Approach: daily AMM deposits

Background on Data

AMMs that's true to the "model"

Return distribution example: Tesla

• average \(F^\pi=11\)bps

\(\bar{\alpha}\approx 2\%\)

almost break even on average (average loss 0.2bps \(\approx0\))

average: 94% of days AMM is better than LOB

average savings: 16 bps

average daily: $9.5K

saves around 45% of transaction costs (measured in bid-ask spread)

average annual saving: $2.4 million

Optimally Designed AMMs with
"ad hoc" one-day backward look

Optimal fee \(F^\pi\)

average benefits liquidity provider in bps (average=0)

actually needed cash as fraction of "headline" amount

quoted spread minus AMM price impact minus AMM fee (all measured in bps)

relative savings: what fraction of transactions costs would an AMM save? \(\to\) about 30%

The Bigger Picture and Last Words

Summary