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

• We can express the equilibrium choice for liquidity provision.
   
• We can measure the benefit for liquidity demanders who use the AMM.
   
• We can determine the fee that maximizes the liquidity demander benefit (it's not zero!)
   
• Next question:
  • How would this look like when applied to stock markets?
  • What are the optimal fees?
  • Is it feasible?
  • What are the empirical benefits?

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

Approach: daily AMM deposits

1. AMMs are closed overnight.
    
2. Market starts with opening auction to determine \(p_0\)
    
3. For fixed fees, LP submit liquidity \(a,c\) at ratio \(p_0=a/c\) until \(\alpha=\overline{\alpha}\)
    
4. Liquidity is locked for the day.
    
5. At the end of the day, remaining deposits are released back to LPs.
    
6. Back to 1.

AMMs that's true to the "model"

Return distribution example: Tesla

• average \(F^\pi=11\)bps
• average \(\overline{\alpha}=2\%\)

average savings: 16 bps

average daily: $9.5K

average annual: $2.4 million

average: 94% of days AMM is better than LOB

lose on average 0.2bps \(\approx0\)

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%

Some Numbers

The Bigger Picture and Last Words

Summary