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"

Seriously?

0. Cynicism aside - big question: Can we improve liquidity for smaller listings?

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
  • one new market institution: automated market makers

Trading Infrastructure

payments network

Stock Exchange

Clearing House

custodian

custodian

 beneficial ownership record

seller

buyer

Broker

Broker

Broker

Exchange

Internalizer

Wholeseller

Darkpool

Venue

Settlement

Application: decentralized trading with automated market makers

New institutions!

  • passive "shared" liquidity provision
  • new pricing function

Key Components

  • Our question:
    1. Can an economically viable AMM be designed for current equity markets?
    2. Would such an AMM improve current markets?
  • pooling of liquidity
  • pro-rated 
    • fee income
    • risk
  • Liquidity providers:
    • use existing assets to earn passive income
  • Liquidity demanders:
    • predicatable price
    • continuous trading
    • ample liquidity

Automated Market Makers

Basics of Liquidity Provision

  • Basic idea of liquidity provision: earn more on balanced flow than what you lose on price movement

    \[\text{fee income}+\text{what I sold it for}-\text{value of net position} \ge 0 \]

in tradFi: bid-ask spread

in AMMs:
protocol fee

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

  • makes asset and cash deposit
  • more deposits flatter price curve
    • attracts more volume
    • but larger "positional" loss when prices move
  • we defined a model to capture the liquidity provision decision
  • measured as "collective" deposit of firm's market cap
  • driven by
    • balanced volume
    • asset volatility/return distribution
    • fee income

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

for orientation:

  • If the stock price drops by 10% the incremental loss for liquidity providers is 13 basis points on their deposit
    • \(\to\) total loss=-10.13%
  • If the stock price rises by 10%, the liquidity provider gains 12 basis points less on the deposit
    • \(\to\) total gain =9.88%

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

  1. AMMs close overnight.
     
  2. Market: opening auction \(\to\) \(p_0\)
     
  3. Determine: optimal fee; submit liquidity \(a,c\) at ratio \(p_0=a/c\) until break even \(\alpha=\overline{\alpha}\)
     
  4. Liquidity locked for day
     
  5. At EOD release deposits and fees
     
  6. Back to 1.

Background on Data

Special Consideration 1: What volume?

  • some volume may be intermediated

  • with AMMs: no need for intermediation
  • \(\to\) intermediate volume should disappear
  • \(\to\) use volume/2

Special Consideration 2: What's \(q\) (the representative order size)?

  • use average per day
  • take long-run average + 2 std of daily averages

All displayed data CRSP \(\cap\) WRDS

  • CRSP for shares outstanding
  • WRDS computed statistics for
    • quoted spreads (results similar for effective)
    • volume
    • open-to-close returns
    • average trade sizes, VWAP
  • Time horizon: 2014 - March 2022
  • Exclude "tick pilot" period (Oct 2016-Oct 2018)
  • All common stocks (not ETFs) (~7550).
  • Explicitly not cutting by price or size
  • All "boundless" numbers are winsorized at 99%.
  • Plots are for per-stock yearly averages.

AMMs that's true to the "model"

Return distribution example: Microsoft

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)

Insight: Theory is OK - LP's about break even

\(\overline{\alpha}\) for \(F=F^\pi\)

Need about 10% of market cap in liquidity deposits to make this work

actually needed cash as fraction of "headline" amount

Only need about 5% of the 10% marketcap amount in cash

AMMs are better on about 85% of trading days

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%

theoretical annual savings in transactions costs is about $15B

The Bigger Picture and Last Words

Summary

  • AMMs do not require a blockchain - just a concept
  • could be run in the existing world (though there are institutional and regulatory barriers)
  • Our question:
    1. Can an economically viable AMM be designed for current equity markets?
    2. Would such an AMM improve current markets?
  • Answers:
    1. Yes.
    2. Massively.
       
  • Source of Savings:
    • Liquidity providers \(\not=\)  Citadel!
    • \(\to\) passive liquidity provision
    • \(\to\) use idle capital
    • \(\to\) + better risk sharing
  • pooling of liquidity
  • pro-rated 
    • fee income
    • risk
  • Liquidity providers:
    • use existing assets to earn passive income
  • Liquidity demanders:
    • predicatable price
    • continuous trading
    • ample liquidity

@financeUTM

andreas.park@rotman.utoronto.ca

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sites.google.com/site/parkandreas/

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