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

  • 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: Microsoft

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 \(F^\pi\)

Insight:

  • large firms have lower optimal fees
  • small firm fees substantially  lower than their bid-ask spread

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

Some Numbers

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.
      Could save up to 30% of transactions costs.
  • 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

slides.com/ap248

sites.google.com/site/parkandreas/

youtube.com/user/andreaspark2812/

Learning from DeFi: Are AMMs better? mathfree version

By Andreas Park

Learning from DeFi: Are AMMs better? mathfree version

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