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?

Current U.S. mindset: everything crypto-related is evil
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

beneficial ownership record

seller

buyer

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

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