Andreas Park PRO
Professor of Finance at UofT
Katya Malinova and Andreas Park
Some Motivation
Basic Idea
Constant Liquidity (Product) AMM
Key Components
Liquidity Supply and Demand in an Automated Market Maker
The Pricing Function
Liquidity Deposit ⇒ slope of the price curve
Basics of Liquidity Provision
fees earned on balanced flowFp0V+∫0∞adverse selection loss when the return is R(Δc(q∗)−q∗pt(R)+fees earned from arbitrageursF⋅Δc(q∗)) ϕ(R)dR≥0.
q∗ is what arbitrageurs trade to move the price to reflect R
Basic idea of liquidity provision: earn more on balanced flow than what you lose on price movement
fee income+adverse selection losswhat I sold it for−value of net position≥0
in AMMs:
protocol fee
in tradFi: bid-ask spread
Basics of Liquidity Provision
∫0∞adverse selection loss when the return is R(Δc(q∗)−q∗pt(R)+fees earned from arbitrageursF⋅Δc(q∗)) ϕ(R)dR+fees earned on balanced flowFp0V≥0
initial deposit1∫0∞(Δc(q∗)−q∗pt(R)+F⋅Δc(q∗)) ϕ(R)dR+initial depositFp0V≥0
∫0∞(initial depositΔc(q∗)−q∗pt(R)+F⋅initial depositΔc(q∗)) ϕ(R)dR+initial depositFp0V≥0
closed form functions of R only
(see Barbon & Ranaldo (2022))
Sidebar: we can quantify how much a PASSIVE LP loses when the price moves by R
for orientation:
initial depositadverse selection loss when the return is R=R−21(R+1)
see Barbon & Ranaldo (2022)
Basics of Liquidity Provision
Liquidity provision measured as "collective" deposit α of firm's market cap as function of
E[IILRAS(R)]+F⋅E[another function of R]+F⋅initial depositdollar volume≥0.
what I sold it for−value of net position+fee income≥0
The Decision of the Liquidity Demander
Fπ=E[∣R−1∣/2]+V1(−2q E[ILLRAS]+−2qV E[ILLRAS]).
Model Summary
How we think of the Implementation of an AMM for our Empirical Analysis
Approach: daily AMM deposits
Background on Data
some volume may be intermediated
AMMs that's true to the "model"
Return distribution example: Microsoft
Return distribution example: Tesla
αˉ≈2%
almost break even on average (average loss 0.2bps ≈0)
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
Literature
AMM Literature: a booming field
Lehar and Parlour (2021): for many parametric configurations, investors prefer AMMs over the limit order market.
Aoyagi and Ito (2021): co-existence of a centralized exchange and an automated market maker; informed traders react non-monotonically to changes in the risky asset’s volatility
Capponi and Jia (2021): price volatility → welfare of AMM LPs; conditions for a breakdown of liquidity supply in the automated system; more convex pricing → lower arbitrage rents & less trading.
Capponi, Jia, and Wang (2022): decision problems of validators, traders, and MEV bots under the Flashbots protocol.
Park (2021): properties and conceptual challenges for AMM pricing functions
Milionis, Moallemi, Roughgarden, and Zhang (2022): dynamic impermanent loss analysis for under constant product pricing.
Hasbrouck, Rivera, and Saleh (2022): higher fee ⇒ higher volume
Empirics:
Lehar and Parlour (2021): price discovery better on AMMs
Barbon and Ranaldo (2022): compare the liquidity CEX and DEX; argue that DEX prices are less efficient.
The Bigger Picture and Last Words
Summary
@financeUTM
andreas.park@rotman.utoronto.ca
slides.com/ap248
sites.google.com/site/parkandreas/
youtube.com/user/andreaspark2812/
By Andreas Park
SNB presentation