Liquidity fragmentation on decentralized exchanges

Alfred Lehar, Christine A. Parlour, Marius Zoican

Discussion by Katya Malinova

DeGroote School of Business

McMaster University

NFA 2023 Annual Meeting

Toronto

Some background stats

What's special about decentralized exchanges?

  • pooling of liquidity
  • pro-rated 
    • fee income
    • risk
  • Liquidity providers:
    • use existing assets to earn passive (fee) income
    • no special skills, no competition on speed
  • Liquidity demanders:
    • predictable price
    • continuous trading, ample liquidity 

Malinova and Park (2023):

propose DEX implementation for equity markets

\(\to\) estimate $-billions saving in transaction costs 

  • better risk sharing
    • LPs assumed passive
  • use of idle capital (shares)

Uniswap V3

  • pooling of liquidity
  • pro-rated 
    • fee income
    • risk
  • Liquidity providers:
    • use existing assets to earn passive (fee) income
    • no special skills, no competition on speed
  • Liquidity demanders:
    • predictable price
    • continuous trading, ample liquidity 

Only partial pooling & pro-rata,

liquidity is fragmented across the pools

LPs gain priority by being in the low-fee pool

Impact on liquidity? Back-of-the-queue LPs supply less? Demand higher fees?

Uniswap V3 & fragmentation: big picture question

  • intended to offer more flexibility
  • price limits (outside this paper) \(\to\) could change the shape of the pricing/bonding curve
  • different fee options \(\to\) multiple pools for the same asset pairs \(\to\) liquidity fragmentation

see also Hasbrouck, Riviera, Saleh (2023) 

Questions:

  • Is this a good/bad design idea?
  • Does it hamper risk sharing?
  • Welfare/cost implications? 
  • Is flexibility always better/worse? 
    • Or only for some assets?
  • Why does (and does it?) fragmentation matter? 

The model (my over-simplified version)

  • flat gas fees
  • bps trading fees proportional to volume traded (\(\to\) larger liquidity deposits earn more in $-terms)
  • Liquidity demanders
    • small:\(\to\) low-fee pool
    • large: exhaust liquidity in in the low-fee pool, trade everywhere
  • Liquidity providers:
    • small: need high bps fee to cover the fixed gas fee
    • large: low bps fee covers the gas fee
      \(\to\) prefer "low fee repeatedly" to "high fee occasionally"

Questions and comments: no round-trip trades?

  • liquidity demanders all buy
    • \(\to\) many small trades exhaust liquidity
    • \(\to\) need to frequently replenish 
  • But if these are small/noise/retail:
    • why aren't they balanced? 
  • Or: Lehar and Parlour (2023): "Decentralized Exchanges"
    • if the trade is uninformed
      \(\to\) an arbitrageur trades
      \(\to\) the pool is back to the initial state

\(\to\) LPs earn fees on round-trip trades, no change in positions, no need to replenish?

\(\to\) are low-fee pools more attractive than the model predicts? 

As an aside: where do LPs get more capital?

Questions and comments: no adverse selection?

  • Basic premise for the trading fees in AMMs:
    • compensation for adverse selection
       
  • Liquidity providers:
    • positional losses against informed
    • neither gain, nor lose against uninformed/noise
      • an arbitrageur trades against the pool & earns
        positional gain (e.g., Lehar and Parlour (2023))
  • This paper: 
    • no adverse selection
    • exogenous fees
      • only compensate for gas prices
      • no positional losses to LPs
  • Do LPs make profits?
    • Is this intended?
  • What if more competition? 
  • Optimal fees?
    • optimal number of pools?

different to the traditional MM models 

same as in canonical MM models

What if there is adverse selection & price impact?

  • All trading at the fundamental
    • no price impact
    • \(\to\) liquidity demanders always exhaust the low-fee pool first
  • If the high-fee pool is larger
    • \(\to\) smaller price impact?
    • \(\to\) when does it outweigh the higher fee?
      • Hasbrouck, Riviera, Saleh (2023)
  • Different implications for different levels of adverse selection?
  • Should DEXes for FX  be structured in the same way as for equities?
  • Is DEX fragmentation equally good/bad/irrelevant for different asset classes?
  • Impact on fragmentation?
    • If gas fees \(\searrow\) 0 & high-fee pool is "toxic,"
      still fragment?

A side note re: volatility

  • Empirical analysis: control for volatility
    • daily range of high vs low prices
  • Is the intra-day volatility critical if withdrawals are at multi-day frequency?
  • Consider a return/volatility measure that proxies for the adverse selection at lower frequencies?

Summing up

  • Many, many cool stylized facts about Uniswap V3
    • fees vs liquidity deposits, volume, trade size
  • Parsimonious model of liquidity provision 
    • gas fees vs. trading fees for different capital constraints
  • Would like to know more about the optimality of the design
    • do we want multiple fees/pools?
    • always? or for select assets?
      • impact of adverse selection? equities vs FX vs fixed income?
    • would fragmentation occur for all tokenized assets?
      • role of adverse selection on it and on the impact of it?

@katyamalinova

malinovk@mcmaster.ca

slides.com/kmalinova

https://sites.google.com/site/katyamalinova/

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