Automated Market Making?

How should one organize DEX trading?

What features do we need a hard-coded pricing rule to have?

• NB: Oracles can be manipulated (e.g. $130M CreamFinance exploit)

1. Liquidity demanders cannot get exploited/get a reasonable indication of the price they trade at
    
2. Liquidity providers get "fair" risk compensation
    
3. Blockchain: There is no excessive amount of trading

Current Practice: constant product pricing

Price mechanism:

• \(X=\) contract balance of asset \(A\)
• \(Y=\) contract balance of asset \(B\)
• \(k=\) invariance factor
• key relation \(k=X\times\ Y\)

Prices

• sell \(x\le X\) \(\to\) receive amount \(y\)
  that maintains invariance. 
• implied fundamental value \(V=Y/ X\)

• maintain constant product post trade: \[k=(X+x)(Y-y)~ \Leftrightarrow~y=\frac{xY}{X+x}.\]

Exploits of Liquidity Demanders

Problem: MEMPOOL Frontrunning is intrinsically profitable

\(X\)

\(Y\)

normal trade: sell \(x\) \(\to\) get \(y'\)

\(Y-y'\)

\(X+x\)

front-running/sandwich trade:

1. front-runner: sells \(x\) \(\to\) gets \(y'\)
2. front-run: sells \(x\) \(\to\) gets \(y''\)
3. front-runner: buys \(x\) \(\to\) pays \(y''\) 

\(Y-y'-y''\)

\(X+2x\)

Disclaimer:

• this problem is well-known
• fees can mitigate it
• several protocols such as the latest iteration by Balancer try to combat it

Mempool \(\Rightarrow\) Front-Running!

a

b

c

d

e

f

g

Dark side of DEx trading: Miner extractable value

Source: flashbots.net

Risk Compensation for Liquidity Providers

Market Making with risk compensation: Biais JF 1993

• Asset with true value \(v\sim N(V,\sigma^2)\)
• Investor with exogenous demand \(Q\)
• market makers w. CARA utility
  • maximize utility of terminal wealth
    • cash flow from trade
    • \(+\) value of risky position  
    • \(+\) value of inventory

hard coded pricing function

Two pricing approaches in the economics literature

• uniform: cash flow = \(p(x)\times x\)
• discriminatory: cash flow= \(\int_0^x p(t)dt\)

Does constant product compensate fairly?

• For apple-apple comparison:
  • \(I=0\) (everyone is at the "desired" risk amount)
  • \(X=N\) (each of \(N\) market markets contributes a unit amount)
  • \(V=Y/X\) (marginal CP price is the expected fundamental value)
• Price functions coincide for \[x'=0~~~\text{ and }~~~ x^*:=\frac{X}{l}\ (l-2V).\]

Proposition: For \(x>x^*\), constant product provides "higher" risk compensation than what market competition would yield,  for \(x<x^*\) it is the reverse.

Excessive Trading?

Simple question: does it pay to split an order?

• buy \(2\cdot x\):
  • Option 1: buy \(x+x\) 
  • Option 2: buy \(2x\) in one go
     
• good news: constant product is invariant

(the papers has some other tests for excessive trading)

Comparison: market vs CPMM

Comparison of pricing

Constant product pricing
 

profitable front-running/sandwich trades

fair risk compensation for LPs

profitable order splitting (excessive trades)

Remedies?

A simple "solution" to front-running

• Front-running requires two trades
  1. pay transactions fees twice
  2. first fee must exceed original fee
  3. second fee can't be too much lower than original fee
      
• Front-runner needs to out-bid the original trade

What does the data say?

A simple calibration exercise

What does the data say?

• Data:
  • Goal: flavor/established stylized facts/indication of the real costs
  • Jan 2020 for USDT-USDC, USDT-ETH, USDT-wBTC
• What is \(\kappa\)?
  • Babcock, Choi, and Eli Feinerman (1993) (Table 1) \(\in(.00001,0.5)\)
  • most values at the small end of the spectrum\(\to\kappa= 0.0005\).
• Rest?
  • Use crypto to stablecoin (aka "money")
  • \(V\): "average price"
  •  \(\sigma\): price volatility
  • \(X\): $-quantity of crypto in contract
• And then?
  • Overpayment to LP in CPMM?
  • (Hypothetical) no-front-running fee?

A simple calibration exercise

What does the data say?

What have I done and what have you learned?

Summing up

• Mempools \(\to\) front-running by transaction reordering is inevitable
  • \(\Rightarrow\) avoid intrinsically profitable design
• A better way:
  • "linear" (marginal) pricing
  • \(\Rightarrow\) Merit of economic thinking in DeFi

@financeUTM

andreas.park@rotman.utoronto.ca

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sites.google.com/site/parkandreas/

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