Wannabe "Stablecoins"

 

Instructor: Andreas Park

 

  • Reserve backing: 1:1 backing of issued stablecoins with “permitted” high-quality liquid assets (e.g. U.S. dollars, short-term Treasuries, repos) (Congress.gov)
     
  • These slides are about "other" stablecoins.

GENIUS Act Stablecoins?

MakerDAO/Sky
based

Ethena Basis Trade

Terra-Luna

Type 1: Collateral-backed, smart contract created
MakerDAO's DAI/USDS

Basic Idea

  • Very similar to the creation of private money
    • Person provides collateral
    • Bank provides new money in the form of a deposit
    • collateral>>deposit
  • Here:
    • Smart contract allows minting of new money 

user perspective

4 ETH
(1 ETH = $375)
(Oct 15, 2020)
\(\approx\) $1,500

\(\vdots\)

1,500 DAI
(1 DAI = $1)

formally: this smart contract is a collateralized debt position (CDP)

user perspective

fractional collateral \(\to\) collateralization factor \(=\) 150%

\begin{array}{rcl} &&\textsf{maximal amount of DAI in \$}\\\\ &=&\frac{\textsf{\$ equivalent of ETH in escrow}}{\textsf{collateralization factor}}\\\\ &=&\frac{1,500}{150\%}=\$1,000 \end{array}

total collateral = $1,500

maximum loan = $1000

overcollateralization = $500

actual loan (example) = $500

buffer = $500

user perspective: what happens if the price of ETH rises?

ETH \(\nearrow\) $500

value of ETH collateral = $2,000

maximum loan = $2,000/150%=$1,333

total collateral = $2,000

maximum loan = $1,333

overcollateralization = $667

actual loan (example) = $500

buffer = $500

overcollateralization = $667

new loan capacity= $333

user perspective: what happens if the price of ETH falls?

ETH \(\searrow\) $187.5

value of ETH collateral = $750

maximum loan = $750/150%=$500

total collateral = $750

maximum loan = $500

overcollateralization = $250

actual loan (example) = $500

buffer = $0

for reference: former value of collateral

user perspective: what happens if the price falls & max loan is exceeded?

Maker DAO

ETH \(\searrow\) $150

value of ETH collateral = $600

maximum loan = $600/150%=$400

total collateral = $600

maximum loan = $400

required overcollateralization = $200

actual loan (example) = $500

buffer = -$100

for reference: former value of collateral

\(\Rightarrow\) triggering of liquidation auction by "keeper"

sell 3.33 ETH=$500=500 DAI

repay $500=500 DAI loan

retain incentive

return  remainding ETH to vault owner

Maintaining the Peg: monetary policy

  1. stability fee
     
  2. DAI savings rate (DSR)
     
  3. debt ceiling

borrowers of DAI need to pay interest \(\to\) stability fee

  • if too much minting (=too much DAI) then
  • \(\to\) interest \(\nearrow\) \(\to\) cost of DAI \(\nearrow\)
  • \(\to\) minting \(\searrow\) \(\to\) supply DAI \(\searrow\)

DSR paid on "locked" DAI

  • DAI deposited to specific contract (demand \(\nearrow\))
  • funded by stability fees
  • \(\to\) SF>DSR

total amount of debt (or DAI) outstanding is limited

Sidebar: how is this decided?
\(\to\) special "governance" token MKR

MakerDAO has no "arbitrage" mechanism. It relies on markets to increase and decrease supply of DAI to bring the price close to $1.

Value locked Oct 27, 2021

Maker DAO

Source: daistats.com (Oct 27, 2021)

Source: daistats.com (Oct 26, 2022)

The March 12, 2020 "BlAck Thursday" Drama

Maker DAO

  • some crypto prices dropped more than 50%
  • cascading liquidations in leveraging platforms
  • network congestion: some liquidations done at near-zero prices
  • collateral shortfall in DAI
  • MakerDAO sold new DAO tokens to collect collateral
  • odd: DAI became riskier but high demand for DAI to trigger liquidations!

PEG stability module (PSM)

Maker DAO

The Problem:

  • in extreme bull/bear runs, the peg may no longer work
  • example: March 2020
    • ETH dropped significantly and suddenly
    • a rush occurred to (a) get out of ETH into save assets and (b) to collect DAI to get keeper fee
    • upward pressure on price of DAI

The Solution:

  • Peg stability module
  •  swap a given collateral type directly for DAI at a fixed rate (no minting/borrowing)
  • like regular vault type with a zero stability fee and a liquidation ratio of 100%
  • accessed through a user-facing smart contract containing the relevant swap functions (no ownership, just straight swap)

Note: In May 2021, ETH prices dropped again by >30% but no drama in DAI

The frontier: DAI loans for real-world assets

Maker DAO

Type 2:
Algorithmic Stablecoin
UST on Terra

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

under-collateralized stablecoin

arbitrageur

issuer

market

  • arbitrageur purchases should raise price in market
  • BUT:
    • will is rise fast enough?
    • does the issuer have enough funds or, rather have funds for long enough?
  • for fully decentralized algo/smart contract stablecoin: there is no dollar to give!

Case 1: price(1 SC) \(>\) 1 FU \(\to\) SC cheap

arbitrageur

issuer

  • for fully decentralized algo/smart contract stablecoin: there is no dollar to give!

The Case of Luna-Terra

 exchange LUNA for newly minted UST tokens at the prevailing $ market rate

market

 LUNA market

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

arbitrageur

issuer

  • for fully decentralized algo/smart contract stablecoin: there is no dollar to give!

The Case of Luna-Terra

 exchange SC for newly minted LUNA tokens at the prevailing $ market rate

market

 LUNA market

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

DISCUSSION

  • backing/collateral is the value of the LUNA/Terra Network
    • \(\to\) must have value(Terra)\(\ge\sum\) SC
  • when you issue new LUNA tokens
    • shift value from current to new owners
    • create inflation\(\to\) price(Luna)\(\searrow\)

       

POTENTIAL PROBLEMS

  • value(Terra)\(<\sum\) SC
    • could be pre-drop SC
  • when SC<FU, LUNA token holders
    • know price(LUNA) will drop
    • \(\to\) pre-emptive selling
    • more LUNA issued
    • \(\to\) more inflation
    • \(\to\) more price drops
    • \(\to\) DEATH SPIRAL!!!
  • So far there has never been an algorithmic stablecoin that did not collapse.
     
  • Disclaimer: I am not aware of a mathematical proof that an algo stableconin cannot work.

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

  • now let's do the maths carefully:
    • price UST: \(p_s\)
    • Assume \(p_s<1\)
    • Arbitrage mechanism:
      1. Borrow $
      2. use $ to buy UST
      3. Sell UST for LUNA at $ price \(p_l'\)
      4. sell LUNA token for $$
      5. Repay $ loan, keep profit
         
  • assumptions
    • arbitrageur trades max \(q_s\) so that \(p_s=1\)
    • \(q_s\) UST buy for Luna with price \(p_l'\) \[\frac{q_s}{p_l'}~\text{LUNA}\]
    • redeemed UST destroyed,  LUNA newly minted
      • \(\to\) dilution.
      • \(\to\) assume MKT anticipated extra quantity of LUNA \(q_s/ p_l'\)
  • assume: TERRA network value unaffected
  • except: validation costly \(\to\) minimum viable price \(\underline{p}_l\)
  • network collapses if \(p_l<\underline{p}_l\)

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

  • exchanges these \(q_s\) UST for LUNA at dollar-price for LUNA
  •  network value not affected:
    \[Q_lp_l=(Q_l+q_l)p_l'\]
  • solve this to get\[p_l'=p_l-\frac{q_s}{Q_l}.\]

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

  • define \(Q_d=Q_sp_s\) aggregate UST $-value
  • arbitrageur buys \(q_s\) such that\[1=\frac{Q_d+P(q_s)}{Q_s-q_s}\]
  • assume AMM pricing (for simplicity): \[q_s=Q_s(1-\sqrt{p_s})\]
  • exchanges these \(q_s\) UST for LUNA at dollar-price for LUNA
  •  network value not affected:
    \[Q_lp_l=(Q_l+q_l)p_l'\]
  • solve this to get\[p_l'=p_l-\frac{q_s}{Q_l}.\]

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

  • \(p_l'\) cannot drop below \(\underline{p}_l\)
  • Maximum feasible quantity forUST: \[\overline{q}_s=Q_l(p_l-\underline{p}_l)\]
  • \(\overline{q}_s=\) collateral value of aggregate LUNA tokens
    • \(Q_s\le\overline{q}_s\):  UST  is fully collateralized
    • \(Q_s>\overline{q}_s\) UST is under- collateralized & \(\exists\)  price deviation that would cause a collapse of LUNA and UST.

Case 2: price(1 SC) \(<\) 1 FU \(\to\) SC cheap

  • Can compute maximal price deviation
  • \(q_s\)  that restablishes depends on peg-deviation price \(p_s\) and \(\sum\) UST \(=Q_s\)
  • minimum price (1-price is max deviation)
    \[\underline{p}_s=\left(1- \frac{Q_l}{Q_s}(p_l-\underline{p}_l )\right)^2\]

     

Type 3:
Basis Trade
USDe by Ethena

Basic Idea

  • use the deposit in a profitable, two-pronged "hedged" carry trade
  • the two legs of the hedged trades are "offsetting" but money-creating

Lifecycle

  • deposit $1 of ETH, mint 1 USDe
    • deposit 0.5 ETH into staking 
    • deposit 0.5 ETH as margin for short ETH perp
  • what is the hedged income?
    • earn 3-4% staking reward
    • longs usually pay shorts in perps

Does this work? Loose intuition

  • value \(e\) of ETH \(\nearrow\)  to \(e+\Delta\)
    • ​staked amount goes up to \(0.5\times (e+\Delta)\)
    • short perp goes down to \(0.5\times (e-\Delta)\)
    • net effect \[\frac{1}{2} (e+\Delta)+\frac{1}{2}(e-\Delta)=e.\]
    • but you earn staking reward + short margin payment
  • value \(e\) of ETH \(\searrow\)  to \(e-\Delta\)
    • ​staked amount goes down to \(0.5\times (e-\Delta)\)
    • short perp goes up to \(0.5\times (e+\Delta)\)
    • net effect \[\frac{1}{2} (e-\Delta)+\frac{1}{2}(e+\Delta)=e.\]
    • but you earn staking reward + short margin payment

A bit more detail: let's start with a $100 in ETH position

  • Initial deposit
    • staked amount: $50
    • short perp margin: $50
  • ​ETH \(\nearrow\) 10%
    • staked: $50+10%=$55
    • short perp loses $5 (costs $55 to buy back short)
    • net: $55-$5=$50
  • ​ETH \(\searrow\) 10%
    • staked: $50-10%=$45
    • short perp gains $5 (costs $45 to buy back short)
    • net: $45+$5=$50
  • so "half-hedged"

Now add yields etc

  • assume
    • staking yield: 3%
    • short-perp funding: 5%
    • price moves to end-year
  • ​ETH  \(\nearrow\) 10%
    • staked:
      • price $50+10%=$55
      • staking 3%=$1.50 worth $1.65 at new price
      • total: $55+$1.65=$56.65
    • short perp
      • price effect: -$5 on the short
      • 5% funding on $50 = $2.50 in stables
      • Net: -$5+$2.50=$-2.50
      • \(\to\) margin is now worth $47.50
    • net: $56.65+$47.50=$104.15
  • assume
    • staking yield: 3%
    • short-perp funding: 5%
    • price moves to end-year
  • ​ETH  \(\searrow\) 10%
    • staked:
      • price $50-10%=$45
      • staking 3%=$1.50 worth $1.35 at new price
      • total: $45+$1.35=$46.35
    • short perp
      • price effect: +$5 on the short
      • 5% funding on $50 = $2.50 in stables
      • Net: $5+$2.50=$7.50
      • \(\to\) margin is now worth $57.50
    • net: $46.35+$57.50=$103.85

What could go wrong?

  • negative funding rate
  • adverse staking returns
  • margin calls and position liquidation
  • counterparty and custodial risks

Like Sky/MakerDAO, Ethena has no "arbitrage" mechanism. It relies on markets to increase and decrease supply of DAI to bring the price close to $1.

Funky "Stablecoins"

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Funky "Stablecoins"

The deck covers "funky" stabelcoins that maybe don't quite deserve their name..

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