collateral

compound Finance

• post 100 DAI 
• factor 90
• $\to$ for each $1 borrow, deposit $100/90=$1.11
• can borrow up to $90

• post 1 ETH=$300 
• factor 60
• $\to$ for each $1 borrowed, deposit $100/60=$1.67
• can borrow up to $180

• post 1 ETH=$300 and 100 DAI $\to$ $400
• factor 60 and 90
• $\to$ for each $1 borrowed, deposit
  $100/(.75$\cdot$60+.25$\cdot$ 90)=$1.48
• can borrow up to $270

Compound

AAVE

Token Accounting: TWO Types

• track ownership of pool holdings with receipt tokens

• continuous updating of wallet balances

How does compound finance work?

Lending

token accounting

Compound

• deposit: add $q_0$ units of $A$-tokens into a  pool that contains \(Q_0$\)
• assume:  $Q^c_0$  units of the  $cA$-receipt tokens outstanding already
• User receives  $q^c$ receipt $$\frac{q^c}{Q_0^c+q^c}=\frac{q_0}{Q_0+q_0}.$$
• Exchange rate: $z_t=\frac{Q_t}{Q_t^c}$  of $A$ to $cA$-tokens.
• Interest accrues so that pool contains $Q_T>Q_t$ of the $A$ token after time $T$
• When withdrawing, users sends $q^c$ tokens to the contract
• Receives $q_T>q_0$ of the $A$-token at exchange rate $z_t>z_0$ where $$q_{T}=Q^c \times z_{T}$$

compound Finance

• Compound escrows tokens
• must account for % ownership
• $\to$ tokenized user share
• $\to$ use the c-token
  • cDAI
  • cETH
• minted/burned based on funds added/removed from underlying
• seamless movement of these shares (reduced transactions costs!)
• ability to use the ctokens in other protocols

Tracking ownership - How do you reclaim a deposit?

Tracking ownership - Example

compound Finance

In Compound

translated

new deposit

1,000 DAI

100 cDAI

500 DAI

add 50 new cDAI

Tracking ownership - Example

compound Finance

In Compound

translated

new deposit

1,000 DAI

150 cDAI

500 DAI

1 year later: 10% interest on compound

150 DAI

(same cDAI, ownership shares don't change, just each cDAI is worth more)

(accrues per block per deposit)

AAVE

Differences to Compound

Aave

• Aave is the second-largest lending protocol to date
• has many features that are similar to Compound
• offers more assets
• offers flash loans (rate ~7bs)
• token accounting done by continuous updating of token balance

token accounting

Aave

• User makes a deposit continuously receives "a-tokens"
• Supply:
  • $Q_0$ units of an asset $A$ token to the Aave pool obtains  
  • $Q_0$ units of $aA$-tokens
• balance updates continuously (\to\) claim on more $aA$ tokens
• To withdraw after $T$ interest periods: sends  her $Q_T$ $aA$-tokens to the contract, where
  $$Q_T= Q_0\prod_{t=1}^{T}{(1+r_t)}$$
• $t$ measured in blocks
• $r_t=$ interest allocated per block $t$

common theme in DeFi: jumping between dApps

dapp-linking

Defi is like real "high" finance

Source: Harvey, Ramachandran, and Santoro (2020)

Dapp composability & Flash loans

YIELD Protocol

• basic idea: zero-coupon loans
• You have:
  • target asset
  • collateral
  • y-token trading at discount price 

• examples: yDAI
• expires in 1 year
• price: $.92
• backed by ETH
• buying = you earn 8/92 cents=8.7% RoR

1 ETH = 150 DAI
collateralization ratio 125%

seller

buyer

Assumptions