Mathematical Basis of the DAO

Mathematical Basis of the Athen DAO

Staking

$$sAOE=AOE$$

$sAOE will always be redeemable for $AOE as a 1:1 swap since the DAO will always convert bond sale profits to AOE rewards.

$$Rebase=1−(AOEDeposited/sAOEOutstanding$$

The treasury deposits AOE into the distributor. The distributor then deposits AOE into the staking contract, creating an imbalance between AOE and sAOE. sAOE is therefore rebased to correct this imbalance between AOE deposited and sAOE outstanding. The rebase brings sAOE outstanding back up to parity with AOE so that 1 sAOE always equals 1 staked AOE. This rebasing mechanism facilitates the sAOE = AOE equation above.

Bonding

$$BondPrice=1+MarketPremium$$

​The price of a bond is governed by the interaction between DAI and the market sentiment of AOE. The sentiment of the market determines the premium applied to bond prices.

$$MarketPremium=DebtRatio∗BCV$$

​The Market Premium is derived from the debt ratio of the system and a scaling variable called BCV, which is in turn governed by market sentiment.

$$DebtRatio=BondsOutstanding/AOESupply$$

​The debt ratio is a variable which allows us to measure the debt of the Protocol to Bonders, allowing for a dynamic Market Premium.

$$BondPayoutReserveBond=MarketValueAsset/BondPrice$$

Bond payout determines the number of AOE sold to a bonder. For reserve bonds, the market value of the assets supplied by the bonder is used to determine the bond payout. For example, if a user supplies 100 DAI and the bond price is 25 DAI, the user will be entitled 4 AOE since 100/25 = 4.

$$BondPayoutlpBond=MarketValuelpToken/BondPrice$$

​For liquidity bonds, the market value of the LP tokens supplied by the bonder is used to determine the bond payout. For example, if a user supplies 0.001 AOE-DAI LP token which is valued at 1000 DAI at the time of bonding, and the bond price is 250 DAI, the user will be entitled to 4 AOE.

$AOE Supply Governance

$$AOESupplyGrowth=AOEStakers+AOEBonders+AOEDAO$$

AOE has a dynamic supply, meaning that it adjusts with market activity.

Supply increases when AOE is minted as a staking or bonding reward.

$$AOEStakers=AOETotalSupply∗RewardRate$$

As each epoch ends, the treasury will determine and mint rewards based upon the reward rate. This reward is then distributed to stakers.

$$BondPayout=AOEBonders$$

When a bond is purchased, a AOE reward is minted. The bond reward willl be vested and released at linear intervals. Different types of bonds require different payout calculations. See above for more information.

$$MintedDAODAO=MintedDAOBonders$$

The DAO always receives a reward equal to that of the bonder - this is the profit of the DAO.

Asset Backing

$$AOEBacking=TreasuryBalance$$

​Every circulating AOE token is backed by the treasury in either stablecoins or non-stablecoins.

$$TreasuryBalancestablecoins=RFVReserveBond+RFVlpBond$$

​When bonds are sold, the stablecoin reserve of the treasury grows. RFV (risk-free value) is calculated differently based upon the bond type.

$$RFVReserveBond=AssetSupplied$$

​Reserve bonds in stablecoins like DAI, the RFV is equal to the value of the asset suppled by the bonder.

$$RFVlpBond=2 C ​ onstantProduct∗$$

​For LP bonds such as AOE-DAI bond, the RFV is calculated differently because the protocol needs to mark down its value.

Why? The LP token pair consists of AOE, and each AOE in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating AOE are backed, the protocol marks down the value of these LP tokens, hence the name risk-free value (RFV).