🧮Vault Math (v1)

You can find a full implementation of our vault mechanics in this spreadsheet.

The function and variable names in this section have been edited to make them intelligible to readers; they might not exactly match the names used in the smart contrats. A correspondance table is available here.

General Notation

Name	Definition
T	Time
T = 0	Initial state of the vault at deployment
T = t	Current epoch (the one that just ended)
T = t-1	Previous Epoch
$\small 𝐸𝑝𝑜𝑐ℎ𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛$	Length of one trading Epoch, currently set to 7 days
DA	Stands for "Deposit Asset", which is the asset users deposit into the vault (initially USDC). Vaults using different deposit assets (e.g. ETH, BTC) might be added in the future

Vault Level Variables

Name	Definition
$\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦_{(t)}$	Total amount of VaultToken in circulation = Total amount minted from users deposits – Total amount burnt from users withdrawals
$\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(𝑡)}$​	Value of one share of the vault denominated in deposit asset (e.g. USDC in a vault where users deposit USDC). At T=0, $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(0)}=1$​
$\small 𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑐𝑡$	Annual Management Fee percentage (initially set at 1.5%)
$\small 𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑐𝑡$	Performance Fee percentage (initially set at 15%)
$\small 𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}$	Management fee charged per vault token for the epoch, denominated in deposit asset (e.g. USDC)
$\small 𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}$	Performance fee charged per vault token for the epoch, denominated in deposit asset (e.g. USDC)
$\small 𝐷𝑒𝑥𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}$	Amount of deposit asset (e.g. USDC) on the DEX where the trading strategy is being executed (e.g. dYdX) = Total amount deposited by users – Total amount withdraw by users +/- Total trading strategy P/L – Management and Perf Fees
$\small 𝑃𝑛𝐿𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}$	Profit/Loss per vault token generated by the trading strategy for the epoch
$\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)}$	Theoretical amount of VaultToken in circulation at the end of the epoch, assuming all users who initiated a withdrawal during that epoch have finalized it before the end of the following epoch (effectively burning their VaultToken and receiving their share of deposit asset). In reality, users can take as much time as they want before finalizing a withdrawal which could lead to a miss-match between what the VaultTokenSupply should be in theory, and what it is reality, which would introduce errors in the subsequent calculations. At T=0, $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(0)}=0$
$\small 𝑁𝑒𝑡𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}$	Net amount to be transferred from/to the vault to/from the DEX wallet depending on deposits, withdrawals, fees and gas reserves for the epoch
$\small T𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑀𝑖𝑛𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒𝐸𝑇𝐻$	Minimum amount of ETH that should be in the TransferBot wallet to pay for gas at each epoch; if ETH balance falls below that threshold, a swap from the Deposit Asset (e.g. USDC) will be initiated, assuming there is enough Deposit Asset in the wallet [NOT IMPEMENTED YET]
$\small 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝐺𝑎𝑠𝑅𝑒𝑠𝑒𝑟𝑣𝑒DA_{(𝑡)}$	Amount of deposit asset (e.g. USDC) to be retain within the TransferBot wallet for the current epoch as a buffer to fund future gas fees [NOT IMPEMENTED YET]
$\small 𝑇𝑟an𝑠fer𝐵𝑜𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA_{(𝑡)}$	Amount of deposit asset (e.g. USDC) in the TransferBot wallet at the end of the current epoch, before accounting for $\small 𝑈𝑠𝑒𝑟𝑁𝑒𝑤𝐷𝑒𝑝𝑜𝑠𝑖𝑡$ [NOT IMPEMENTED YET]
$\small 𝑇𝑟an𝑠𝑓er𝐵𝑜𝑡𝑀𝑖𝑛𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA$	Minimum amount of deposit asset (e.g. USDC) in the TransferBot wallet required to initiate a swap for ETH to fund future gas fees [NOT IMPEMENTED YET]
$\small 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑇𝑎𝑟𝑔𝑒𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA$	Targeted deposit asset (e.g. USDC) reserve in the TransferBot wallet to be swapped for ETH to fund gas fees [NOT IMPEMENTED YET]
$\small 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒𝐸𝑇𝐻_{(𝑡)}$	Current ETH balance in the TransferBot wallet [NOT IMPEMENTED YET]

Individual Users Variables

Name	Definition
$\small 𝑈𝑠𝑒𝑟𝑁𝑒𝑤𝐷𝑒𝑝𝑜𝑠𝑖𝑡_{(𝑡,i)}$	Amount of deposit asset (e.g. USDC) deposited by user i during the epoch t (when user called the InitiateDeposit() function). This amount is stored in the vault until the end of the current epoch, and then is sent to the DEX wallet to be used as trading capital
$\small 𝑈𝑠𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙_{(𝑡,i)}$	Amount of VaultToken requested for withdrawal by user i during the epoch t (when user called the InitiateWithdrawal() function). The corresponding amount of deposit asset (e.g. USDC) will be withdrawn from the DEX wallet at the end of the current epoch and stored in the vault, where it will be available for the user to withdraw anytime after the end of the current epoch
$\small 𝑈𝑠𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡,i)}$	Total amount of VaultToken user i owns at the end of epoch t

TransferBot End of Epoch Routine & Math

Sequence of event is important given some variables dependency from one step to the next.

Step	Description
	Call UpdateDexWalletBalance() function that call GetAccount() from dy/dx API and read the portfolio Equity value, then update that value into the vault smart contract ($\small 𝐷𝑒𝑥𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}$), except if the vault is empty (e.g. at T=0): IF: $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)}=0$, THEN: $\small 𝐷𝑒𝑥𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}=\sum_{i=0}^{n}𝑈𝑠𝑒𝑟𝑁𝑒𝑤𝐷𝑒𝑝𝑜𝑠𝑖𝑡_{(𝑡,i)}$, ELSE: $\small 𝐷𝑒𝑥𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}=Read$ $\small value$ $\small from$ $\small dy/dx$ $\small API$
	Call MgtFeePerVaultToken() function: IF: $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)}=0$, THEN: $\small 𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}=0$, ELSE: $\small 𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}=𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(𝑡)}*\frac{𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑐𝑡 ∗ 𝐸𝑝𝑜𝑐ℎ𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛}{365}$
	Call PnLPerVaultToken() function: IF: $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)}=0$, THEN: $\small 𝑃𝑛𝐿𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}=0$, ELSE: $\small 𝑃𝑛𝐿𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}=\frac{𝐷𝑒𝑥𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}}{𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)}}-𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(𝑡)}$
	Call PerfFeePerVaultToken() function: IF: $\small 𝑃𝑛𝐿𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}\le 0$, THEN: $\small 𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}= 0$, ELSE: $\small 𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}= 𝑃𝑛𝐿𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}*𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑐𝑡$
	Call UpdateVaultTokenPrice() function: IF: $\small T=0$, THEN: $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(𝑡)}=1$, ELSE: $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(𝑡)}= 𝑀𝐴𝑋((𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(𝑡)}+𝑃𝑛𝐿𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)} −𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}−𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}), 0)$
	Call CalculateTransferBotGasReserveDA() function: [NOT IMPLEMENTED YET] $\small 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝐺𝑎𝑠𝑅𝑒𝑠𝑒𝑟𝑣𝑒DA_{(𝑡)}= 𝑀𝐼𝑁( 𝑀𝐴𝑋(𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑇𝑎𝑟𝑔𝑒𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA −$ $\small 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA_{(𝑡)}, 0),$ $\small (𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}+𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)})$ $\small ∗𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡−1)})$
	Call CalculateNetTransferBalance() function: $\small 𝑁𝑒𝑡𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}=\sum_{i=0}^{n}(𝑈𝑠𝑒𝑟𝑁𝑒𝑤𝐷𝑒𝑝𝑜𝑠𝑖𝑡_{(𝑡,𝑖)})$ $\small ‒\sum_{i=0}^{n}(𝑈𝑠𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙_{(𝑡,𝑖)})∗𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(𝑡)}$ $\small −(𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}+𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)})$ $\small ∗𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)}$
	Call DexTransfer() function: IF: $\small 𝑁𝑒𝑡𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}\gt 0$, THEN: $\small \text{𝑆𝑒𝑛𝑑 }𝑁𝑒𝑡𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}\text{ 𝑓𝑟𝑜𝑚 Vault 𝑡𝑜 DEX wallet}$, ELSE: $\small \text{𝑆𝑒𝑛𝑑 }𝑁𝑒𝑡𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑎𝑙𝑎𝑛𝑐𝑒_{(𝑡)}\text{ 𝑓𝑟𝑜𝑚 DEX to Vault wallet}$
	Call FeesTransfer() function: $\small \text{𝑆𝑒𝑛𝑑 } \bigl((𝑀𝑔𝑡𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(𝑡)}+𝑃𝑒𝑟𝑓𝐹𝑒𝑒𝑃𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛_{(t)})*𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(t)}-𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝐺𝑎𝑠𝑅𝑒𝑠𝑒𝑟𝑣𝑒DA_{(𝑡)}\bigl)\text{ 𝑓𝑟𝑜𝑚 Vault 𝑡𝑜 protocol Tresaury wallet}$
	Call UpdateVaultTokenSupplyPostWithdrawals() function: $\small 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)} =𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑆𝑢𝑝𝑝𝑙𝑦𝑃𝑜𝑠𝑡𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙𝑠_{(𝑡)}+\text{𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛 𝑡𝑜 𝑏𝑒 𝑚𝑖𝑛𝑡𝑒𝑑} −\text{𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛 𝑡𝑜 𝑏𝑒 𝑏𝑢𝑟𝑛𝑡}$ WITH: $\small \text{𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛 𝑡𝑜 𝑏𝑒 𝑚𝑖𝑛𝑡𝑒𝑑}=\sum_{i=0}^{n}\frac{𝑈𝑠𝑒𝑟𝑁𝑒𝑤𝐷𝑒𝑝𝑜𝑠𝑖𝑡_{(t,i)}}{𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑃𝑟𝑖𝑐𝑒_{(t)}}$ $\small \text{𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛 𝑡𝑜 𝑏𝑒 𝑏𝑢𝑟𝑛𝑡}=\sum_{i=0}^{n}𝑈𝑠𝑒𝑟𝑉𝑎𝑢𝑙𝑡𝑇𝑜𝑘𝑒𝑛𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙_{(t,i)}$
	Call SwapDAforETH() function to swap some deposit asset (e.g. USDC) to ETH for future gas fees: [NOT IMPEMENTED YET] IF: $\small (𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒𝐸𝑇𝐻_{(t)}<𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑀𝑖𝑛𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒𝐸𝑇𝐻)$ AND $\small (𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA_{(t)}>𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑀𝑖𝑛𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA)$ THEN: $\small \text{Swap }𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐵𝑜𝑡𝑊𝑎𝑙𝑙𝑒𝑡𝐵𝑎𝑙𝑎𝑛𝑐𝑒DA_{(t)}\text{ for ETH using Uniswap}$