Maker Withdrawal
The jth Maker’s payout is a linear function of the current Market Yield according to their proportional share, depending on whether the protocol is in Surplus or otherwise. At withdraw-time, the jth Maker’s withdrawal can be calculated as:
![](https://docs.bumper.org/~gitbook/image?url=https%3A%2F%2F2925207410-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-x-prod.appspot.com%2Fo%2Fspaces%252FV8jHRr0VdEnbO32zKxTc%252Fuploads%252FYTAnIYjixLzRZwZTPpAv%252Fimage.png%3Falt%3Dmedia%26token%3Dacc5e78c-fd11-4bf5-95b6-a9fe83c551fb&width=768&dpr=4&quality=100&sign=1c164348&sv=1)
Note, "ExpiredProtocolFee" is the protocol fee for the period that the position was in an expired state.
Similar to Takers, we must also capture the time period that a Maker accrues the ‘expired’ (penalty) rate. For the positive yield case, the withdrawal amount:
![](https://docs.bumper.org/~gitbook/image?url=https%3A%2F%2F2925207410-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-x-prod.appspot.com%2Fo%2Fspaces%252FV8jHRr0VdEnbO32zKxTc%252Fuploads%252FzjYJ2lso9ORmIsF3Uc3S%252Fimage.png%3Falt%3Dmedia%26token%3D56797e35-5105-4bdb-be97-811ef5c59776&width=768&dpr=4&quality=100&sign=c9e8591e&sv=1)
becomes:
![](https://docs.bumper.org/~gitbook/image?url=https%3A%2F%2F2925207410-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-x-prod.appspot.com%2Fo%2Fspaces%252FV8jHRr0VdEnbO32zKxTc%252Fuploads%252FwcgLuFoh7KJzBhdDywco%252Fimage.png%3Falt%3Dmedia%26token%3Dad0fb7d3-f5e5-4f6c-ac1c-0d983ec625b5&width=768&dpr=4&quality=100&sign=4d484e7&sv=1)
For the negative Yield case, the withdrawal amount:
![](https://docs.bumper.org/~gitbook/image?url=https%3A%2F%2F2925207410-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-x-prod.appspot.com%2Fo%2Fspaces%252FV8jHRr0VdEnbO32zKxTc%252Fuploads%252F62gtGlmct003udeYON8W%252Fimage.png%3Falt%3Dmedia%26token%3Dbde152e6-36d1-45f4-86ec-ce5b3a49f676&width=768&dpr=4&quality=100&sign=c482b6bd&sv=1)
becomes:
![](https://docs.bumper.org/~gitbook/image?url=https%3A%2F%2F2925207410-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-x-prod.appspot.com%2Fo%2Fspaces%252FV8jHRr0VdEnbO32zKxTc%252Fuploads%252FgJS0q49w403TdMNUw5Hc%252Fimage.png%3Falt%3Dmedia%26token%3D13e945ce-8981-4342-ac7b-8c31a1186612&width=768&dpr=4&quality=100&sign=9915d194&sv=1)
Global state mutates at withdraw-time:
![](https://docs.bumper.org/~gitbook/image?url=https%3A%2F%2F2925207410-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-x-prod.appspot.com%2Fo%2Fspaces%252FV8jHRr0VdEnbO32zKxTc%252Fuploads%252FjqB3M3b1M1FPwM0YNxAh%252Fimage.png%3Falt%3Dmedia%26token%3D9d656005-3fdd-40b1-8ec7-9cea24fca0a7&width=768&dpr=4&quality=100&sign=b1af426a&sv=1)
When a Maker leaves, the market’s Debt decreases by their deposit amount. After this point, the Yield Target (E) will increase less aggressively each time a new premium is computed and applied. E is also decreased after a Maker leaves, irrespective of whether they have a positive or negative actual yield, according to their simple share of Debt.
Note that it is important that we mutate the state of E before D to ensure correctness, given that Et+1 = f(Dt) , at Maker Withdraw and Renew. We do not increase E at Maker Deposit (it is incremented when computing the premium).
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