Anchor Protocol
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# Deposit Rate Subsidization

Anchor Protocol's deposit rate stability is supported by borrow demand from borrower ANC distribution and direct subsidization. Anchor defines a target deposit rate (
$r_{target}$
), and a threshold deposit rate (
$r_{threshold}$
) and constantly attempts to retain a deposit rate close to
$r_{target}$
and always above
$r_{threshold}$
.
Every epoch, the average deposit rate during the last epoch (
$r_{current}$
) is calculated and compared with the target and threshold rates. Appropriate measures are then made to readjust the deposit rate.

## Borrower ANC Incentives

Anchor's deposit rate is primarily adjusted by calibrating the rate of ANC emission to borrowers (
$e$
), updated through a feedback control algorithm.

### ANC Emission Feedback Control

Anchor alters the ANC emission rate based on a multiplicative increase / multiplicative decrease feedback control algorithm, which adjusts the ANC emission rate of the next epoch
$e_{n+1}$
based on the previous emission rate of
$e_n$
:
$e_{n+1} = k \cdot e_n$
The feedback control algorithm adjusts incentives with
$r_{average}$
- the average of
$r_{target}$
and
$r_{threshold}$
- as the reference point:
$r_{average}=\frac{r_{target}+r_{threshold}}{2}$
• If deposit rate is approaching the threshold (
$r_{current} < \frac{r_{threshold}+r_{average}}{2}$
), increase emission by 0.7% (
$k \approx 1.007$
)
• If deposit rate approaches the target (
$r_{current} > \frac{r_{target}+r_{average}}{2}$
), reduce emission by 0.3% (
$k \approx 0.997$
)
where the set
$k$
values result in a 50% emission increase over a week-long period or a 15% decrease over a week-long period.

## Direct Subsidization

As an additional layer of safety, the protocol directly subsidizes the deposit rate if it is below the threshold rate (
$r_{current}
), funded from the yield reserve's stockpiled stablecoins.
An amount required to raise the deposit rate to the threshold is distributed to depositors, which is limited to 10% of the yield reserve's balance per subsidization to prevent excessive drainage. Distributed subsidies are added to the money market’s liquidity, increasing the aTerra exchange rate and appreciating the value of aTerra.