# 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.Anchor's deposit rate is primarily adjusted by calibrating the rate of ANC emission to borrowers (

$e$

), updated through a feedback control algorithm.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.As an additional layer of safety, the protocol directly subsidizes the deposit rate if it is below the threshold rate (

$r_{current}<r_{threshold}$

), 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.

Last modified 2yr ago