Compounded Rebases

Understanding APY
The APY measures the real rate of return on your principal by taking into account compounding interest. As we have seen with all other OHM forks, the APY has always been set very high. This is unsustainable, and these high APYs are used as a marketing ploy to attract holders once the protocols have launched.
D3 Protocol is not designed to give absurd APYs from the offset. It is designed to give users the highest APY that is possible over the longest time period possible. Part of the sustainability equation has been addressed by adding in our unique [3.3.3.3] tokenomics layer but there may be a way to further increase the sustainability of the protocol by making tweaks to the APY formula.
Understanding the formula for APY
For those of you that do not wish to go deep into the formulas, you can scroll down to understand the end result and benefits in simple terms. The general formula for APY is calculated as follows:
APY=[1+(inom/N)]N−1APY = [1+ (i_{nom}/N)]^{N}-1APY=[1+(inom​/N)]N−1
Where; 
inom is the nominal interest rate and 
N is the number of compounding periods per year
The way this formula translates to D3 Protocol is as follows:
APY=[(1+RewardYield)1095]−1APY=[(1+RewardYield)^{1095}] -1 APY=[(1+RewardYield)1095]−1
Understanding the variables
1095 refers to the number of compounding periods per year. In almost every OHM fork, this is 1095. 3 rebases per day x 365 days = 1095. We can control this. 
Then rewardYield is calculated with the following formula:
RewardYield=DEFIdistributed÷DEFIstakedReward Yield = DEFI_{distributed} ÷ DEFI_{staked}RewardYield=DEFIdistributed​÷DEFIstaked​
To calculate rewardYield we must understand DEFIdistributed, calculated as follows:
DEFIdistributed=DEFItotalsupply∗rewardRateDEFI_{distributed}= DEFI_{totalsupply}*  rewardRateDEFIdistributed​=DEFItotalsupply​∗rewardRate
DEFIdistributed is determined by the DEFI total supply and the reward rate. In order to keep paying out rewards, the total supply will always increase. Capping the total supply would prove to be detrimental as after this cap has been reached, no one would be rewarded and this defeats the purpose of the protocol.
rewardRate however is a controllable variable. For most OHM forks, this is set around 0.3 but even the slightest change to this can have somewhat of a big effect on the distributed amount. You may have seen recently that in an attempt to control inflation, OHM issued a proposal to reduce the reward rate from 0.35 to 0.2975. We 
DEFIstaked also is variable we cannot control. The reason being we cannot control if and when people choose to stake their DEFI tokens. We can incentivise them as much as we can but ultimately the decision lies with the individual to stake or not stake. 
Compounded rebases
Given the variables within our control, our solution is to reduce the occurrence of the compounding event (rebases). In doing so we can have a direct impact on the APY straight away, in order to make it far more sustainable. We have tapered rebases over 4 week repeating cycles. The longer you stake DEFI, the more you are rewarded.
Week
Daily Rebases
Annual Rebases
1
2.00
730.00
2
2.25
821.25
3
2.60
949.00
4
3.00
1,095.00
The average rebase over the 4-week period will be 2.46 rebases per-day. Once the 4-week cycle is complete (when daily rebases are at 3), the protocol will reset the rebase amount to 2 for week 5, and begin a new 4 week increasing rebase cycle. This encourages long-term staking of DEFI as individuals benefit from more rebases the longer they hold whilst helping to control inflation.

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Outline

Understanding APY

Understanding the formula for APY

Understanding the variables

Compounded rebases