Staking Rewards($prCHAOS)

Staking rewards

The OrderNChaos protocol incentivizes holders of $CHAOS to stake their $CHAOS in a savings account. Staking removes $CHAOS from circulation, increasing its scarcity, and consequently its market value. The incentives come in the form of a special token: pre-CHAOS, or $prCHAOS (taken from the Sanskrit word for "life").

The prCHAOS token

The $prCHAOS token is a special financial instrument that can perhaps best be described as an option with a dynamic strike price. A $prCHAOS token entitles its owner to purchase $CHAOS at the current floor price. This entitlement is of value to the holder, since the market price of $CHAOS will almost certainly be higher than its floor price.
The act of purchasing $CHAOS by means of $prCHAOS is called realizing $prCHAOS. The user pays 1 $prCHAOS plus the floor price for $CHAOS in exchange for 1 $CHAOS. The protocol subsequently burns the $prCHAOS token.
It may be financially advantageous to realize $prCHAOS or to hold it, depending on one's projection on the price of $CHAOS. The maximum value $prCHAOS can represent is the difference between $CHAOS market price and its floor price. Once a person realizes $prCHAOS, they are now exposed to the upside of $CHAOS beyond its difference from the floor price.
"Rebase" currencies (such as Olympus) use a different instrument for rewards: their own native token. This decision creates a need to monitor the "runway" of the reward rate. The "runway" is how long can they sustain these rewards before the protocol will run out of money in the treasury. OrderNChaos takes a more sustainable approach and has an infinite runway. By distributing $prCHAOS, the protocol never diminishes its ability to back $CHAOS at the existing or future floor price.

Reward distribution

The prCHAOS rewards are distributed once every epoch, and their magnitude is simply a function of the global supply of $CHAOS.
RewardPot=RewardRateSupplyCHAOSRewardPot = RewardRate * SupplyCHAOS
Obviously, as the supply of $CHAOS grows, so will the size of the reward pot. This fact acts as incentive for users to realize their prCHAOS in order to extend the amount of rewards they receive.
The actual amount of prCHAOS an individual account receives is determined by the proportion of staked $CHAOS that the account holds. If one account hold 100% of all the staked $CHAOS -- even if this amounts to only 1 single $CHAOS -- then they will receive 100% of the reward pot of prCHAOS. If there are only 2 accounts that are staking $CHAOS, and they are each staking the same amount, then will receive an even 50% split of the reward pot.
IndividualReward=RewardPotIndividualStakedCHAOSTotalStakedCHAOSIndividualReward = RewardPot * \frac{IndividualStakedCHAOS}{TotalStakedCHAOS}
There are 2 reasons behind distributing rewards based upon the proportional amount of staked $CHAOS.
  1. 1.
    To disincentivize bank runs or massive simultaneous unstaking. If people unstake, the ones who still hold will receive larger rewards. The incentive to stake intensifies as stakers become more scarce.
  2. 2.
    From the opposite side, the incentive to stake diminishes as more people stake. This feature is healthy for the protocol insofar as it puts a natural, market-driven cap on how much $CHAOS becomes staked. There must, after all, be $CHAOS circulating in the open market. And so staking rewards must naturally taper off in order to incentivize people to find other uses for their $CHAOS.

Compound reward rate

Rewards for stakers are paid in $prCHAOS, which can subsequently be executed for more $CHAOS. Staking the new $CHAOS creates compounding rewards.
The profit ratio for $prCHAOS is computed as the delta between the floor and the market price of $CHAOS, divided by $CHAOS' market price.
Profit=pmpfpmProfit = \frac{p_m - p_f}{p_m}
This profit can be compounded continuously over a year. Given a certain daily percentage rate of emitted $prCHAOS, the estimate for compound APY is:
APY=(1+DPRProfit)3651DPR=Daily prCHAOS rateAPY = (1+ DPR * Profit) ^ {365} - 1 \newline DPR = Daily \ prCHAOS \ rate
With a daily $prCHAOS emission rate of 0.7% and $CHAOS at $10 with a $4 floor, this equates to an estimated APY of 361.2%.

Infinite runway

One key benefit of rewarding stakers with $prCHAOS is that the rewards are value- neutral to the health of the protocol. If the protocol were to pay out with $CHAOS, it would be diminishing the treasury's ability to raise the floor, since each new $CHAOS token would require an existing amount of treasury surplus equal to the floor price.
Since $prCHAOS can only become realized as $CHAOS through paying the treasury the floor price for $CHAOS, the protocol is able to sustain an infinite amount of $prCHAOS rewards without breaking its contract to back every $CHAOS token.