Auto-Compounding Substantially Boosts ApeCoin Staking Yields

Parallel is the first on-chain money market to support permissionless borrowing, lending, and staking ApeCoin. Users can deposit their Bored Ape Yacht Club or Mutant Ape Yacht Club NFT's and borrow ApeCoin for staking with no liquidation risk for their NFT's (if the user only borrows ApeCoin they stake via Parallel). It is likewise the first crypto protocol to support auto-compounding of staking rewards in Peer 2 Peer ApeCoin staking, and indeed this is how we maximize yields for the same BAYC, MAYC, and ApeCoin holders.

Put simply: use the power of auto-compounding to significantly boost ApeCoin staking rewards.

Compounding - Use it to Your Advantage when ApeCoin Staking

Users can enjoy high ApeCoin staking yields with one catch--the official ApeCoin DAO contract does not support auto-compounding. Why does this matter? It's the difference between linear and exponential growth.

Linear versus exponential? It turns out that our brains can't really appreciate the difference in abstract. Say someone offers you the choice between $100,000 upfront OR a penny which doubles in value every day for 30 days. Easy decision, right? $100,000 sounds like a lot more money than $0.01 doubling.

Well that penny sees exponential growth from $0.01 at the start to $42,949,672.96 at the end of those 30 days. This is the power of compounding and exponential growth.

On-chain data as measured via Parallel shows the current yield for the single-side ApeCoin pool at 90%--an impressive return by any metric. If an ApeCoin holder deposited 1,000 $APE token they could in theory finish with 1,900 $APE after a year's time at the same APR. But what if they claimed their rewards every day and re-staked them on a daily basis? That APR grows exponentially.

$$Effective \ APY\% = (1 + \frac{90\%}{{365}})^{{365}} - 1 = 148\%$$

For that same 90% non-compounding staking yield the user could theoretically collect up to 148% if they claimed rewards and re-staked them on a daily basis.

Comparing Non-Compounding and Compounding ApeCoin Staking Positions

The compounding makes the difference between finishing the year at 1,900 $APE token with non-compounding yield versus 2,500 $APE with daily compounding. And indeed this is exactly why users should stake their ApeCoin via Parallel's auto-compounding pools.

How do we Optimize The Rate of Compounding?

Parallel will automatically claim and re-stake ApeCoin staking rewards for the Single-Side ApeCoin staking pool and will not charge users any fees for the service. Parallel can do so because it only pays Ethereum gas once regardless of how many users stake in the single-side ApeCoin Pool. And indeed users do not pay any fees for the service for Single-Side ApeCoin staking.

Given Zero Fees, Parallel will Compound Single-Side ApeCoin Rewards at Least Daily

For the NFT-specific pools, however, compounding must be done on a per-NFT basis and is sensitive to gas prices on Ethereum Mainnet and total amounts staked in NFT pools. How frequently should we claim our ApeCoin staking rewards and re-stake them?

How Often do we Claim and Compound Rewards for BAYC/MAYC Pools?

Each 'Claim' of ApeCoin and re-stake against the ApeCoin DAO contract costs between 100,000 to 200,000 gas per NFT if we batch multiple NFT's in the same transaction. If we take an average base fee gas cost of approximately 20 Gwei this translates to approximately 0.018 ETH per compound. And to bring this back to ApeCoin we take the current APE/ETH exchange rate and estimate that it costs 5 $APE per claim-and-compound transaction.

To calculate effective yields we will modify our APY formula to include the effects of gas fees on each transaction and further add recursion to calculate the effective APY for NFT pools.

We claim $Interest_{NFT}$, which represents the staking rewards from BAYC or MAYC pools, every $N$ days:

$$Interest_{NFT} = Principal_{NFT} \times APR_{NFT} \times \frac{N}{365} - Gas_{APE}$$

We can then calculate the ongoing $Principal_{APE_t}$ which represents the total amount staked to the single-side ApeCoin staking pool. If the user is only staking to the BAYC or MAYC pool this value starts at 0 at $t=0$:

$$For \ t \in (1,\frac{365}{N})): \\ Principal_{APE_t} = (Principal_{APE_{t-1}} + Interest_{NFT} - Gas_{APE}) \times \\(1+APR_{APE} \times \frac{N}{365})$$

The resulting $APY_{NFT}$ is thus the combination of $APY_{APE}$plus the earned $APR_{NFT}$, rewritten to $APY_{All}$:

$$For \ t = \frac{365}{N}: APY_{All} = \frac{Principal_{APE_t}}{Principal_{NFT} + Principal_{APE_0}}$$

We can then measure the $APY_{All}$given the above assumptions as shown on the chart below. At current rates, Bored Ape Yacht Club NFT pool stakers earn approximately 160% APR, while single-side ApeCoin stakers earn 91%. If we use the above formula to translate this into a compounding APY, we see $APY_{All}$ reach above 260% with regular compounding:

Our calculations show Bored Ape Yacht Club NFT holders would maximize their returns if we auto-claim and compound rewards approximately every 3-5 days.

Parallel makes available the above functionality available to all who stake their ApeCoin via its user interface and contracts. And users may further borrow ApeCoin and earn interest on ApeCoin staked and made available to Parallel's money market.

Users can likewise see these auto-compounding contracts have been audited by third-party professionals: External Audits.

Introducing cAPE - Compounding ApeCoin Token

Parallel is the first on-chain protocol to support ApeCoin borrowing and staking, and it is likewise the first to provide the $cAPE$ liquid staking token and money market.

Users who deposit ApeCoin into the Parallel auto-compounding contract receive $cAPE$ on a 1:1 basis with their $APE staked and rewards claimed and accumulated. The same users may elect to supply their $cAPE$ to the Parallel money market which allows them to collect further yield.

Borrowing and Lending cAPE on Parallel

Users can add further yields to their $cAPE$ auto-compounding returns via the $cAPE$ money market, but why might a user elect to borrow $cAPE$ given such high built-in interest rates? Indeed, the effective $Borrow_{APY}$is at minimum the $APY_{cAPE}$ and grows by a factor of the nominal APR of the same token:

$$Effective \ BorrowAPY_{cAPE} = (1+APY_{cAPE}) \times (1+BorrowAPY_{cAPE})-1$$

A user would logically only choose to borrow $cAPE$ if they were able to generate higher returns in their own ApeCoin staking and in the Bored Ape Yacht Club, Mutant Ape Yacht Club, and Bored Ape Kennel Club pools. Specifically:

$$APY_{cNFT} \ge Effective \ BorrowAPY_{cAPE}$$

Rewriting the above, the user might potentially borrow $cAPE$ as long as the $BorrowAPY_{cAPE}$ fell below the following:

$$BorrowAPY_{cAPE} \le \frac{1+APY_{cNFT}}{1+APY_{cAPE}} -1$$

At time of launch the $APY_{cNFT}$ was approximately 250% while the $APY_{cAPE}$ is roughly 170%. The user could in theory at least break even as long as the $BorrowAPY_{cAPE}$ is less than 30%.

According to our interest rate models and current $cAPE_{APY}$of 13% we can see this relationship below:

Effective Borrow APY for cAPE

Let's look at this by example:

User Bob deposits 10,000 $APE into the Parallel auto-compounding pool when the single-side ApeCoin staking pool APR is 140%. They receive $cAPE$and supply it to the Parallel money market. If this sum is compounded daily, they would theoretically receive up to 304% APY, which is in turn the minimum $BorrowAPY_{cAPE}$.

User Mary has a Bored Ape Yacht Club NFT and looks to borrow 10,094 $APE to pair and stake with her BAYC NFT. If the Bored Ape pool staking reward APR is 210%, she could theoretically receive up to 457% APY in auto-compounding rewards at the end of a year. Mary would in turn be willing to borrow $cAPE$ to then unstake and restake with her Bored Ape Yacht Club NFT as long as the $BorrowAPY_{cAPE}$ is comfortably below 33% using the above equation.

In lending his $cAPE$ to the money market, Bob could in theory receive up to 457% Effective APY on his single-sided ApeCoin position.

In practice we expect $Effective \ BorrowAPY_{cAPE}$ to stay below the NFT-only ApeCoin staking yield rewards.

Single Side ApeCoin pool compounding will almost certainly continue to drive their related APY's lower as there is no supply cap on the Single Side pool. On the other hand, BAYC and MAYC holders will likely continue to enjoy relatively higher yields given the hard supply cap on both NFT-specific staking pools.

Parallel Automatically Pays off cAPE Borrowing to Prevent Debt from Auto-Compounding

If a user borrows ApeCoin for staking they should likely withdraw rewards and pay down debt in order to boost their returns. And in fact Parallel will automatically do this on the user's behalf for the same reason.

Any interest charged to borrow positions on Parallel simply add to the total amount the user owes. Or in other words: without auto-repay debt positions auto-compound and debt grows at a compounding rate according to the on-chain interest rate model:

$$Actual \ Borrow \ APY = (1+Theoretical APY/secsperyear)^{secsperyear}-1$$

But given auto-repay the user will keep debt smaller and effectively pay the non-compounding cAPE APR plus the Borrow APR on the money market rates.

Below see a chart that shows the differential of passive ApeCoin staking with 10,094 ApeCoin borrow at 100% APY interest versus 210% APR staking rewards from the BAYC pool. The blue line shows the basic net returns for the ApeCoin staker who borrows and stakes but takes no further action. Their net profit accrues at a slowing pace given the auto-compounding in their ApeCoin debt position.

The red line shows the theoretical returns if the same user claims staking rewards on a daily basis, pays off ApeCoin interest, and supplies excess ApeCoin to the the single-side ApeCoin pool at 140% APY.

Our data and calculations show that it is clearly beneficial to auto-compound ApeCoin staking rewards at regular intervals and similarly pay off any ApeCoin debt in order to maximize returns.

Indeed users will automatically see compounding rewards on their ApeCoin staking via Parallel, and we will likewise auto-repay interest in order to boost their longer-term rewards from ApeCoin staking.