blockbuilder97/crop

This is a collateral adapter for Dai that allows for the distribution of rewards given to holders of the collateral.

This adapter is then used to implement a leveraged cUSDC strategy, depositing the underlying USDC collateral into Compound and farming COMP.

Rewards Adapter

We distinguish between push and pull rewards:

• in push rewards, the rewards are sent to holders without their input.
• in pull rewards, holders must actively claim their rewards.

push rewards are supported by default. In principle any pull-based token rewards are supported, e.g. Compound claimComp() and SNX-staking getReward(), with a little custom claiming logic.

Usage

Developers need to

1. Override the crop function with the logic for claiming the given reward token and then return the tokens gained since the last crop. The default is the difference in the token balance and will work for push-reward tokens.

2. Override the nav function to show the underlying balance of the adapter (the Net Asset Valuation). The default is gem.balanceOf(adapter).

Users can join and exit as with regular adapters. The user receives their pending rewards on every join / exit and can use e.g. join(0) to receive their rewards without depositing additional collateral.

There are two additional functions:

• flee allows for exit without invoking crop, in case of some issue with the crop function.

• tack is for transferring stake between users, following collateral transfers inside the vat.

tack

Collateral can be transferred in [dss] in several ways: simply via flux, but also via grab and frob. frob and flux are publically callable, which means that the rewards for a user may not match their collateral balance. This is not a problem in itself as it isn't possible to exit collateral without having the appropriate stake, so it isn't possible to game rewards through e.g. join($$$); flux(me, me2, $$$); flee($$$).

However, recipients of auction proceeds will need the appropriate stake if they wish to exit. The winner of a collateral auction claims their collateral via flip.deal. This increases their collateral balance, but not their stake. tack allows this stake to be acquired, from other users that have an excess of stake.

It isn't strictly necessary to alter the collateral auction contract, as tack can be called by users, but it would be convenient to add a tack after every flux:

vat.flux(ilk, a, b, x);
join.tack(a, b, x);

Then rewards will continue to accumulate throughout the auction and will be distributed appropriately to the winner and the CDP owner, with the winner able to reap their rewards following deal.

Terms

• gem: the underlying collateral token
• nav: Net Asset Valuation, total underlying gems held by adapter
• nps: nav per stake
• stake: gems per user
• total: total stake
• bonus: the reward token, e.g. COMP
• stock: last recorded balance of reward token
• share: accumulated bonus per gem
• crops: accumulated bonus per gem per user

cUSDC Strategy

Compound allows supplying and borrowing against the same asset. COMP is distributed according to the total amount borrowed and supplied. This allows for a low risk strategy: supply USDC and then borrow USDC against it. We will continually lose USDC to interest, but this is more than offset by COMP income.

Given an initial supply s0 (the amount of underlying USDC in the adapter), and a USDC Collateral Factor of 75% cf = 0.75, we can supply a maximum of

s = s0 / (1 - cf)

i.e. s = 4 * s0 for USDC, where the amount borrowed b = s * cf and the utlisation u = b / s = cf.

The real value of the underlying collateral, our Net Asset Valuation, is given by

nav = g + s - b

where g accounts for any underlying that remains in the contract.

wind

In order to approach this supply it is necessary to go through several rounds of mint / borrow, as we cannot exceed cf at any point. The maximum amount that can be borrowed in each round is given by

x <= cf * s - b

Which will achieve a new utilisation u' of

u' = cf / (1 + cf - u)

We can reduce the number of rounds necessary by providing a loan L, then

x1 <= cf * (s + L) - b

but we must also remain under our target collateral factor tf after paying back any loan

x2 <= (tf * s - b) / (1 - tf)

therefore

x <= min(x1, x2)

Wind performs this calculation for each round of borrowing, ensuring that we never exceed our target utilisation.

We can determine the minimum necessary loan to achieve a target utilisation in a single round given an initial (s, b) = (s0, 0),

L / s0 >= (u' / cf - 1 + u') / (1 - u')

e.g. for u' = 0.675 (90% of cf), we require a loan of 177% of the collateral amount.

L / s0 >= 1.77

unwind

Our utilisation may increase over time due to interest, and if we exceed u > cf we may be subject to compound liquidation. To lower the utlisation we must go through rounds of redeem / repay, with the maximum redeem amount given by

x <= L + s - b / cf

We must also redeem an extra amount e if we are to allow a user to exit, giving a minimum redeem amount of

x >= (b - s * u' + e * u') / (1 - u')

We have three different regimes depending on the value of u', if we are to have only one redeem / repay round. When u > cf, then u' <= cf and

L / s0 >= (u / cf - 1) / ((1 - u) * (1 - cf))
          + (e / s0) * cf / (1 - cf)

i.e. we must always provide a loan.

When tf < u < cf, then u' < u and

L / s0 >= (u / cf - 1) / (1 - u)
          + (e / s0) * u / (1 - u)

i.e. a loan is necessary for

e / s0 >= 1 / u - 1 / cf

and our maximum exit is given by

e / s0 <= 1 / u - 1 / cf + (L / s0) * (1 - u) / u

Finally when u < tf, u' = tf and

L / s0 >= (u / cf - 1 + u - u * tf / cf) / ((1 - u) * (1 - tf))
          + (e / s0) * tf / (1 - tf)

Then for a full exit of all of the underlying collateral, e / s0 = 1, from u = 0.675, cf = 0.75, we again find that we need a 177% loan,

L / s0 >= 1.77

Without a loan we are limited to

e / s0 <= 1 / tf - 1 / cf

or 14.8% of the underlying collateral for tf = 0.675. Adding further rounds will allow for larger exits and smaller loans.

Risks

• Liquidation
• Compound Governance
• Compound