ETHRISE Rebalancing Mechanism

The rebalancing mechanism of ETHRISE - 2x Long ETH

ETHRISE rebalancing mechanism is designed to have small volatility decay as small as possible. This document explain the math behind the rebalancing process of ETHRISE.

Background

We need to do the rebalancing in order to maintain the target leverage ratio. The leverage ratio is defined below:

Rebalancing Problem

We can simplify the rebalancing problem as follows:

Where:

Leveraging Up

We can easily solve the equation (3) by using equation (1) and (2) as follows:

Then we can use the equation (4) with (3) as follows:

Example of Leveraging Up

Suppose we want to rebalance the ETHRISE.

We have the following initial states:

Each ETHRISE is collateralized by 0.01 ETH.

Then we can calculate the collateral value per ETHRISE token ($C$) as follows:

Each ETHRISE have collateral value 40 USDC.

Each ETHRISE have 20 USDC as debt.

The net-asset value of ETHRISE is 20 USDC.

The current leverage ratio is:

To recap:

  • Collateral value per ETHRISE: 40 USDC

  • Debt per ETHRISE: 20 USDC

  • NAV: 20 USDC

  • Leverage ratio of ETHRISE: 2

Suppose the ETH price is going up to 4300 USDC. Now the leverage ratio is going down:

As you can see, when the price of ETH is going up from 4000 USDC to 4300 USDC:

  • The net asset value is going up from 20 USDC to 23 USDC

  • The leverage ratio is going down from 2 to 1.869565217.

We will borrow 23000 USDC from the vault, then swap it to ETH. Assuming there is no slippage when swapping, we will get 5.348837209 ETH as the collateral.

Now we have the new states:

Let's calculate the net-asset value once again after rebalancing:

Now the new leverage ratio after rebalancing:

As you can see, we have successfully leveraging up the leverage ratio from 1.869565217 to 1.969565217 without changing the net-asset value of the ETHRISE.

Leveraging Down

We can use equations (4) and (5) to solve equations (6).

Example of Leveraging Down

Suppose we want to rebalance the ETHRISE.

We have the following initial states:

Each ETHRISE is collateralized by 0.01 ETH.

Then we can calculate the collateral value per ETHRISE token ($C$) as follows:

Each ETHRISE has a collateral value of 40 USDC.

Each ETHRISE has 20 USDC as debt.

The net-asset value of ETHRISE is 20 USDC.

The current leverage ratio is:

To recap:

  • Collateral value per ETHRISE: 40 USDC

  • Debt per ETHRISE: 20 USDC

  • NAV: 20 USDC

  • Leverage ratio of ETHRISE: 2

Suppose the ETH price is going down to 3800 USDC. Now the leverage ratio is going up:

As you can see, when the price of ETH is going down from 4000 USDC to 3800 USDC:

  • The net asset value is going down from 20 USDC to 18 USDC

  • The leverage ratio is going up from 2 to 2.111111111.

We will repay 18000 USDC debt to the vault. We do this by selling 4.736842105 ETH, assuming there is no slippage.

Now we have the new states:

Let's calculate the net-asset value once again after rebalancing:

Now the new leverage ratio after rebalancing:

As you can see, we have successfully leveraging down the leverage ratio from 2.111111111 to 2.011111111 without changing the net-asset value of the ETHRISE.

Rebalancing Rule

Maximum Borrow Value and Repay Value

Future Improvements

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