Euler Leveraged Strategy

Table of Contents

• Euler Leveraged Strategy
  • Table of Contents
  • How to caluculate Euler health score
    • Peusdocode
  • Calculate amount to mint or burn to maintain a target health score.
  • Minting
  • Burning
    • References

How to caluculate Euler health score

To avoid to be liquidated, keep

$HealthScore$ greater than 1.0 .

Generally

$HealthScore$ is denoted as

$$HealthScore=\frac{RiskAdjustedCollateral}{RiskAdjustedLilability}$$

Here assume a user deposit a single asset and leverage its position.

Let

$a^c$ denote the balance of collateral and

$s^c$ denote the self-collateralized balance of collateral.
Let

$f^c$ denote the collateral factor of a asset,

$f^b$ denote its borrow factor and

$f^s$ denote the collateral factor of a self-collateralized asset (called self-collateralized factor).

Risk-adjusted collateral is calculated as

$$\begin{array}{}\text{(1)}& v^c=f^c[a^c-\frac{s^c}{f^s}]+s^c\end{array}$$
where

$f^c\leqq f^s$.

A pdf is found on Euler fi Discord.
Risk-adjusted collateral seems to be calculated differently. I think the formula in the pdf is wrong. link

Risk-adjusted lilability is calculated as

$$\begin{array}{}\text{(2)}& v^b=\frac{a^b-s^b}{f^b}+s^b\end{array}$$

where self-collateralized part of any asset have always 1.0 borrow factor.

$s^b$ is always equal to

$s^c$ ??

In Euler self-collateralized part of any asset has always 0.95 collateral factor and 1.0 borrow factor.

In case of our leveraged strategy

$a^b$ is always equal to

$s^b$.

$a^c$ is eToken.balanceOfUnderlying(strat).

$s^c$ is dToken.balanceOf(strat).

for example,

deposits 1000 USDC and mints 9000 USDC. normal CF of USDC is 0.9

now collateral 10000 USDC and liability 9000 USDC.

so, risk adjusted collateral = (10000 - 9000/0.95) * 0.9 + 9000 * 0.95 = 9023
risk adjusted liability  = 9000*1

Peusdocode

  function getCurrentHealthScore() public view returns (uint256) {
        IMarkets.AssetConfig memory config = EULER_MARKETS.underlyingToAssetConfig(token);
        uint256 cf = config.collateralFactor;
        uint256 balanceInUnderlying = IEToken(config.eTokenAddress).balanceOfUnderlying(address(this));
        uint256 selfAmount = dToken.balanceOf(address(this));

        require(selfAmount != 0, "strat/no-borrow");

        // selfAmountAdjusted = selfAmount * CONFIG_FACTOR_SCALE) / SELF_COLLATERAL_FACTOR;
        uint256 riskAdjustedCollateral = (cf *
            (balanceInUnderlying - (selfAmount * CONFIG_FACTOR_SCALE) / SELF_COLLATERAL_FACTOR)) /
            CONFIG_FACTOR_SCALE +
            selfAmount;
        uint256 riskAdjustedLilability = selfAmount;
        return (riskAdjustedCollateral * EXP_SCALE) / riskAdjustedLilability;
}

Calculate amount to mint or burn to maintain a target health score.

Minting

Let

$h_{target}(>1)$ denote the target health score we want to maintain.

Let

$x$ denote its newly added collateral and

$x^s$ denote its newly added collateral with recursive borrowing (eToken.mint()).

Strategy deposits its underlyings with eToken.deposit(amount x) and eToken.mint(amount x^s).

$$\begin{array}{}\text{(4)}& h_{target}=\frac{f^c[a^c+x+x^s-\frac{s^c+x^s}{f^s}]+s^c+x^s}{s^c+x^s}\end{array}$$

Resolve the equation for

$x^s$.

$$\begin{array}{}\text{(5)}& x^s=\frac{f^c(a^c+x)-(h_{target}+f^c/f^s-1)s^c}{h_{target}+f^c(1/f^s-1)-1}\end{array}$$

Burning

Strategy withdraws its underlyings with eToken.withdraw(amount x) and eToken.burn(amount x^s).

References

How to calculate Euler’s health score