Return on equity

Return on Equity (ROE) combines supply income and borrowing cost into an annualized estimate relative to a position's equity. It is useful for Borrow and Multiply positions, where a supply or borrow rate alone shows only one side.

Euler defines equity as supplied market value minus borrowed market value, also called Net Asset Value (NAV). ROE estimates rate exposure, not realized profit. Rates, rewards, prices, eligibility, execution costs, and liquidation risk can change.

Base formula

Let S be supplied value, B borrowed value, r_s supply APY, and r_b borrow APY:

equity = S − B
ROE = ((S × r_s) − (B × r_b)) / (S − B)

Supply and debt must use the same quote currency and price timestamp. ROE is undefined or not economically meaningful when equity is zero or negative.

A calculation divided by supplied value is net APY, not ROE:

net APY = ((S × r_s) − (B × r_b)) / S

Multiplier form

For multiplier M = S / (S − B):

ROE = (M × r_s) − ((M − 1) × r_b)

For a single collateral and debt pair where current LTV = B / S, M = 1 / (1 − LTV). The position's current LTV is not its configured borrow limit.

Example

For $1,000 supplied at 7.5% APY and $800 borrowed at 4.5% APY:

equity = $1,000 − $800 = $200
multiplier = $1,000 / $200 = 5
ROE = (($1,000 × 7.5%) − ($800 × 4.5%)) / $200
    = 19.5%

The same net rate amount is 3.9% when divided by the $1,000 supplied value. Leverage magnifies both positive and negative rate differences because equity is smaller than total supplied value.

Rewards and intrinsic yield

Euler's SDK can include several contributions before dividing by equity:

base lending   =  supplied value × base supply APY
base borrowing = −borrowed value × base borrow APY
supply rewards =  supplied value × eligible LEND APR
borrow rewards =  borrowed value × eligible BORROW or BORROW_COLLATERAL APR
loop rewards   =  equity × eligible LOOPING APR
intrinsic      =  supplied intrinsic yield − borrowed intrinsic yield

ROE = included contributions / equity

Campaign APR is an estimate, may depend on the connected account and campaign rules, and does not compound through the vault. See Rewards.

Comparing ROE

Confirm that figures use NAV as equity, the same price timestamp and annualization conventions, and comparable rate, reward, and intrinsic-yield components. Check whether reward eligibility is account-specific and whether gas, swaps, slippage, taxes, external fees, and liquidation losses are excluded.

Max ROE applies rates to a modeled maximum multiplier. It is not a forecast or a promise that the position can be opened or maintained at that size.