Sum the deposits and debt
For initial capital E, loop rate l, and n borrowing loops, collateral C = E × (1 + l + l² + … + lⁿ). Debt D = C − E, and gross leverage is C ÷ E. With zero loops, collateral equals initial capital and debt is zero. Use a whole-number loop count and a rate from zero up to, but not including, 100% for the usual convergent model.
Trace a three-loop example
Start hypothetically with $1,000 and a 50% loop rate. The three new deposits are $500, $250, and $125. Total collateral is $1,875, debt is $875, and gross leverage is 1.875 times initial capital. A fourth loop adds $62.50 to both collateral and debt. The initial equity remains $1,000 in this unchanged-price setup; larger collateral does not represent newly created net wealth.
Recognize the omitted constraints
The formula assumes every borrowed amount can be redeposited without a swap loss, fee, delay, or borrowing cap. Interest rates and liquidation thresholds are not allowed to change during the scenario. Actual collateral and debt may respond differently to price shocks, and higher gross exposure magnifies those effects. The infinite-series limit of 1 ÷ (1 − l) is a mathematical reference, not an attainable execution promise or an appropriate leverage target.