Recursive lending is repeatedly supplying collateral to a lending protocol, borrowing against it, and supplying the borrowed value again—either directly or after exchanging it for more collateral. Each round expands the supplied balance and the debt. For a quant evaluating the strategy, the essential distinction is between gross deposits and the investor's own equity: repeating the loop creates leverage, not new capital.
In decentralised finance, this is often called looping. Aave's supply documentation describes the underlying building block: eligible supplied assets can earn interest and support borrowing. Recursive lending chains that building block into a larger position. It can be used to increase asset exposure or pursue lending incentives; neither purpose establishes a positive net return.
Follow the purchases and the debt
Consider a fictional protocol that permits the following loop. The investor initially owns 10 units of a volatile token, worth USD 100 per unit, and supplies them as collateral. Starting equity is USD 1,000. After every new deposit, the investor borrows stablecoins worth 50% of that new deposit, uses all proceeds to buy the same volatile token, and supplies the purchase.
Assume the stablecoin stays at USD 1, collateral stays at USD 100 per unit during construction, every purchase executes at that price, all supplies qualify as collateral, and liquidity and risk limits permit each step. Ignore fees and interest during the loop. The 50% rule is an assumed borrowing choice; it is not a quoted Aave parameter.
| Completed position | Collateral, USD | Stablecoin debt, USD | Equity, USD |
|---|---|---|---|
| Initial deposit | 1,000 | 0 | 1,000 |
| First purchase and redeposit | 1,500 | 500 | 1,000 |
| Second purchase and redeposit | 1,750 | 750 | 1,000 |
| Third purchase and redeposit | 1,875 | 875 | 1,000 |
| Mathematical limit | 2,000 | 1,000 | 1,000 |
The first USD 500 loan buys five more units. The next loan is USD 250, half of that new USD 500 deposit, buying another 2.5 units. It is not another USD 750 loan against the full USD 1,500 collateral: the existing debt must remain in the account's borrowing calculation.
For starting equity and loop fraction , with , collateral after completed borrow–buy–redeposit rounds is a geometric series:
Under these assumptions,
At , gross asset leverage approaches 2. The limit contains 20 collateral units supported by USD 1,000 equity and USD 1,000 debt. It is a limiting balance sheet, not a claim that infinitely many transactions can be executed. Finite loops stop short; fees, available liquidity and protocol limits can stop them earlier.
The owned lesson on geometric series derives the partial-sum identity and convergence argument. The full lesson requires membership; its public page provides a preview.
A borrowing limit and a liquidation threshold do different jobs
A protocol's loan-to-value limit governs borrowing capacity. Its liquidation threshold governs when collateral becomes insufficient for an existing debt position. Aave's reserve documentation distinguishes these parameters and also lists supply caps, borrow caps and whether borrowing is enabled. Settings differ by reserve and market and can change through governance. The geometric formula does not override them.
For a single collateral asset with liquidation threshold , a simplified health factor is
For several collateral assets, the numerator sums their individually threshold-adjusted values. Aave describes positions with health factor below 1 as eligible for liquidation: a liquidator repays debt in return for collateral plus a liquidation bonus. Crossing the boundary therefore has consequences before equity is exhausted.
Use the limiting balance sheet above and assume a fictional 80% liquidation threshold, independent of the 50% loop fraction. Initially,
Now freeze token quantities, debt and the threshold. If the collateral price becomes a fraction of its starting price while the stablecoin stays at USD 1,
Health factor reaches 1 at : USD 62.50 per collateral unit, a 37.5% fall. At that boundary, collateral is worth USD 1,250 and equity before liquidation costs is still USD 250. The investor has lost 75% of starting equity even though the collateral price has fallen by 37.5%. The calculation locates a boundary; it does not predict an execution price or a realised liquidation loss.
Original fictional ledger and fixed-balance stress. The 50% loop fraction and 80% liquidation threshold are assumptions, not live protocol settings. The dashed segment below health factor 1 extends the formula only; it does not model a position surviving liquidation.
The debt asset changes the stress. Suppose instead that both collateral and debt are identical token units, with quantities and . For positive common price , fixed quantities and a fixed threshold,
The common price cancels. Applying the earlier collateral-only price shock to this same-asset loop would be wrong. The investor still has token-price exposure on net holdings, while interest accrual, parameter changes and operational failures remain relevant. Related tokens, wrapped assets and liquid-staking derivatives are not automatically the identical asset: conversion ratios, market prices and oracle treatment can differ.
Larger supplied balances can have negative carry
A larger interest-earning balance is only one side of the ledger. As a separate simple annual carry illustration, hold the USD 2,000 collateral and USD 1,000 debt notionals fixed for one year, with a hypothetical 2% supply rate and 8% borrowing rate. Assume no compounding, price change, fees or incentives:
That is a 4% cost relative to starting equity. The supply rate earns USD 40, while borrowing costs USD 80. These are invented rates used to expose the financing arithmetic, not a yield forecast. Aave's v3 overview explains that rates respond to utilisation and that debt balances accrue interest. A fixed starting-rate calculation cannot establish realised annual performance. Incentives also need their own valuation and eligibility assumptions.
Finally, the ability to unwind is part of the position. Aave's supply discussion notes that withdrawals depend on unborrowed liquidity and the collateralisation of active debt. Selling collateral to repay debt can require several dependent operations and incur slippage and network costs. A stablecoin's fixed dollar price is a modelling assumption, so debt-token repricing must be included when that assumption fails. The protocol's oracle valuation and the price achievable in a sale can also differ. Aave's risk documentation identifies smart-contract, oracle, collateral and network risks; these can impair a position even when a simple price-and-interest spreadsheet looks viable.
Sources
- Aave: Supply Tokens, Introduction — supplied assets, collateral use and interest accrual.
- Aave v3: Reserve, Key Reserve Parameters; Dynamic Parameters and Governance — borrowing limits, liquidation thresholds, caps and changing market-specific settings.
- Aave: Health Factor & Liquidations, Health Factor; Managing Health Factor; Liquidation Process — threshold-adjusted collateral, both sides' valuations and liquidation eligibility.
- Aave v3 Overview, Supply; Borrow; Interest Rates — withdrawal constraints, accruing debt and utilisation-sensitive rates. This article uses v3 as a documented example, not as a statement about every protocol version.
- Aave: Risks, Smart Contract Risk; Oracle Risk; Collateral Risk; Network / Bridge Risk — failure channels beyond the toy balance sheet. Documentation checked 29 October 2026; the numerical scenario is original and hypothetical.