DeFi Rate Arbitrage and Looping

DeFi lending protocols set supply and borrow rates for each asset independently, driven by utilization — how much of the deposited pool is currently borrowed. It is common for a protocol to pay, say, 3% to suppliers of a liquid-staking token while charging only 2% to borrow the stablecoin used to acquire more of it. Whenever a supply rate on one asset exceeds the borrow rate on a correlated asset used to fund it, a trader can capture that spread — and can do it more than once by looping: deposit collateral, borrow against it, use the borrowed funds to buy more of the collateral asset, deposit that too, and repeat.

How the loop compounds

Protocols cap this with a maximum loan-to-value ratio, which limits how many loops are actually possible: each pass through the loop only unlocks a fraction of the previous deposit as new borrowing capacity, so the position converges to a maximum leverage multiple rather than growing without bound.

Worked example

Suppose a liquid-staking token yields 3.2% and can be posted as collateral to borrow a stablecoin at 1.8%, with a maximum loan-to-value of 75%. Starting with $10,000 of the staking token:

1. Loop 1: deposit $10,000, borrow 10{,}000 \times 0.75 = \7{,}500$, buy more staking token with it.
2. Loop 2: deposit that $7,500, borrow 7{,}500 \times 0.75 = \5{,}625$.
3. Loop 3: deposit $5,625, borrow 5{,}625 \times 0.75 = \4{,}219$.

Continuing this geometric series to its limit, total collateral held converges to 10{,}000 / (1 - 0.75) = \40{,}000, funded by \30,000 of borrowing — a 4x leverage multiple on the original $10,000. Net yield: 40{,}000 \times 3.2\% - 30{,}000 \times 1.8\% = 1{,}280 - 540 = \740$per year, roughly 7.4$10,000, more than double the raw 3.2% spot yield.