Eliminating Impermanent Loss Through Leveraged Liquidity

Sources:

YieldBasis Leveraged Liquidity Paper by Michael Egorov
YieldBasis Intro Video

TL;DR

YieldBasis uses 2x leverage on Curve AMM liquidity positions to eliminate impermanent loss while still earning trading fees. By leveraging LP tokens, the position's value becomes proportional to the underlying asset's price (instead of its square root), effectively removing IL. Simulations show ~20% APR over 6 years for BTC/USD, with price exposure matching BTC directly.

The Problem: Impermanent Loss

What Is IL?

In standard AMMs (like Uniswap V2 with the xy = k invariant), liquidity providers suffer from impermanent loss: the value of their LP position often underperforms simply holding the underlying assets.

Mathematical root cause: LP token value is proportional to √p, where p is the asset price.

Why this matters: √p < (1/2 + p/2) for all p ≠ 1

This means if BTC starts at $50k and goes to $100k, your LP position gains less value than if you'd just held BTC.

Visual Intuition

Imagine BTC/USD pool:

You deposit 1 BTC ($50k) + $50k USD = $100k total
BTC doubles to $100k
Due to the bonding curve, arbitrageurs rebalance your position
You now have ~0.707 BTC ($70.7k) + $70.7k USD = $141.4k total
But if you'd just held: 1 BTC ($100k) + $50k USD = $150k total
Impermanent loss: $8.6k

The loss comes from the square root relationship in the bonding curve.

The Solution: Compounding Leverage

The Core Insight

If LP value is proportional to √p, and you take 2x leverage on it, you get (√p)² = p

This means the leveraged position tracks the asset price 1:1, just like holding the asset directly!

The Math (Simplified)

Compounding Leverage (L) is defined by maintaining debt at a fixed ratio to collateral:

d = Vc × (1 - 1/L)

Where:

d = debt (borrowed stablecoins)
Vc = value of collateral (LP tokens)
L = leverage multiplier

For L = 2:

d = Vc × (1 - 1/2) = Vc/2

Debt is always 50% of collateral value.

Why This Works

The paper proves that with this debt constraint, when collateral value changes, the leveraged position value changes according to:

δV*/V* = L × δVc/Vc

Integrating this differential equation:

V* ∝ Vc^L

Since Vc ∝ √p (the LP token value), we get:

V* ∝ (√p)^L

For L = 2:

V* ∝ (√p)² = p ✓

The position now has linear exposure to the asset price - impermanent loss is eliminated!

The Intuition (For Humans)

Think of it this way:

LP tokens have √p exposure - they move with the square root of asset price due to constant product bonding curves
2x leverage doubles your exposure - gains and losses are amplified 2x
Squaring cancels the square root - (√p)² = p

By leveraging something that moves at √p by 2x, you create something that moves at p.

It's like using leverage to "undo" the mathematical dampening effect of the AMM bonding curve.

You still earn trading fees from the AMM, but now your position moves with the asset price as if you were just holding it directly.

The Rebalancing Challenge

The Problem

Maintaining constant leverage (d = Vc/2) requires continuous rebalancing. Every time the price moves, you need to adjust your position.

This costs money. The paper calls these "releverage losses" (rloss).

The Formula

APR = 2 × rpool - (rborrow + rloss)

Where:

rpool = AMM pool return rate (fees earned)
rborrow = interest rate on borrowed funds
rloss = losses from rebalancing the leverage

Key question: Is (2 × rpool) > (rborrow + rloss)?

Why xy = k Fails

With Uniswap V2's xy = k invariant:

rpool ≈ 3% APR (from simulations)
rloss ≈ 2 × rpool (also ~6% APR)
Result: APR ≈ 0 or negative

The releverage losses eat up all the gains.

Why Curve Solves This

Concentrated Liquidity + Rebalancing Budget

Curve Cryptoswap has two key advantages:

Automatically managed concentrated liquidity
- Liquidity is focused near the current price
- Automatically moves as price changes
- Much more capital efficient than xy = k
Built-in rebalancing budget
- 50% of AMM fees go to a "rebalancing budget"
- This budget pays for moving concentrated liquidity as prices change
- Reduces effective slippage and improves capital efficiency

The Numbers

From simulations (2023-2024 data):

Uniswap V2: ~3% APR
Curve Cryptoswap (current): ~5.5% APR
Curve + YieldBasis leverage: ~9% APR (2 years), ~20% APR (6 years)

The concentrated liquidity earns significantly more fees relative to rebalancing costs.

The YieldBasis Enhancement

YieldBasis adds another innovation: using borrow rate to subsidize the rebalancing budget.

How It Works

When you leverage the LP position:

You borrow stablecoins (e.g., crvUSD) against the LP collateral
The borrowing has an interest rate (e.g., 5-10%)
Part of this interest rate is streamed into the Curve pool's rebalancing budget
This allows even more frequent/efficient rebalancing
Which increases overall returns

From simulations: With a 5% borrow rate feeding the rebalancing budget, APR jumped from 5.5% to 13% in the same time period.

Why L = 2 Is The Sweet Spot

The paper specifically uses L = 2 (2x leverage). Why?

Mathematical Elegance

At L = 2:

Debt = 50% of collateral value
USD portion of LP ≈ 50% of LP value (on average)

This means the LP position contains roughly enough USD to pay off the debt.

This is incredibly convenient for:

Unwinding positions (you can close without external funds)
Risk management (lower liquidation risk)
User experience (simpler mental model)

Risk Profile

Higher leverage (L > 2) would:

Amplify returns further
But also amplify volatility
Increase liquidation risk
Require more careful risk management

L = 2 hits the sweet spot of eliminating IL while maintaining reasonable risk.

The Complete Picture

What You're Actually Doing

When you deposit into YieldBasis:

Deposit crypto (e.g., BTC) → receives equivalent value LP tokens from Curve pool
Borrow stablecoins against the LP tokens (debt = 50% of LP value)
Use borrowed funds to buy more BTC and create more LP tokens
Maintain 2x leverage via automatic rebalancing through a special AMM

What You're Earning

Trading fees from the Curve pool (2x due to leverage)
Price exposure matching the underlying asset (no IL)
Minus borrowing costs (interest on the loan)
Minus rebalancing costs (from maintaining constant leverage)

Net result: Positive APR if Curve fees > (borrow rate + rebalancing losses)

The Special Rebalancing AMM

YieldBasis uses a custom AMM (not manual rebalancing) to maintain constant leverage. This AMM:

Uses an oracle for asset prices
Holds LP tokens as collateral and debt as "reserves"
Automatically adjusts debt/collateral ratio as price moves
Much more efficient than manual threshold-based rebalancing

From simulations: Rebalancing via AMM has ~0.06% loss rate vs ~0.08% for manual rebalancing with 10% threshold.

Simulations & Results

BTC/USD Performance

6 year backtest (2019-2024):

Average APR: ~20%
Peak APR (2021): ~60%
Trough APR (2023-2024 bear): ~9%

The position value grows in BTC terms, meaning you earn yield while maintaining BTC price exposure.

Key Observations

Flat fee dependency - Releverage AMM fee has very flat performance curve (optimal around 0.7%)
Volatility matters - Higher volatility increases both fees and rebalancing costs
Parameter sensitivity - Setting concentration parameter A too high can cause temporary losses during extreme volatility, but average returns remain stable

Comparison

| Strategy | APR | IL Exposure | |----------|-----|-------------| | Hold BTC | 0% | None | | Uniswap V2 LP | ~3% | High | | Curve LP (current) | ~5.5% | Medium | | Curve + YieldBasis | ~9-20% | None |

The Fundamental Innovation

Why This Is Brilliant

Most attempts to solve IL focus on:

Better price oracles
Loss protection mechanisms
Single-sided liquidity

YieldBasis does something different: use leverage to mathematically transform the payoff function.

It doesn't fight IL - it uses leverage algebra to make IL disappear from the math entirely.

The Trade-offs

Advantages:

Eliminates IL while earning fees
Asset price exposure maintained
Automated and composable
Works with any volatile asset pair

Risks:

Leverage introduces liquidation risk (though L=2 is conservative)
Dependent on borrow rates staying reasonable
Requires efficient rebalancing (hence Curve-specific)
More complex than standard LP

Questions For Further Research

How robust is this to extreme volatility? (2021 simulation shows temporary losses but recovery)
What happens if borrow rates spike? (APR formula shows it could go negative)
Can this work on other AMMs? (Paper suggests no for xy=k, but what about Uniswap V3?)
Liquidation mechanics? (Not fully detailed in paper)
How does this compare to perp funding rates for hedging? (Alternative IL hedge strategy)

Conclusion

YieldBasis represents a genuine innovation in DeFi: using leverage not for speculation, but as a mathematical tool to transform payoff functions.

The core insight is elegant: LP tokens move at √p, so 2x leverage creates p exposure. The execution requires sophisticated engineering (Curve Cryptoswap, custom rebalancing AMM, optimal parameter tuning), but the fundamental idea is beautifully simple.

For liquidity providers who want to earn fees without suffering IL, this could be transformative - if the simulated results hold up in production.

Status: Audits in progress as of paper date (June 2025). Real-world performance TBD.