impermanent-loss Checked

| Scenario | Constant-Product IL | CLMM IL (±20%) |

|---------------|--------------------:|----------------:|

| SOL → $180 | -0.62% | ~-3.1% |

| SOL → $200 | -1.03% | 100% SOL (exit) |

| SOL → $120 | -1.80% | ~-9.0% |

| SOL → $100 | -3.42% | 100% USDC (exit)|

IL vs Fees: Breakeven Analysis

The core question for any LP is: **Do fees earned exceed IL incurred?**

Net Position = LP_value + accrued_fees - hold_value

Profitable when accrued_fees > IL.

### Breakeven Fee Rate

For constant-product pools, the expected IL per period is approximately:

expected_IL ≈ σ² / 8

Where σ is the standard deviation of log returns for that period. This means:

| Daily Volatility (σ) | Expected Daily IL | Min Daily Fee Rate to Break Even |

|----------------------|------------------:|--------------------------------:|

| 1% | 0.001% | 0.001% |

| 3% | 0.011% | 0.011% |

| 5% | 0.031% | 0.031% |

| 10% | 0.125% | 0.125% |

| 20% | 0.500% | 0.500% |

Daily fee income for an LP:

daily_fee_income = (deposit / TVL) * daily_volume * fee_rate

For a full breakeven framework, see references/breakeven_analysis.md.

Modeling IL Over Time

### Monte Carlo Simulation

Simulate many random price paths using geometric Brownian motion (GBM):

import numpy as np

def simulate_price_path(
    initial_price: float,
    daily_vol: float,
    days: int,
    drift: float = 0.0,
) -> np.ndarray:
    """Simulate a price path using geometric Brownian motion."""
    dt = 1.0  # daily steps
    log_returns = np.random.normal(
        (drift - 0.5 * daily_vol**2) * dt,
        daily_vol * np.sqrt(dt),
        days,
    )
    prices = initial_price * np.exp(np.cumsum(log_returns))
    return np.insert(prices, 0, initial_price)

For each path, compute the IL at each timestep and the cumulative fees earned. After N simulations, analyze the distribution of outcomes.

See scripts/il_scenario_modeler.py for a complete Monte Carlo simulation.

### Historical Analysis

Use actual OHLCV price data to compute what IL would have been for a historical period. This gives a more realistic (but backward-looking) estimate.

IL Mitigation Strategies

### 1. Stablecoin Pairs

Pairs like USDC/USDT have near-zero IL because the price ratio barely moves. Fee income is almost pure profit.

### 2. Correlated Pairs

Pairs like SOL/mSOL or ETH/stETH move together, so the price ratio stays close to 1.0. IL is minimal.

### 3. Wider CLMM Ranges

A wider range reduces concentration factor, reducing IL at the cost of less fee income per unit of capital.

### 4. Active Range Management

Monitor price and rebalance your CLMM range when price approaches boundaries. This reduces the risk of price exiting your range entirely.

### 5. Fee Tier Selection

Higher fee tiers (e.g., 1% vs 0.3%) compensate for higher IL in volatile pairs. Match fee tier to expected volatility.

When IL Is Acceptable

• **High volume pools**: Fee income significantly exceeds expected IL.
• **Stable or correlated pairs**: IL is structurally minimal.
• **Token accumulation strategy**: You want to accumulate the cheaper token anyway.
• **Short time horizons with active management**: Fees compound, and you rebalance before large moves.

When to Avoid LPing

• **Low volume, high volatility**: IL dominates, fees are insufficient.
• **Trending markets**: Strong directional moves create large, sustained IL.
• **Illiquid new tokens**: Price can move 10x+ in hours, causing catastrophic IL.
• **Wide-spread pools**: Low volume means fees don't compensate for any IL at all.

Related Skills

• **lp-math**: AMM mechanics and reserve calculations that underpin IL formulas.
• **yield-analysis**: Compare LP yields net of IL against other DeFi opportunities.
• **liquidity-analysis**: Assess pool depth and volume to estimate fee income.
• **volatility-modeling**: Forecast volatility inputs for IL modeling.

Files

### References

• references/il_formulas.md — Full IL derivations for constant-product, CLMM, and multi-asset pools
• references/breakeven_analysis.md — Fee vs IL breakeven framework with practical tools

### Scripts

• scripts/il_calculator.py — Calculate IL for any price change across pool types, with tables and comparisons
• scripts/il_scenario_modeler.py — Monte Carlo simulation of LP positions over time with fee and IL modeling