Break-Even

Break-Even primitives answer “when am I made whole?” — find the price at which fees offset IL, or the holding period at which fee income compensates current IL drag.

Two primitives:

• FindBreakEvenPrice — both alpha values where accumulated fees exactly offset IL
• FindBreakEvenTime — linear projection of how long until current fees catch up to current IL

All primitives in the Agentic Primitives section follow the same contract: stateless construction, computation at .apply(), typed dataclass return.

Setup

from defipy.twin import MockProvider, StateTwinBuilder

provider = MockProvider()
builder = StateTwinBuilder()
lp_v2 = builder.build(provider.snapshot("eth_dai_v2"))

FindBreakEvenPrice

Purpose. Find both alphas (price ratios vs entry) where accumulated fee_income exactly offsets impermanent loss. Useful for setting alert thresholds.

Signature.

FindBreakEvenPrice().apply(
    lp, lp_init_amt, fee_income,
    lwr_tick=None, upr_tick=None,
) -> BreakEvenAlphas

V2/V3 supported (V3 via the range-scale factor). When fees are large enough that sqrt(f_scaled) >= 1, the upside break-even is None and upside_hedged=True (downside still exists for f > 0). Zero fee_income returns the degenerate case (both alphas = 1.0). Prices are in token1/token0.

from defipy import FindBreakEvenPrice

result = FindBreakEvenPrice().apply(
    lp_v2,
    lp_init_amt = 10000.0,
    fee_income = 50.0,    # 50 ETH of accumulated fees
)

print(f"break_even_alpha_down:   {result.break_even_alpha_down:.6f}")
print(f"break_even_alpha_up:     {result.break_even_alpha_up:.6f}")
print(f"break_even_price_down:   {result.break_even_price_down:.4f}")
print(f"break_even_price_up:     {result.break_even_price_up:.4f}")
print(f"fee_to_entry_ratio:      {result.fee_to_entry_ratio:.6f}")
print(f"upside_hedged:           {result.upside_hedged}")

break_even_alpha_down: 0.667907 break_even_alpha_up: 1.658962 break_even_price_down: 66.7907 break_even_price_up: 165.8962 fee_to_entry_ratio: 0.050000 upside_hedged: False

FindBreakEvenTime

Purpose. Estimate days (and blocks) until fee income compensates current IL drag at the current fee accrual rate. Simple linear projection; no rate uncertainty modeling.

Signature.

FindBreakEvenTime(blocks_per_day=7200).apply(
    lp, lp_init_amt, entry_x_amt, entry_y_amt,
    holding_period_days,
    lwr_tick=None, upr_tick=None,
) -> BreakEvenTime

V2/V3 only (delegates to AnalyzePosition). diagnosis ∈ {"already_broken_even", "no_il_drag", "no_fee_income", "projected"}. The "no_fee_income" branch sets days_to_break_even and blocks_to_break_even to None.

from defipy import FindBreakEvenTime

# ETH up 25% from entry, 30 days held — same scenario as the position-analysis pilot.
result = FindBreakEvenTime().apply(
    lp_v2,
    lp_init_amt = 10000.0,
    entry_x_amt = 1000.0,
    entry_y_amt = 80000.0,
    holding_period_days = 30.0,
)

print(f"current_il_drag:         {result.current_il_drag:.4f}")
print(f"fee_income_to_date:      {result.fee_income_to_date:.4f}")
print(f"fee_rate_per_day:        {result.fee_rate_per_day:.4f}")
print(f"days_to_break_even:      {result.days_to_break_even}")
print(f"blocks_to_break_even:    {result.blocks_to_break_even}")
print(f"already_broken_even:     {result.already_broken_even}")
print(f"diagnosis:               {result.diagnosis}")

current_il_drag: 11.1456 fee_income_to_date: 211.1456 fee_rate_per_day: 7.0382 days_to_break_even: 0.0 blocks_to_break_even: 0 already_broken_even: True diagnosis: already_broken_even

Protocol coverage

Protocol	Supported	Notes
Uniswap V2	✅	Both primitives, closed-form
Uniswap V3	✅	Both primitives, with lwr_tick/upr_tick for the range-scale factor
Balancer	❌	Weighted-pool break-even math not yet ported
Stableswap	❌	Flat-curve regime makes break-even semantics ill-defined; not in v1

MCP tool exposure

Neither primitive is in the curated 10. Break-even questions are downstream of position-analysis — agents typically derive break-even thresholds LLM-side after running AnalyzePosition. The category exists for the explicit request “give me the break-even price” without requiring the LLM to derive it.