CHAPTER 04 / 8 · Evaluate the strategy
Account for the whole result.
Reconcile cash flows without counting fees twice.
Fees are revenue for providing a service. Profit also depends on what happened to your inventory, when you added or removed capital, and what execution cost. Keep these questions separate.
Jump to the interactive experiment ↓Three questions, three different answers
Did I earn fees? Did my total wealth grow? Did this beat my chosen alternative? A position can answer yes to the first two and no to the third. Separate fee income, absolute P&L and performance relative to a benchmark before annualizing anything.
Fix the reporting currency and cutoff. ETH fees and USDC fees cannot be added as token quantities. Converting them requires a stated price and timing convention; an estimate at current pool prices is not necessarily their realized sale value.
Impermanent loss compares with holding the starting tokens
In the standard fee-free illustration, start a full-range position worth 10,000 USDC, split equally in value between ETH and USDC. If ETH doubles, simply holding those starting tokens is worth 15,000; the AMM principal is worth about 14,142.14. The LP has gained 4,142.14 versus starting capital and trails holding by 857.86, or 5.72%. Both statements are true.
The name “impermanent” does not mean the difference is guaranteed to disappear. With fixed liquidity and no fees, returning to the entry price restores the original comparison; withdrawal, range changes and fees alter the accounting. Concentrated ranges use their own inventory equations, not the full-range percentage formula.
- VLP: fee-free principal value; Vhold: value of the original tokens at the same price.
- r: ending price / entry price. Multiply the result by 100 for percent.
AssumptionsThe second identity assumes full-range constant product, fixed liquidity and initially equal value weights. Concentrated ranges require their own amounts.
GO DEEPERImpermanent loss: relative to what?
Define the comparison before the trade
Let P be USDC per ETH. Holding the initial token quantities gives H(P) = x₀P + y₀. Let V(P) be LP principal excluding fees. Define the signed divergence D = V − H, or IL% = V/H − 1. We report a negative number for underperformance; some sources quote its positive magnitude as “loss”. Compare identical starting capital, valuation time and currency. All-ETH, all-cash and an execution schedule are different benchmarks, not alternative definitions of the same IL.
Why a standard fee-free curve falls below holding
For a full-range constant-product position initially worth C, let r = P/P₀. With equal initial token values, V = C√r and H = C(1+r)/2, so IL% = 2√r/(1+r) − 1. This is nonpositive because the LP value curve is concave and the holding line is its tangent at entry. At r = 2 and C = 10,000, principal is 14,142.14 versus holding at 15,000: a 4,142.14 absolute gain AND an 857.86 holding shortfall. Concentrated positions require their own piecewise inventory formula, not this full-range shortcut.
- VLP: fee-free principal value; Vhold: value of the original tokens at the same price.
- r: ending price / entry price. Multiply the result by 100 for percent.
AssumptionsThe second identity assumes full-range constant product, fixed liquidity and initially equal value weights. Concentrated ranges require their own amounts.
Judge the mandate without hiding the shortfall
An ETH accumulator may prefer receiving ETH on a decline to staying entirely in USDC. Record ETH acquired, average acquisition cost, remaining budget and drawdown, alongside the cash/holding comparison. A staged seller may accept limited upside to reduce exposure. A neutral desk may benchmark against a hedged strategy instead. Set these objectives before entry; changing the benchmark after a loss is not risk management. Wanting inventory can reduce a hedging requirement, but cannot make its market risk or capital opportunity cost vanish.
Your mandate changes the decision, not the historical difference
An investor deliberately selling ETH in stages may judge execution against a planned sale schedule, while a long-term ETH holder may compare with holding ETH. Someone accumulating ETH needs to track ETH acquired, cost and unfilled budget. Choose these comparisons before seeing the outcome.
In the full-range example, adding 1,000 of LP fees and subtracting 50 of costs produces 15,092.14: net P&L of 5,092.14 and 92.14 above holding. Fees can offset divergence, but need not. The next experiment uses a concentrated 2,400–3,600 position, so its starting weights and results differ from that full-range example.
TEST IT HERE · CHANGE ONE ASSUMPTION
P₀ = 3,000 · [a,b] = [2,400, 3,600] · C = 10,000 USDC
Fee income is an independent assumption, held at the same USDC value across the chart. It is not inferred from the price path. No interim flows, compounding or benchmark trading costs; all values use the same ending price. Cash and all-ETH alternatives change initial allocation. Only the entry-token comparison is labeled IL.
Reconcile actual contributions and withdrawals
For a position starting empty, contribute 10,000 USDC, then another 2,000. Withdraw 500, including 100 in fees. Finish with 11,700, including 50 of unclaimed fees. Gross P&L is 11,700 + 500 − 12,000 = 200. After 20 of separately paid gas, net P&L is 180.
The 150 of fees is already inside withdrawals and ending value. Adding it again would double count. Maintain token amounts, transaction links, timestamps and your valuation convention so another person can reconstruct the result.
- W: distributions; D: contributions; C: costs not already included. All in one valuation currency.
AssumptionsPosition starts empty. Include unclaimed fees in ending value and collected fees in distributions, then do not add them again.
TRY IT YOURSELF
Make the mechanics visible.
Adjust ending value in the reconciliation below. Find a case where fee income is positive but net P&L is negative. Fees remain included in the displayed cash flows; do not add them twice.
Synthetic accounting exercise. 100 settled fees are within the 500 distribution; 50 unclaimed fees are within ending value. No return forecast or live prices.
Annualization is a convention, not a forecast
With constant capital of 1,000 USDC, earning 10 USDC in fees over 10 days gives 10 / 1,000 × 365 / 10 = 36.5% simple fee APR. It is not compound APY, total return or a forecast. With changing capital, specify how capital-time exposure is measured and distinguish money-weighted from time-weighted performance.
AMM Markets separates live state from finalized history. A delayed ledger value is unknown until reconciled, not proof of zero fees or a failed operation. Hook contract balances also do not by themselves establish cumulative platform income.
CHECK YOUR UNDERSTANDING
What does this mean for you?
For your next review, can you identify the cutoff block, valuation source and every contribution or withdrawal?
CONNECT IT TO AMM MARKETS
From understanding to a real decision.
AMM Markets Portfolio separates live position reads from historical accounting. Compare settled and unclaimed fees, inspect history coverage and transaction links, and allow for finalized-ledger delay. Pool-derived USDC equivalents are valuation references, not guaranteed exit prices or tax statements.
Explore Portfolio in the LP App ↗Opens a live service. Exploring is separate from submitting a transaction.References and scope
Course edition: October 2026. Distinguish protocol principles from product instructions; actual market parameters come from the live interface and on-chain state.