LP ownership and impermanent loss

EN source master · P11-L04 · 30 minutes estimated · needs_review

Offline formative study. No wallet connection, real funds, private keys, signatures, live trade or personal portfolio inputs. Visuals are specifications; this is neither runtime content nor certification.

Owning an LP claim can establish a proportional accounting interest without establishing the safety or redeemability of its contents.

Keep the model narrow

The v2 reference derives a full-range constant-product LP comparison while neglecting fees [RET]. Our original fixture holds x10 X,y1000 Y with initial price100 Y/X. Assume no deposit/withdrawal, no fees, constant k and arbitrage aligning the pool to a later supplied external price. Concentrated positions need different accounting and are excluded.

Reconstruct reserves

At later price p, y/x=p and xy=k. Therefore x=sqrt(k/p), y=sqrt(kp). A stipulated 10% pro-rata LP interest gives10% of each modeled reserve. Real claim permissions, supply changes and redemption state would require independent verification.

Compare to the same holding baseline

At price ratio r=4, no-fee LP value divided by original asset holding value is2sqrt(r)/(1+r)=0.8. Relative difference is−20%. It is a comparison to holding the same initial quantities, not automatically a20% loss of initial capital. Both values can rise or fall together in another unit.

Do not let terminology erase risk

'Impermanent' does not promise that prices return or that a loss disappears before withdrawal. Fees can alter the net comparison; asset depeg, transfer restrictions or contract failure can dominate it. LP-token ownership, locked liquidity, audit or mathematical invariant is not an asset-safety guarantee. Our fixture has no such evidence.

• LP interest: stipulated share of modeled pooled reserves.
• Relative LP difference: value versus holding original quantities.
• Price ratio r: later price divided by initial price.
• Holding baseline: same original asset quantities, not starting marked value.

ILLUSTRATIVE full-range no-fee pool x10 X,y1000 Y, k10000. Initial p100 Y/X; later supplied p400 Y/X. LP share 10%, fixed. Compare modeled LP redemption and original share holdings1 X+100 Y at later price.

LP structure comparison: initial share 1 X/100 Y; later modeled share 0.5 X/200 Y; values400 Y versus holding500 Y. Label−20% relative gap and+100% LP initial-mark change separately.

Conditional no-fee reserve/share calculations and relative value comparison.

Actual LP ownership, redeemability, future price return, fee income or asset safety.

• OBSERVED: FIX-P11-L04 stipulates share 10% and later price400.
• INFERRED: relative LP-versus-holding gap−20% under full-range no-fee assumptions.
• UNKNOWN: actual contract redemption and asset behavior.
• INSUFFICIENT EVIDENCE: LP ownership guarantees safe underlying assets.

• Calling−20% an absolute capital loss here.
• Applying full-range formula to concentrated positions.
• Treating impermanent as guaranteed recovery.

Compute later reserves, LP share quantities, LP value, holding value and relative gap. Compare LP value with its initial marked value and state three excluded risks.

Deliver calculations or annotations, claim/source table and limitations. Suggested allocation: study 12 minutes, exercise 8, correction/quiz 10; estimate subject to calibration.

• State full-range/no-fee assumptions.
• Use identical holding baseline.
• Separate relative from absolute change.
• Keep ownership distinct from safety.

The no-fee LP comparison measures relative performance against identical original holdings; it is not a safety or recovery guarantee.

• Calculate a full-range no-fee LP comparison.
• Separate ownership share, relative loss and asset safety.

P11-L05 after correction review.

NONE in the authoritative catalog. The supplied offline fixture/package is sufficient; no paid feature or unverified Production capability is required. Lab/certification metadata denotes downstream associations, not access gates or live awards.

• [RET] Uniswap v2 — Understanding returns — No-fee constant product and relative LP-versus-holding formula, full-range v2 assumptions. Checked 2026-10-01; locator turn9view5.