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Understanding Returns

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Liquidity providers earn fees from every trade in their pool, but face a tradeoff: sustained, directional price movement in the underlying assets can reduce the value of a position relative to simply holding. This section explains the mechanics.

Risks

For an in-depth analysis of LP economics, see CenturionDEX: A Good Deal for Liquidity Providers? (legacy URL slug).

Worked example

A liquidity provider deposits 10,000 DAI and 100 WCTN into a pool (total value: $20,000), receiving liquidity tokens representing 10% of a pool containing 100,000 DAI and 1,000 CTN. The implied price is 1 CTN = 100 DAI.

Price moves from $100 to $150. Arbitrageurs rebalance the pool until the reserve ratio reflects 150:1. The pool now holds approximately 122,400 DAI and 817 CTN (verify: 122,400 × 817 ≈ 100,000,000 and 122,400 / 817 ≈ 150). The LP's 10% share is worth 12,240 DAI + 81.7 CTN = $24,500. Had they simply held, they'd have $24,600 (10,000 DAI + 100 CTN × $150). The ~$100 gap is impermanent loss.

Fee income offsets the loss. 0.3% of all trade volume is distributed pro-rata to LPs and auto-compounded into reserves. Whether fee income exceeds impermanent loss depends on the volume-to-price-movement ratio — more chop and reversion is better for LPs.

Why does impermanent loss occur?

Neglecting fees, the constant product formula gives:

  • ctn_liquidity_pool * token_liquidity_pool = constant_product

At any given price:

  • ctn_price = token_liquidity_pool / ctn_liquidity_pool
  • ctn_liquidity_pool = sqrt(constant_product / ctn_price)
  • token_liquidity_pool = sqrt(constant_product * ctn_price)

For an LP who deposits 1 CTN and 100 DAI (1% of a pool with 100 CTN and 10,000 DAI) at 1 CTN = 100 DAI:

If the price moves to 1 CTN = 120 DAI, the pool rebalances to ~91.29 CTN and ~10,954.45 DAI. The LP's 1% share (0.9129 CTN + 109.54 DAI) is worth 219.09 DAI. Holding would have been worth 220 DAI — a 0.91 DAI impermanent loss.

If the price returns to 100 DAI, the loss disappears — hence "impermanent." The loss formula in terms of the price ratio r (current price / entry price) is:

  • impermanent_loss = 2 * sqrt(r) / (1 + r) − 1

Approximate losses at various ratios:

  • 1.25× → 0.6%
  • 1.50× → 2.0%
  • 2× → 5.7%
  • 3× → 13.4%
  • 5× → 25.5%

The loss is symmetric — a doubling and a halving produce the same result.