50/50 Pools

Delving Deeper into Impermanent Loss: The Dynamics of 50/50 Pools

One common scenario in AMMs (Automated Market Makers) is a 50/50 pool, where the liquidity of both assets is kept equal. Let's delve into a scenario with JLY and BTC to understand this.


  • Starting Point:

    • JLY is priced at $0.5. We have 8000 JLY (valued at $4,000).

    • BTC is priced at $25000. Thus, 0.16 BTC tokens equal $4,000.

    • Both assets are added to the pool, totalling $8,000, for which we receive pool tokens.

  • Price Evolution:

    • After some time, JLY’s price surges to $1 (a 100% gain), while BTC moves to $30,000 (a 20% gain).

    • This unequal price movement introduces the phenomenon of impermanent loss. Even though we are still in profit in USD terms, we haven't maximized our potential gains due to the liquidity mechanism.

  • Impermanent Loss Mechanics:

    • The key lies in the invariant, a mathematical constant in AMMs. It defines the product of the quantities of the tokens in the pool and must remain constant.

    • Given the price changes, the new quantities of JLY and BTC in the pool will be different from our initial quantities. This deviation is what constitutes the impermanent loss.

Comparative Analysis:

  • Initial liquidity: $8,000

  • Value by holding (HODLing) both assets: $12,800

  • Value as a liquidity provider: $12,393.52. However, with an additional 5% annual yield, it increases to $13,137.13.

From the above, if we had simply held the tokens (HODL), our total would be $12,800. As a liquidity provider, even after the yield, our value is slightly above the HODL amount.

Impermanent Loss Reversibility:

Let's analyse a case where the prices of JLY and BTC continue to shift:

  • JLY drops to $0.75 while BTC surges to $37,500. Despite the disparity, this represents a 50% gain for both assets compared to our original liquidity.

  • Since the invariant ratio mirrors the price action ratio, there is no impermanent loss.

  • The token balances remain consistent with our initial liquidity, indicating the impermanent loss has been neutralized. Moreover, if the pool attracted significant trades, we would have earned swap fees, augmenting our profits.


The nature of impermanent loss means it can potentially be "erased" with the right price movements. It's a dance of asset prices where the final positions can restore initial Balance. As prices moves, impermanent loss can both appear and vanish.

The central strategy for a liquidity provider revolves around understanding these dynamics. The volatility of assets can be both a risk and an opportunity. While impermanent loss poses potential reductions in gains, the swap fees from large trading volumes might compensate or even outweigh these losses. It's a balancing act of assessing impermanent loss against the benefits of "volatility farming."

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