The Tranche Rebalancing Premium
Because of Tranche-ing, when a large swap causes an AMM's active tick to rapidly change, the price might move into a new tranche whose liquidity is not yet deployed. This means that tranche's liquidity will miss out on that swap's fees. That sounds bad at first, but there's actually upsides as well. Let's take a look.
Position Balances
Let's examine the example of a sudden price move up, and a single unit of liquidity. We'll pretend the liquidity is deposited in an infinitesimally small range since that can generalize to any tick width by simply adding them together. Let's say that range is right around the price 3000.
For any liquidity position, it always holds the less valuable token on either side of its price range. So for ETH/USDC, if the price goes above the range it'll swap to all USDC and if the price goes below the range the position is swapped to entirely ETH. This is where IL comes from, you miss out on the gains of ETH, but still capture its downsides.
So for our position, above 3000 we'll have all USDC below 3000 we'll have all ETH. Now in our scenario, this unit of liquidity is "tranched", so it isn't deployed to the AMM and doesn't get swapped into USDC. This means as the price shoots up, it actually gains in value and profits from the move.
And that profit as a percent is exactly the percentage increase of the resulting ETH price over the liquidity's price of 3000.
Positional Profit vs. Swap Fees.
Therefore, we really just need to compare if this profit is larger than the swap fee. Given that most swap fees are as small as 0.05% and 0.3%, it is extremely likely the price will go more than 0.05% or 0.3% past the liquidity's range. This is basically the heart of the Loss vs. Rebalancing argument you might have seen on crypto Twitter.
Our tranche sizes are typically set to a band width of the 1-day price volatility around the current price and rebalanced when the price moves halfway to either end. So a swap would have to jump half of 1-day's price volatility to go out of tranche. Therefore if the price is jumping 5-10% to go out of tranche, what is the probability that it only goes less than 0.3% past the liquidity tick's price.
"There are decades where nothing happens and weeks where decades happen" is an apt quote for crypto. We'll present data later on as this strategy plays out, but given the volatility of crypto we believe suddens moves are sudden, and the probability that your tick is within the very last 0.05% or 0.3% of the price move is very low. In fact if the price moves just a bit more than 0.06% past the tranche range a random un-swapped tranched tick is more like to be profitable than not.
Caveats
But you might say "what if you miss multiple swaps?". And that's a good point, because the position's profit is a one time thing, but there can be multiple swaps back and forth before a tranche rebalance happens. We've partnered with great data providers and RPCs to minimize that delay but I can't promise there won't be any, so it is possible. On the other hand though, avoiding all passive strategy yields is a much bigger opportunity cost than these marginal swap fees.
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