Loss Versus Rebalancing Actualized in the Modular Ecosystem via Shogun’s DIMM Vaults
In this article, we quantify the benefits provided by the Decentralized Interchain Market Maker (DIMM) in regards to enhanced impermanent loss (IL) protection using the concept of Loss Versus Rebalancing (LVR). When a liquidity provider (LP) weighs the costs and benefits of adding liquidity to a pool, the criteria is typically weighing swap fees earned and incentives (benefits) versus impermanent loss (costs). However, what is not typically considered is the implicit costs from adverse selection of counterparties (arbitrageurs and market makers) who capitalize on stale orders of AMM LPs because of information asymmetry. To expand further, AMM LPs are susceptible to being on the wrong side of the trade when “informed traders”, namely arbitrageurs, swap assets on the AMM that are mispriced relative to the market and buy or sell on another centralized or decentralized exchange at a profit. LVR (Loss Versus Rebalancing) is a formula quantifying the amount rebalancing saves LPs on implicit costs earned by arbitrageurs, the counterparties who profit at the expense of LPs because of information asymmetry aka ‘adverse selection’.
The LVR is the difference between the total value of pool reserves (not including trading fees) and the value that would be produced by using dynamic rebalancing strategies. The LVR formula is as follows: LP P&L=(Rebalancing P&L)−LVR+(Trading Fee Income). LVR is a function of volatility, such that the greater the volatility of an asset, the higher the profits “informed traders” are able to earn via arbitrage. DIMM can help AMM LPs save on some of the costs associated with volatility by way of rebalancing. We walk through a detailed example below.
Hidden Costs Not Included in IL Calculation
Let’s use an example wherein a deposit of 100 ATOM and 1000 USDC [ATOM = $10] ends up with the same value a month later. The price may have gone from $10 ATOM to $40 ATOM in between, but ultimately ends up at $10 when you withdraw. Using only IL as a metric, it would appear your costs are 0 (if initial price = final price → IL = 0). However, a simple IL calculation traditionally used does not tell us the entire costs implicit in the volatility induced by adverse selection, namely in the form of arbitrage by informed traders. Market movements obscure the underlying adverse selection cost hidden in favourable market movements.
· More volatility → more arbitrage opportunities → higher opportunity costs for LPs
Loss Versus Rebalance (LVR) Example
ATOM Increases in Price
Using the canonical AMM, whereby x*y=k curve is used, the AMM by default sets spot price p as a function of quantities x and y so that the USD value of pools match: px = y, i.e., p = y/x. Thus trades in the AMM’s invariant function force the preservation of the x*y equation; or said in simpler terms, the cash value of both assets in the x*y=k curve must remain equal for both assets and any trades in the pool force a rebalance of the assets with the predetermined bonding curve conditions.
Example: pool with 100 ATOM, 1000 USDC.
· ATOM market price jumps from $10→$40
· Arbitrageurs update the pool to 50 ATOM, 2000 USDC
· In effect, sold 50 ATOM at a price of $20 USDC/ATOM
· New pool value is $4000
Alternatively, through a dynamic rebalance strategy, you could copy the trade of the AMM used by arbitrageurs by selling 50 ATOM yourself for a market price of $40 on an external marketplace via an auto-rebalancing model.
· Portfolio value: 50 ATOM + 3000 USDC = $5000
· Loss Versus Rebalance (LVR) = $5000 — $4000 = $1000
Hence, the above example shows us that an auto-rebalancing strategy allows AMM LPs to retain higher cash value of their assets versus being subject to adjustments of the bonding curve of the AMM; LPs save on costs from both IL and LVR.
ATOM reverts back to initial price after price increase
Let’s say ATOM jumps back to initial price, $40 → $10; if no dynamic rebalancing is involved:
· AMM returns to original state (100 ATOM, 1000 USDC, value = $2000)
· In effect, bought 50 ATOM back at the (same) price of $40 USDC
Alternatively, if dynamic rebalancing is involved: 50 ATOM is bought at the current market price of $10, thus:
· Portfolio value: 100 ATOM + 2500 USDC, value = $3500
· Thus, cumulative LVR = $3500 — $2000 = $1500
This proves LVR depends on the trajectory of prices, not just initial and final price as is used in normal IL calculations. If price never moved, LVR = 0; when price does move, and even if it goes back to initial price, LVR would increase LP’s portfolio value. LVR increases with every trade given every instance a buy or sell transaction occurs, the LP is at risk of being on the wrong side of the trade versus an informed trader, i.e., adverse selection. In effect, LVR quantifies arbitrage and adverse selection. The dynamic rebalancing strategies will be automated with optimized parameters based on the volatility profile of the asset and is a key value feature of DIMM that’s designed with the LPs in mind.
LVR and Dynamic Rebalancing in Practice via Shogun’s DIMM
Using IBC and Interchain Accounts, Shogun’s DIMM module can execute customized cross-chain market making strategies putting into practice cost savings for LPs demonstrated in the Loss Versus Rebalance equation. Through dynamic rebalancing and hedging on third party DEXs using parameters that align with the LPs’ risk appetite, enhanced impermanent loss protection and high capital efficiency can be realized for JIT (Just-in-time) LP vaults. An illustrative example is displayed below using ATOM/USDC as a vault with a 5% deviation threshold for rebalancing:
What is DIMM
The core problem that DIMM aims to solve is to provide capital-efficient market-making services for retail and institutional LPs across a modular world, using automated and dynamic rebalancing strategies with parameters that are optimized based on historical market data for asset-pairs under consideration. DIMM implements a combination of off-chain order-matching, otherwise known as Coincidence of Wants (CoW) mechanism, and a just-in-time (JIT) liquidity allocation strategy in concentrated liquidity pools and on-chain Central Limit Order Books (CLOBs) . DIMM offers superior UX for the user in that the complexities of cross-chain bridging and liquidity management are removed for the individual; DIMM, through the use of IBC and interchain accounts (ICA) would run automated logic for dynamic rebalancing strategies by utilizing any available on-chain liquidity for LPs who can set and forget while earning fees and rewards. In summary, DIMM solves the challenges of interchain liquidity by providing capital-efficient market-making services, automating dynamic rebalancing strategies, and removing the complexities of cross-chain bridging and liquidity management for the individual.
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