More and more DeFi protocols are trying to address the issue of impermanent loss. What are the specific effects?

Author: alertcat.eth ，Chain Hunter

Impermanent loss is one of the unavoidable risks for DeFi liquidity providers. According to Dune data, the monthly trading volume of decentralized exchanges (DEX) has exceeded $50 billion, making the management of impermanent loss a significant challenge for AMM protocols.

Essentially, impermanent loss refers to the temporary loss of funds that occurs when providing liquidity. For liquidity providers, when the price drops, not only is the principal at a loss, but they are also forced to increase their positions, leading to greater losses; conversely, when the price rises, they are forced to decrease their positions, resulting in smaller gains. This is somewhat similar to grid trading (ignoring all grid profits). The chart below shows the PnL of impermanent loss when the price of ALT changes against USD and the corresponding values of shorting ALT to hedge risks, which reduces volatility.

In an article published by crypto analyst charliemarketplace.eth on December 24, 2022, he analyzed the closed trades of WBTC-USDC and ETH-USDC on Uniswap prior to September 20, 2022, and conducted a divergence loss analysis of these trades.

The analysis revealed that 55% of ETH-USDC 0.05% positions had profits and losses exceeding HODL. 40% lost to HODL. This indicates that the returns of the AMM model outweigh the risks of impermanent loss. The chart below shows the profit and loss analysis of ETH-USDC LP relative to HODL.

In the analysis, even the treasury of projects built on Uniswap had slightly better profit and loss situations than individuals. The chart below shows the positions of institutions versus individuals.

The conclusion is that Uni v3 LP is (moderately) feasible for ordinary people to counter HODL. In terms of quantity, the number of positions that outperform the market while providing liquidity is greater than those that underperform. However, the presence of a few massive Omega losers (the Omega ratio, a new metric for describing returns, utilizes all information from the return distribution, considering all higher moments and characterizing all features of return risk) distorts everything. A single position accounts for 15% of the total losses across all positions.

Thus, a few losers describe the tail effects of impermanent loss when constructing a portfolio.

Note: The BTC market is a multifractal market with long memory characteristics. By using more than one method to calculate the Hurst exponent, it was found that the logarithmic return series is between 0.5302 and 0.6565, while the squared return series representing volatility is between 0.6876 and 0.9837. The calculated Hurst exponent falls within the range of 0.5 to 1, proving that the fractal market hypothesis is valid in the BTC market, indicating the presence of long-term shock persistence. The fractal market hypothesis assumes that in financial markets, long-term investors tend to become short-term speculators during extreme market fluctuations, leading to volatility that does not follow a normal distribution, resulting in the fat tail effect in financial markets.

There are several DeFi projects in the market aimed at reducing or mitigating impermanent loss. Below are examples analyzing the feasibility and robustness of these projects, including Clipper Finance, Tarot Finance, Tsunami Finance, Deltadex, Vader protocol, Krypton exchange, Platypus Finance, Shieldex, and others.

First is Clipper Finance, which has been widely criticized by retail investors for having a hard cap on liquidity, limiting participation (not following the permissionless principle, as only whitelisted users can form LPs). Below, we will analyze the feasibility of its mechanism from the perspective of the project’s white paper.

The white paper proposes two basic assumptions: the first definition is that the invariant is a positive homogeneous scalar field, meaning that the increase and decrease of liquidity are linear. For example, in a positively homogeneous case, two liquidity providers responsible for half of the pool's liquidity will each have half of the pool's profits. The second definition is that the price arrangement invariant uses risk-neutral pricing, where the wealth of each asset is equal, meaning that the initial values of the two assets in the LP are equal.

The white paper considers an equation:

When k=0, it represents a case of a fixed exchange rate with zero curvature, where all coins are at a constant price and can be exchanged at a 1:x ratio without slippage. This model is called a Constant Sum Market Maker. Since prices do not change due to supply and demand, when there is a price difference between stablecoins in the external market, arbitrageurs will come in until one side's liquidity pool is exhausted, causing these coins to lose liquidity in the pool.

When k=1, it represents Uniswap's model, known as the Constant Product Market Maker, which follows the inverse function model xy=k. However, with shallow trading depth, prices will change significantly. This model has excessive curvature, leading to rapid price changes, so we need a smoother curve.

Clipper's k value is between 0 and 1, somewhat similar to Curve. The chart below shows the price changes of Curve.

The table below shows the impact of trade size on slippage for Clipper. Choosing a middle value for k can reduce arbitrageurs' exploitation of the fixed exchange rate pool and also reduce slippage for traders according to AMM. Due to Clipper's relatively small pool size, it can only accommodate smaller-scale trades based on the proportion of total liquidity, and choosing a middle value can better concentrate liquidity. The red line in the chart represents Clipper, the blue line represents the fixed exchange rate model, and the green line represents the Uniswap v2 model.

Since Clipper adopts a multi-asset model, it is essentially an initial distribution of an index fund that is proportionally distributed. According to the mathematical formula, the following chart (simulating the impact of different k values on profit and loss) is derived: the green line represents the profit and loss results of HODL, the red line represents the profit and loss of Uniswap (k=1), the black line represents the profit and loss of Clipper (k=0.5), and the blue line represents the profit and loss of the fixed exchange rate model.

As can be seen, Clipper's concentrated liquidity architecture improves capital utilization efficiency, reducing slippage for small trades, but this comes at the cost of increased impermanent loss for LPs. Mathematically, any k value between 0 and 1 will have a higher impermanent loss than the Uniswap v2 model.

Clipper has also made some efforts to reduce liquidity providers' losses, such as limiting pool size to create higher slippage for large trades, reducing toxic order flow, and using off-chain oracles and the ratio of assets in its pool to consider external market prices. This means that when the market fluctuates, Clipper will update its prices without requiring arbitrage flow to balance pool size. The low returns for arbitrageurs mean reduced losses for LPs! Its mechanism is somewhat similar to GLP, which bundles a basket of tokens to form LPs and then achieves trades with lower slippage under a smaller pool size through concentrated liquidity's mathematical curve. However, this indeed results in higher impermanent loss mathematically. Whether the reduced arbitrageurs and toxic order flow can offset these losses should be analyzed on a case-by-case basis.

Next is Tarot Finance, which essentially shifts the leverage risk to the borrower while the lender earns a certain return, thereby reducing their impermanent loss. This is a general leveraged mining model, a form of risk transfer.

Tsunami Finance, a project still on the Aptos testnet, has a mechanism very similar to Clipper, involving a basket of tokens and obtaining prices from off-chain oracles. The profit source is the betting between LPs and traders. Tsunami provides aggregated LP tokens (TLP), minimizing the risk of impermanent loss through diversification of blue-chip cryptocurrencies and stablecoins (essentially the same mechanism as Clipper), while maximizing returns by generating leveraged trading fees on top of swap fees.

Deltadex, an options platform, proposes a method to hedge impermanent loss by buying put options on its platform. This is indeed a method, but it does not address impermanent loss from the AMM perspective; rather, it is akin to insurance.

The NIL protocol has not yet launched a substantive prototype product, but we can look forward to its next product.

Vader protocol essentially constructs a reserve pool from which liquidity providers can receive compensation when they suffer impermanent loss. A portion of the fees generated from operations funds the reserves to provide permanent loss protection and allows for the minting of synthetic assets. The compensation issued increases linearly from 0 to 100% over 100 days. The tokens have undergone a devastating death spiral, proving that the fees generated from operations cannot subsidize liquidity providers; while the mechanism makes sense, it is insolvent.

Krypton exchange is a decentralized exchange aimed at minimizing toxic order flow by packaging and executing trades over a period of time (using continuous batch auctions for price discovery). These toxic activities hinder the implementation of effective dynamic trading strategies, leading to suboptimal exposure to systemic risk factors and unnecessary exposure to specific risks. Similarly, this approach reduces traders' losses to some extent, but it still needs to launch products to withstand the test of time.

Shieldex is a platform that provides on-chain perpetual options, using oracles to provide price information, minimizing price discrepancies and reducing opportunities for arbitrage traders, thereby lowering impermanent loss. Its mechanism is similar to Clipper (eliminating toxic order flow).

Platypus Finance is a platform that allows users to provide unilateral liquidity. Platypus adopts a debt model instead of AMM, determining the liquidity provider's ability to redeem tokens based on the amount of remaining assets in the pool and the risk of a run. The coverage represents the asset-liability ratio of a certain stablecoin in the Platypus finance liquidity pool. Platypus finance uses a single-variable slippage function instead of an invariant curve. When the coverage of a certain stablecoin is high, the slippage for exchanged trades will be quite low; conversely, when the coverage is low, the slippage will increase.

This design is undoubtedly novel, cleverly transferring the risk of impermanent loss to every depositor in the pool. When panic selling occurs, the funds obtained by the first users to exit are greater than those obtained by later users.

Thus, this mechanism eliminates impermanent loss, transforming the original risk into the risk of exiting liquidity.

The project is led by Three Arrows Capital, with a public offering price of 0.1, which has now fallen below the offering price.

Therefore, from the analysis of projects aimed at impermanent loss protection, we can see that the risk of impermanent loss cannot be effectively hedged through on-chain mechanism design. These projects often claim to reduce or eliminate impermanent loss risk; however, the pioneer of this sector, Bancor, announced the cessation of subsidies because its token value was insufficient to subsidize impermanent loss. Thus, these projects often indirectly reduce traders' losses by eliminating toxic order flow, using off-chain oracles, and employing packaged trades. Alternatively, they may transfer risk by using their tokens for subsidies (increasing selling pressure on their own tokens), or construct unilateral pools or lending pools to transfer their risks to counterparties.

Heavenly principles are constant; they do not exist for Yao nor perish for Jie. Impermanent loss is a conundrum, unsolvable, but there are optimization methods. Impermanent loss is a mathematical characteristic of the AMM model and should not be defined as a defect, as LPs are essentially analogous to a "perpetual cross-period sell" position in traditional finance. The following is its profit and loss situation.

Conclusion

The feasibility and robustness of projects aimed at impermanent loss protection are quite limited. They employ financial risk transfer strategies in the Web3 space. Depending on the financial instruments used, financial risk transfer strategies can be categorized into:

1. Hedging strategies: These primarily utilize forward contracts to eliminate risk.
2. Risk transfer strategies: These mainly use insurance and options contracts to transfer risk to others.
3. Diversification strategies: These reduce overall risk by constructing portfolios.

This is the essence of impermanent loss protection protocols, built on the foundation of risk transfer in DeFi protocols.