How LP Returns Work

Because Clipper’s FMM design is novel, it generates LP yields differently than other DEXs. They come from the rebalancing process.
tldr; Clipper generates superior returns for LPs by rebalancing continuously at zero-cost, not from fees charged to traders. A foundation of Modern Portfolio Theory is that a diversified rebalancing portfolio actually generates yield from the rebalancing process itself in cases where the portfolio assets are relatively mean-reverting day-to-day, as is the case with BTC and ETH (despite tending to grow year-to-year). Clipper quotes prices that make the pool track this benchmark. As a result, the pool tends to grow in value because of the rebalancing process itself. These returns can be extremely attractive because crypto has such high daily volatility. Intuitively, it makes sense that yields are higher from harvesting volatility that can be 5% per day than could be earned from staked ETH and US Treasuries that yield only 5% per year.

Rebalancing Generates Yields

One of the most persistent, well-documented sources of returns in all of finance is portfolio rebalancing. When a diversified portfolio contains assets that exhibit high short-term volatility as well as short-term mean reversion (as is often the case with commodities and with BTC/ETH), frequent rebalancing can systematically harvest this volatility.
For context, rebalancing is the act of adjusting a diversified portfolio’s asset allocations to match its initial target allocations. Rebalancing is necessary for diversified portfolios because asset prices do not move in lockstep, so initial allocations will change over time.
Example: Imagine a $2,000, two-asset portfolio with target allocations of 50% ETH and 50% USDC. On day 1, ETH doubles in price to $2,000 from $1,000. The portfolio allocation is now 66% ETH ($2,000) and 33% USDC ($1,000), and must be rebalanced. This is accomplished by selling $500 ETH for USDC, returning the portfolio to 50% ETH ($1,500) and 50% USDC ($1,500)
When the assets are short-term mean-reverting (even if they grow long-term), a rebalancing portfolio can outperform a static (”held” or "hodl) portfolio consisting of any initial combination of the assets themselves. This is because as long is there is relatively more short-term volatility than long-term volatility, rebalancing is equivalent to systematically “buying low and selling high,” which generates additional profits. This is a well-researched phenomenon that earned Harry Markowitz the Nobel Prize in Economics in 1990.
Example: Imagine the aforementioned 50-50 ETH-USDC portfolio. On day two ETH returns to its original value of $1,000. The portfolio again must be rebalanced by selling $375 USDC for ETH, resulting in $1,125 ETH and $1,125 USDC, totalling $2,250. This is a 1.125x return, vs. 1x for simply holding the original assets for the two days.
👉 Spreadsheet showing how this works.
👉 See Appendix for the math on a rebalancing portfolio vs. HODLing returns
How often should rebalancing occur for optimal results? Theoretically, the answer is as frequently as possible. However, in practice transaction costs prevent this. Transaction costs are typically proportional to transaction volume, which is proportional to short-term volatility. These costs are referred to as "Performance Drag" and tend to eat up any gains from frequent rebalancing. That's why investment portfolios typically rebalance at a slower quarterly or even annual basis, and why most people conceive of diversified portfolios as a risk mitigation strategy instead of yield-generating strategy.
Clipper, however, has no transaction costs because it facilitates swaps at advantageous prices with the noisy order flow from traders. This noisy flow is ensured by only transacting with human traders; deterring over-informed whales and banning bots. Volume in Clipper's pools turns over extremely fast—sometimes multiple times per week. This means Clipper can quickly rebalance its pools simply by using organic trade flow. In other words, traders pay the transaction costs instead of Clipper. This is how Clipper is able to provide superior returns for liquidity providers.
More on rebalancing portfolios:

The Diversified Portfolio Also Reduces Risk

A well-diversified, rebalancing portfolio has other benefits as well. Modern portfolio theory states that such a portfolio results in better returns at a lower level of risk than investing solely in any one asset. Many financial advisors recommend a classic personal portfolio of 60% stocks and 40% bonds. Theoretically, this is an optimal way to gain exposure to an asset class.

Crypto Prices Have Become More Mean Reverting As They Have Matured

Bitcoin and Ethereum are commodities like gold and oil. High short-term volatility and mean reversion are typical features of commodities. Rebalancing works well in such regimes.
A Hurst Exponent test (below) we ran on the price movements of ETH from late 2015 through May 2023 shows that from mid-2018 onward, ETH has typically been either memoryless or mean reverting, whereas prior to that it was noticeably momentum driven. This verifies that ETH prices seem to be more mean reverting as it has matured, making it a prime candidate for rebalancing. This is typically the case with blue chip crypto assets, such as the Core Assets included in Clipper's Core pools.
In a memoryless price series, variance over 90-day windows should be 3x the variance at the 30-day window. A momentum price series will be above 3, and a mean-reverting series will be below 3.

Clipper's Benchmark: The Daily Rebalancing Portfolio ("DRP")

Clipper tracks a theoretical daily rebalancing portfolio with zero-transaction costs composed of roughly 60% ETH & BTC and 40% stablecoins). This benchmark is analogous to the “standard” 60-40 stocks-bonds portfolio recommended for individuals by many financial advisors.
Note that this benchmark is an extremely high and attractive bar, because real-world attempts to track it would require either substantial transaction costs or carry a hefty fee premium (if using derivatives). Indeed, a16z uses this same benchmark to compare AMM yields, but refers to it as "Loss versus Rebalancing" because they did not conceive that it would actually be perfectly achievable. In other words, the benchmark is in and of itself historically impossible to hit because is it costless.
Clipper, however, simply quotes prices that will rebalance the pool such that it tracks this benchmark, and it can do so since traders pay transaction fees. This is the source of its superior returns.

How Clipper Stacks Up Against the Benchmark

If we look at Clipper’s performance from September 11, 2022 through October 10, 2022 (which includes the “ETH Merge” event), we see that ETH fell more than 20% in price, while Bitcoin lost closer to 5% of its value. ETH’s large price drop is why both portfolios lost money (in dollar terms) over this interval.
Overall, Clipper closely tracks the DRP while staying slightly ahead of it, finishing the interval almost 40 basis points ahead of the benchmark. Clipper was within one basis point of the benchmark for more than three-quarters of the days in the period. For those days where Clipper LP and the benchmark diverged by more than one basis point, Clipper was ahead of the benchmark more than two-thirds of the time (23% vs. 10% of days).
The reason for return divergence is that Clipper’s Formula Market Maker will make trades continuously with traders over the course of a day, while the theoretical Daily Rebalanced Portfolio is simulated to costlessly rebalance once each day. Despite the divergences, the daily correlation of percent returns to the returns of the Daily Rebalanced Portfolio was extremely high at ρ = 0.9996.
For real-time performance vs. benchmark over the last 30 days, visit

The DRP vs. The CPMM

Both the DRP and the CPMM (used by most DEXs) provide beta exposure (return attributed to overall market returns) to the assets in their respective pools. But the similarities end there. Instead of rebalancing as conceived of in Modern Portfolio Theory, the CPMM trades according to its inherent x*y = k function. While the DRP provides alpha, the CPMM generates negative alpha, commonly referred to as impermanent loss. At best, if prices haven’t moved by the end of the period, the CPMM generates no loss. If prices have moved in either direction, there is substantial loss. The CPMM generates no profit from short-term volatility and loses money from long-term volatility. Meanwhile, yield comes not from the rebalancing process but rather from arbitrary fees charged to traders on top of trade prices.
In other words, impermanent loss is not an attribute of all DEXs, rather it is an attribute solely of all CPMM-based AMMs. Conceptually, the CPMM “sells low and buys high” as prices change, which is the opposite of the DRP (and common sense). The below figure shows how CPMMs only account for an asset’s beginning and ending prices. In contrast, DRPs are a function of the specific way prices move in the interim; DRPs profit from volatility.
As you can see, the attributes of the CPMM are not very favorable to LPs. Why, then, is it used by all first-generation DEXs? Because it is extremely simple to implement and it was probably a wise decision at the time to start simple. It is also simple to calculate on-chain, which made gas costs low. This tradeoff between gas and complexity is what Clipper's FMM architecture overcomes.
👉 See Appendix for math on the CPMM vs the DRP
👉 Spreadsheet showing how the DRP works differently than the CPMM (same spreadsheet as above)

How Clipper's Yields Compare to CPMM Yields

Because the DeFi community is so used to understanding DEXs as CPMMs, APY comparisons assume all pools are structured as CPMMs with trading fees and impermanent loss. Because Clipper does not have explicit trading fees or impermanent loss, it’s difficult to directly compare Clipper’s bottom-line LP figures with the top-line revenue numbers CPMM-based DEXs use. To ensure full transparency and keep LPs informed, Clipper reports comparable metrics and historical earnings on Clipper's data dashboard.
These metrics include:
  • Comparable APY: Top-line yield that includes the impermanent loss avoided by Clipper’s FMM design. These APYs are directly comparable with the APYs reported by most other DEXs (like Uniswap and Sushi), which advertise inflated figures that don't account for hidden costs.
  • Avoided Impermanent Loss: Calculated by comparing Clipper LPs' gain or loss on a crypto-basis (as opposed to a USD basis) to the crypto-basis loss of the CPMM mechanism used by Uniswap, etc. This crypto-basis loss can be calculated from (and will change based on) the difference in dollar values of the assets at the start and end of the given period.
👉 See Appendix for crypto-basis yield calculations

How Clipper's Yields Compare to HODLing

The DRP has an objectively better risk-return profile than HODLing and should outperform HODLing in current market regimes (see Hurst Exponent test above). Still, there are price series that could result in better returns from HODLing. To provide concrete data, here are the last few months of DRP Performance vs. HODLing an equivalent initial portfolio:
Month (2023)
DRP Performance (bps)
HODL Performance (bps)