Providing Liquidity on Uniswap vs. Selling Options on Smilee—Which performs better?
🚨 This is the shortened version of our research. Click here for the FULL VERSION with mathematical formulas.
These days, everyone compares providing liquidity on a DEX to selling options (see this article by Guillaume Lambert to understand how Uniswap v3 LP tokens effectively behave like short puts and short calls). However, contrary to options sellers, DEX LPs are compensated with trading fees, directly monetizing DEX trading volumes and not implied volatility.
But what if LPs actually sold volatility? This is what Smilee enables. Does it make sense? Are yields better than those offered by DEXs?
Let’s find out…
In this article, we’ll compare providing liquidity on Uniswap V3 with selling “Impermanent Gain” on Smilee.
Data
We collected historical daily ETH prices, one-week ETH implied volatility and historical daily data related to the ETH-USDC 0.05% Uniswap V3 pool.
The dataset covers a time period of 358 days from June 8, 2022, to May 31, 2023.
Methodology
In our analysis, LPs give liquidity in a range [KA,KB], where lower and upper bounds log-symmetrically deviate from strike price K by different multiples of the standard deviation, i.e. the one-week market implied volatility. Every seven days we set the new strike equal to the current ETH price and define the new liquidity range using the one-week ETH implied volatility. Smilee’s LPs receive weekly premia from selling impermanent gain at the fair price given market implied volatility, while on Uniswap V3 fees are collected every day, as long as the price is within the range.
Assumptions
In the following discussion, we assume that liquidity providers do not collect fees outside the liquidity range and never reinvest fees during the period. Moreover, since on Uniswap V3 LPs accumulate fees proportionally to their shares of in-range pool liquidity, we need to make an assumption about how liquidity is distributed:
We take the liquidity distribution on July 10, 2023, and every week we rebase the same distribution around the current ETH price.
We also assume that half of Smilee users buy and hold their positions and that the other half instead buys and sells positions two times a week with an average trade size of $250. This is equivalent to a weekly turnover of 2.5, which we believe is fairly conservative.
The comparison is made by depositing the same $1,000,000 on both Smilee and Uniswap every week. Please note that for the sake of our comparison, we only check that the price belongs to the range at the end of the day, ignoring the intra-day volatility due to lack of intra-day data.
This approximation may slightly overestimate or underestimate Uniswap fees, however, we expect it to have a relatively small impact on the final results.
Numerical Results
Let’s consider a strategy with a liquidity range of 3 standard deviations, i.e. a range [KA,KB], where lower and upper bounds log-symmetrically deviate from strike price K by 3 weekly implied volatility. We will present results for different utilization rate scenarios: first, a limit case where U = 100% and then two more realistic scenarios with U = 75% and U = 50%.
3 standard deviations liquidity range, U = 100%
If we compare the Smilee weekly premia with Uniswap V3 weekly fees collected by LPs we can see that for a utilization rate equal to 100% Smilee outperforms Uniswap.
Indeed, Smilee's cumulative returns are almost three times Uniswap's cumulative fees.
Regarding risks, from a theoretical point of view when the utilization rate is 100% we expect the impermanent loss of LPs to be exactly the same on Smilee and Uniswap V3. This is what occurs in practice, as shown by the plots.
Under the assumption of a constant 100% utilization rate Smilee LP strategy with 3 standard deviations range has a cumulative APR over the period equal to 162.89%, while Uniswap V3 guarantees to LPs a cumulative APR of 55.74%. Therefore in the extreme scenario of a 100% utilization rate, Smilee offers liquidity providers much higher returns, almost three times the returns of Uniswap V3, for the same level of risk.
Nevertheless, given the relationship between utilization rate and implied volatility expressed by Smilee’s bonding curve (see the full research), it is not reasonable to assume a utilization rate of 100%. Instead, it is more informative to study cases with a lower utilization rate.
3 standard deviations liquidity range, U = 75%
We can immediately notice that by lowering the utilization rate the LPs returns on Smilee are lower than previous case, due to the fact that LPs collect less premia.
Nevertheless, Smilee's cumulative returns are still bigger than Uniswap fees, as shown in the plot.
Lower returns, however, correspond to lower risks, indeed when the utilization rate is less than 100% the LPs on Smilee will suffer only part of the impermanent loss.
As expected the following figures show a significantly smaller impermanent loss for liquidity providers on Smilee than on Uniswap V3.
Smilee's cumulative APR in the observed period is 66.8%, which is still significantly higher than Uniswap's APR, always equal to 55.74%, but while fees on Uniswap are extremely volatile, Smilee premia are a lot more consistent.
Moreover, impermanent loss is significantly less. Therefore, under these assumptions, selling volatility on Smilee offers higher returns compared to providing liquidity on Uniswap, but with a smaller risk.
3 standard deviations liquidity range, U = 50%
By further lowering the utilization rate to 50%, we obtain returns for the LPs on Smilee lower than Uniswap fees.
However, the risk is significantly smaller too, in fact, the impermanent loss suffered by LPs on Smilee is exactly half that suffered on Uniswap V3, as shown in the following plots.
In this case, Smilee's cumulative APR is 29%, therefore we can conclude that in this case selling volatility on Smilee guarantees a return that is slightly more than half the return of providing liquidity on Uniswap, while the associated impermanent loss is exactly half.
Conclusion
In our research, we find that selling volatility on Smilee provides more stable returns to providing liquidity on Uniswap with significantly lower impermanent loss.
Moreover, at high levels of utilization rate, selling volatility shows much higher returns with the same or lower level of risk, while at low utilization rate, Smilee provides lower returns than Uniswap, but with significantly less impermanent loss.
As shown by Atis E. in his paper, the implied volatilities of Uniswap pools are definitely underpriced. Moreover, while Uniswap LPs are vulnerable to MEV, selling volatility is MEV-resistant as impermanent loss is not generated by swappers. Additionally, on Uniswap, Just In Time (JIT) liquidity can further reduce returns for LPs, while on Smilee this is not possible as liquidity can only be added at the start of each epoch.
Overall, selling volatility seems to have a more favorable risk-reward profile than providing liquidity on Uniswap for the pool selected.
