Modeling DeFi Pt VI – Sustainability, A Practical Example


Hello again, Ludwigs et al. I published an article on Analyzing Incentives a few weeks ago. The core principle introduced was about the sustainability of a protocol’s investment in delivering yield to users. I believe the piece was well received and even prompted some discussion around how it could apply to an actual protocol. I set out to find a protocol to analyze and provide readers with more to consider regarding sustainability (or not!) or at least trends to consider.  For this article, I decided to listen to music written over at Beethoven X. Are all the instruments hitting the right notes, or are some playing off-key?

While there are many ways to model sustainability considerations, in this piece, I aim to explain some of my logic and considerations and demonstrate findings using real data.

Beethoven X

Beethoven X is a community-driven DEX and DeFi powerhouse, governed by fBEETS and living on the Fantom Opera and Optimism chains. Built on Balancer V2 technology, Beethoven X leverages best-in-breed DeFi protocols to offer novel decentralized investment strategies. It is the first next-generation AMM protocol on Fantom Opera and Optimism. Their stable pools allow assets to trade at near parity, and their weighted pools allow for broad asset exposure, rebalanced by traders seeking arbitrage. Their $BEETS token is emitted to yield farmers who provide liquidity to the protocol, and that incentive structure is the crux of their potential yield sustainability.

The Show Must Go On

The simplest consideration for a protocol’s investment sustainability is to look at ‘money in’ and ‘money out’. For Beethoven X, this means swap fees that the protocol earns (money in) and $BEETS emissions (money out). The trick here is that $BEETS emissions decay over time, so the challenge for Beethoven X is to increase DEX usage and generate swap fees while emitting fewer tokens. They need to create more value to counteract less quantity. A sustainable incentive model requires the following simple equation.

money in = money out

If we look at these two parameters in dollar values, there is no need to normalize or account for market conditions. We want raw market data.

‘Money out’ changes distinctly when emissions run out. At the moment, the cost of emissions is $0 because Beethoven X has not yet emitted all $BEETS tokens. Once emissions run out, Beethoven can only emit what they can afford to buy. This introduces the concept that I intend to explore. If Beethoven X invests their Swap Fee revenue in buying back emissions, how long can they sustain the current yields?

For the purpose of this article, I have focussed on the emissions model employed on Fantom. The incentive structure on Optimism is different and will provide a case study for another time.

Composing the Model

Beethoven X is super transparent and provides a ton of data for users to see on Datastudios. Moreover, when I spoke to them about using their data to generate my model, souvlaki went out of his way to dig up an extra ton of data for me to use. I exported the daily value of $BEETS emitted, and the daily Swap Fees earned by the protocol, back to the start of this year. I have 203 days of data.

First, we look at revenue over time:

The chart shows daily swap fees (from stable and weighted pools) earned by the protocol over 203 days. We can model ‘money in’ as swap fees earned by the protocol.

At this stage, I would like to explain some logic regarding the proceeding model. I believe it is more indicative to model sustainability based on a shorter preceding time frame (within reason). Over time, protocols aim to achieve more adoption, changing their revenue: investment dynamics, particularly during their infancy, when adoption grows quickly, and emissions decay rapidly. For this purpose, I have opted to run calculations on the last 100 days of the data.

As such, the average daily revenue is $248 from stable pools and $3,003 from weighted pools. If we add all respective daily earnings together, we get $24,756 from stable pools and $300,330 from weighted pools. That is how much money Beethoven X can now spend on emissions (note, we are assuming minted emissions end with this data. In reality, there is much more time for Beethoven X to gain adoption and generate revenue, at a $0 investment cost basis).

Second, we can look at the daily value of emissions over the same 203 days:

The easiest way to replicate the investment trend going forward is to take an average from the last 100 days. The average daily investment value is $705 in stable pools and $8,949 in weighted pools.

Finally, we can model investment sustainability.

Beethoven X starts with $24,756 (stable) and $300330 (weighted) capital as investment runway. Each day, they earn $248 (stable) and $3,003 (weighted) from swap fees, and they spend $705 (stable) and $8,949 (weighted) on yield investments for liquidity providers.

We can see that based on 100 recent days of performance, Beethoven X can independently sustain the yield in stable pools for around 54 days and weighted pools for approximately 50 days. By the time their emissions run out, we should hope that 100 days of performance can sustain another 100 days of the performance. And to gauge their progress, we can run the same model for the first 100 days of data. Ideally, their recent 100 days outperform an older 100 days. Let’s take a look at the output of the first 100 days of data:

The first 100 days of data suggest around a week of sustainability, so based on these metrics, Beethoven X is well on the way to sustainable performance! Keep in mind there are many ways to model sustainability, and I have only looked at one. Endless variables can change moving forwards.

Recall the surface plot presented in Modelling Defi, Part 3 – Analysing Incentives. If the Beethoven X team decreases their investments, they can stretch their runway. If their TVL increases, yields will fall. So on and so forth.

If you understand these basics, think about the second-order effects. If TVL increases, perhaps usage increases, earning more swap fees, and yield does not decrease. There are so many considerations in the market that we can never really know what will happen. Models are fantastic for understanding variable interactions, but we should always think critically about what results mean.


We have demonstrated 203 days of Beethoven X data, in particular, the first and last 100 days, and assumed, for our discussion, that it provides a snapshot of Beethoven X emissions performance. It is critical to note that Beethoven X emissions started before my collected data and will continue until long after my collected data. They have a lot of time to bolster more adoption and revenue and consider novel investment strategies to maintain protocol performance. During that time, their actual cost of investment remains $0. The purpose of this piece was to demonstrate sustainability considerations, not to provide a finite determination of Beethoven X’s sustainability.

Thanks for reading along. I recommend that all readers consider what moves protocols are making to bring value to their investments and generate more adoption. It will be interesting to revisit this article when emissions run out. A big thank you to souvlaki from the Beethoven X team for his thoughtful discussion around sustainability indicators.

Stay tuned for the next article,

BEETS there or BEETS square,


Scroll to Top