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In this article, we summarize learnings from the Bonding Curve Research Group’s latest research in the parameterization and performance of bonding curve tokens and their use in Primary Issuance Markets (PIMs). We also share more about the bonding curve modeling infrastructure we are building and our work in identifying further research questions to enable better design, engineering, and operational decision-making in dynamic supply token economies.
Bonding curves are a mathematical encoding of the relationship between two or more tokenized assets in smart contracts. They can be used in secondary markets to facilitate exchange between two tokens already in existence, or in primary markets for continuous direct token issuance (minting) and redemption (burning). Their adoption in secondary exchange markets like Uniswap has become mainstream, and revolutionized the way liquidity is approached in token design. We are now seeing more interest in their application as Primary Issuance Markets, because of their ability to dynamically expand or contract the token supply based on market demand. This can help to stabilize otherwise volatile token prices, and even generate native revenue for projects from fees and arbitrage between primary and secondary markets.
The bonding curve design space is massive and we have only begun to scratch the surface of this novel economic mechanism’s potential to create more resilient token economies. We have explored their applications in token ecosystems for bootstrapping early-stage economies, price discovery, and product-market fit, briefly shared our methodology and process for modeling and simulation, and contrasted fixed and dynamic supply tokens. The Bonding Curve Research Group, in a research collaboration with Inverter Network and BlockScience, is now working on open-source modeling infrastructure for bonding curves, building out tools and dashboards for their analysis and design. For example, in Figure 1 below we contrast the historical market data of a token with its simulated performance if it were issued on a bonding curve, to see how a Primary Issuance Market would have fared in comparison to the status quo.
Figure 1. A model simulation contrasting a token’s ‘historical’ price performance (bottom line) with how it would have performed as a token on a Primary Issuance Market (solid blue line).
Our next step will be to open source this tool such that it can pull in market data for any token and produce similar results, as well as allowing parameter configuration to explore the impacts of these design choices on a token economy.
Early research already reveals valuable insights in understanding the decisions in bonding curve design and parameter tuning. Based on these findings, our researchers have analyzed some of the trade-offs in this design space by examining volatility, reserve drawdown, and fee collection under different parameter conditions. Our data science team has also been comparing the performance of various tokens in the Web3 ‘public goods’ space, and found that primary issuance bonding curve tokens outperformed non-bonding curve tokens by a sizeable margin, and even held price stability better than Ethereum through the bear market of 2022, until the market flattened out in 2023.
Compared with static supply tokens that struggle to adapt to market conditions, dynamic supply tokens offer much-needed flexibility and stability in crypto’s unpredictable market environments, demonstrating the benefits that primary issuance bonding curves offer in the design of more resilient economies.
Token Engineering is a new field applying engineering principles to the holistic design, validation and verification of token economies. Token engineers apply complex systems modeling, simulation, and data science, upholding an adherence to ethics to build safe digital public infrastructure. In the process of designing any complex system, teams and communities should engage in an engineering process starting with requirements gathering, which enables them to balance trade-offs and optimize for certain goals based on the needs of participating stakeholders.
Figure 2. Parameter configuration choices often result in trade-offs for achieving system goals. From BlockScience's "How to Perform Parameter Selection Under Uncertainty: Configuring Complex Systems to Handle the Real World". (SOURCE: https://medium.com/block-science/how-to-perform-parameter-selection-under-uncertainty-976931ba7e5d)
Bonding curves are highly configurable and there are many dimensions by which these mechanisms can be launched and dynamically tuned. The parameters, depending on how they are set, can have various effects on things like price volatility, drawdown pressure on reserve assets, and the amount of fees collected. Modeling enables systems engineering and data science practices to be applied to the design and deployment of bonding curve token ecosystems. The goals of the system can be mapped to a suite of evolving KPIs in order to produce economic systems that continue to benefit the communities that steward them. The BCRG produced this table to explore the parameter selection impact of the following fundamental parameters for bonding curves:
Figure 3. Parameters of a Primary Issuance Market. An important point to note is the relationship between supply, price, reserve, and reserve ratio which can be understood as: initial_price
To learn more about the findings for each parameter, check out the BCRG Gitbook, watch this Narrative Model Walkthrough, and try our params simulator.
The following table indicates the effects of parameter selection on a set of common goals that a community may have regarding its token economy - price volatility, reserve asset drawdown, and fees collected. The table introduces four categories of relationships: directly proportional, inversely proportional, no effect, and non-linear effects. No effect indicates an absence of a relationship between the parameter and the goal, and non-linear effects indicate that the relationship dynamics are non-linear and require more sensitive analysis when making deployment decisions.
Figure 4. An initial parameter exploration created by the Bonding Curve Research Group. The table represents preliminary results in testing the outcomes of parameter selection in a modeling environment. Note that the analysis only considers linear interactions between bonding curve-issued tokens in relation to secondary market trading.
Studying these parameter sets and their combinatorial effects offers a glimpse at the possibility for these tools to facilitate and improve the economic management and value accrual systems of Web3. Using these tools, token designers can lay an economic foundation that addresses some of the major challenges of distributed economic systems, such as bootstrapping small economies, providing necessary exchange liquidity, and facilitating demand-responsive dynamic token supply.
Through this work, we aim to provide a toolkit for exploring the design space of bonding curves, and produce re-usable tooling as infrastructure for future research to support builders in better understanding their behavior, features, parameters, and risks.
In addition to modeling parameter sets, historical analysis of the economic performance of various tokens and their financial performance can also inform design choices. In an initial study commissioned by the Token Engineering Commons, the BCRG analyzed price movements of several public goods tokens by pulling their historical price data, normalizing the data to the price of Ethereum, and looking at the relative change in price over time, using a common financial metric known as the Sharpe Ratio, which measures risk-adjusted relative returns.
The tokens analyzed included Ethereum, Bright, Gitcoin, Giveth, Metagame, Honey, Radworks, and TEC of the Token Engineering Commons (the only bonding curve token in the analysis) throughout May 2022 to January 2024. Note that our TEC data goes only until July 2023 at which point the TEC DAO migrated from Gnosis chain to Optimism chain, and our experiments only included TEC data from Gnosis chain.
Figure 5. A historical price chart of Ethereum ecosystem public goods tokens showing relative change in price over time from a BCRG analysis. You can see the $TEC token of the Token Engineering Commons in purple, which outperformed the other tokens and even Ethereum itself for a period of time.
The results showed that the TEC token, issued via an Augmented Bonding Curve (ABC), exhibited the best price preservation performance compared to the other tokens. It even outperformed Ethereum for a significant period during the 2022 bear market, and was the best performing token in maintaining value against Ethereum even in the ensuing bull market. This consistent performance is further supported by the calculation of the Sharpe ratio, showing the TEC token compared favorably to other public goods tokens in terms of risk-adjusted returns.
Figure 6. Output of financial analysis on public goods tokens, demonstrating that $TEC has the highest risk-adjusted return (Sharpe Ratio). (Source: Image and analysis by Shawn Anderson).
Discover more in the BCRG’s Public Goods Token Comparison walk through video:
This analysis presents further evidence that Primary Issuance Markets offer more market resilience and can enable better financial performance over time. However, the data set in this case only examined a small set of public goods tokens in the Ethereum ecosystem. To draw more rigorous conclusions, this analysis could be expanded to a wider data set of more tokens on various blockchains, examine performance over longer time periods, or blend historical and simulated data to compare parameter sets and performance.
As the token engineering space continues to evolve, bonding curves are emerging as a powerful tool for creating dynamic token economies, providing projects with native revenue and additional price stability. The research, education, and development of token engineering primitives has profound potential and implications for token ecosystems; these tools are poised to play a key role in shaping the future of token economics.
While initial results are promising, the Bonding Curve Research Group is planning further research to build on these findings and continue to explore the potential of dynamic supply tokens, Primary Issuance Markets, and primary and secondary market interactions.
In addition to exploring bonding curve performance and parameterization, the Bonding Curve Research Group also plans to explore the technical and economic risks of using yield-bearing tokens as collateral, expanding our models of agent behavior and market interactions, and studying the effects of a ‘nested control system’ with the primary issuance market as a passive filter and an arbitrage bot as an active filter, acting together to ‘smooth’ otherwise more volatile token price changes.
Continuing research and experimentation is key in unlocking the potential of these novel economic primitives that are redefining liquidity and market making in Web3. We look forward to continuing our research, and welcome further collaboration with ecosystem partners to study the use of bonding curves in creating more resilient token economies.
This article was written by Jessica Zartler and Jeff Emmett with edits and research by Shawn Anderson. It presents information and research carried out by the Bonding Curve Research Group including additional contributors Rohan Mehta, Hashir Nabi, and Rex. We would like to offer special thanks to GoGoPool for commissioning this article and the token analysis walk through video, and Inverter Protocol and BlockScience for the ongoing research collaborations exploring Primary Issuance Markets. This article is not intended as investment or tax advice. Header image by Jessica Zartler with Adobe Firefly.
The BCRG is dedicated to the research, development, education, and application of bonding curves in their various forms. As a collective of multidisciplinary researchers, we are on a mission to empower projects with reliable token ecosystem tooling, creating new collaboration opportunities through Web3 education and token engineering.
