Alpha Bonds: Risk-adjusted Bonding Curves for Financing Impact
BlockScience, Impact Financing, Algorithmic Policy, Alpha Bonds, Risk-Adjusted Bonding Curves

Alpha Bonds: Risk-adjusted Bonding Curves for Financing Impact

A Research Collaboration with ixo & the Interchain Foundation

BlockScience and ixo, with the support of the Interchain Foundation, have designed an innovative crypto-economic primitive that implements Risk-Adjusted Bonding Curves (RABC) for financing impact. RABCs are the first formalized instance of a dynamic bonding curve that integrates risk signals from the real-world into decentralized finance, using an internal prediction market mechanism.

Alpha Bonds are the ixo solution that implements Risk-adjusted Bonding Curves for results-based finance. As a versatile crypto-economic primitive, this has a wide number of potential applications, from Regenerative Finance (ReFi)Social Impact Bonds, to local currency systems that incentivize collective action towards desired outcomes.

BlockScience performed simulations using a cadCAD model to demonstrate how this mechanism could be used to de-risk financing of sustainable development investments in a way that also aligns stakeholder incentives towards achieving success. Our findings show promising possibilities for this new financing instrument, however there are still many research questions ripe for exploration, and we look forward to collaborating on further research and development of this new ReFi primitive.

From Static to Dynamic — A New Class of Bonding Curves

Token bonding curves are continuous liquidity mechanisms used in market design for cryptographically-supported token economies whereby tokens are automatically issued using buy and sell functions. Current bonding curve implementations act as automated market makers (AMMs), however, they are generally static, with fixed invariants and reserve ratios.

Since these bonding curve implementations are static, they cannot incorporate new information such as external risk or variable factors during live operation — even when such information is available and variability can be calculated. The inability to incorporate new information does not allow flexibility in the mechanism, and can have devastating effects on the economy. Ignoring these variable factors results in pricing and supply anomalies, such as tokens being misallocated on both buy-side and sell-side, with loss in risk correlation as a result. Systems with compound economic mechanisms (e.g. staking deposits also being used as debt collateral) contain interdependencies that produce non-linear effects. In the case of static bonding curves, this can lead to exploitation of information asymmetries and possible systemic collapse.

The goal of this initiative was to design a bonding curve implementation that can dynamically adapt its underlying parameters to new information about project risks over time — a Risk-Adjusted Bonding Curve. We aimed to provide a generalized reusable economic design pattern for a risk-adjusted bonding curve, but anchored the design in a motivating use case: tokenized development impact bonds in the ixo ecosystem. Alpha Bonds solve some of the major challenges in the way traditional impact bonds operate.

Meeting the Need for Better Impact Bonds

Impact bonds are an economic mechanism to finance the delivery of products and services in a way that incentivizes the achievement of pre-defined outcomes. They transfer the operational risks of a development project to capital investors and in return, these investors receive financial returns as compensation for the risks — if outcomes of the project are successfully met. Traditional Social and Development Impact Bonds face a range of issues, including a lack of transparency regarding project risks over the life cycle of the project. This deters investors, increases the costs of borrowing funds, and raises the barrier to financing projects for social, environmental, and economic development, and climate impact mitigation.

The impact bond process is capital-intensive and highly reliant on intermediaries to negotiate the rules of engagement, to monitor compliance, measure and validate outcomes and enforce contractual terms. Once the project has launched, timely impact data is not readily available to evaluate risk and support decision making during its life cycle. The absence of this data (or the time it takes to collect and process data) can cause delays in releasing tranches of funding, resulting in missed milestones and other project inefficiencies.

Results-based interventions are expensive, and tend to be applied only on large projects, thus exacerbating capital concentration and resulting in “too big to fail” outcomes. Important stakeholders, such as project beneficiaries, are also excluded from the decision making process, having an inadequate voice in the project’s implementation or risk assessment.

Dynamic financing mechanisms, with the capability to internalize and respond to new information, such as changes in risk over time, have huge potential to transform this capital formation and allocation process. Connecting supply chains of capital and data by leveraging AMM technology can support in creating more sustainable impact economies. This allows greater transparency of risk, and aligns incentives for investors and project participants towards success. Alpha Bonds are a step towards a new era of Smart Impact Bonds (originally conceptualized by ixo in 2018) that can facilitate this connection. They have the potential to bring impact financing mechanisms from an “analog”, low-definition stage to the next evolution of high-definition decentralized financing mechanisms.

How RABCs (Alpha Bonds) Work

Risk-Adjusted Bonding Curves are composed of four mechanisms: two bonding curve mechanisms (bond-to-mint & burn-to-withdraw), and two prediction mechanisms (attest-positive & attest-negative). The invariant properties of these mechanisms can be seen below, and their in-depth mathematical derivation can be found in this invariant derivation notebook.

Agents may choose to participate in just the bonding curve, or both the bonding curve and the prediction market mechanism. Tokens minted through the bonding curve can be burned back to the curve to reclaim collateral, but note that once tokens are attested towards project success or failure, they cannot be unattested and burned or re-cast. However, an agent may attest both positively and negatively with subsequent actions, denoting a change of agent sentiment towards a project’s chances of success.

The diagram below demonstrates how the alpha coefficient is updated through agent attestations in the prediction mechanism:

Alpha Bonds draw their name from, and dynamically price impact bonds according to the risk coefficient — “Alpha (α)” — that adjusts based on the attestations of project participants. Alpha can be considered a probability of project success, ranging from zero to 100 percent. This parameter is set according to a dynamic average consensus of all prediction market participants, and serves as a “wisdom of the crowd” measure to surface an estimation of project risk to funders & decision makers.

A varying Alpha impacts the shape of the bonding curve and thus the price of the token, as well as its reserve ratio. This is explained in mathematical detail in the System Specification notebook. In this model, a lower Alpha denotes lower confidence in project success, which increases the collateralization of the bonding curve to reduce risk for participants.

The prediction market avoids the Keynesian Beauty Contest problem (aka “voting with the crowd”) through the ‘Heavy Underdog’ property. This is the same reason you might bet on a severely outmatched team in the playoffs if you think they are going to win — because the payout is worth it to vote accurately according to your belief, rather than engage in tactical voting. With a risk-adjusted bonding curve, estimates of project success are updated with each transaction — making these tools essentially estimators of collective sentiment, a powerful new tool in the Token Engineering toolkit.

Implementations & Further Research

Alpha Bonds have the potential to solve some of the biggest challenges in impact financing. Ixo is currently working on a pilot program, implementing Alpha Bonds for education with Global XPRIZE winner Chimple, in collaboration with a global financial institution. The teams are applying insights from simulations run with this model, to test the capabilities of applying this primitive “on the ground” and collect data that can prove that this works in a complex real-world context.

In addition to using Risk-Adjusted Bonding Curves to improve impact bonds, we foresee this instrument being used in a variety of applications for outcome-based payments, i.e. blockchain projects “dogfooding” this tool to align incentives towards, and pay for, work completion.

While our initial findings show promise that this mechanism could be a revolutionary tool, in the research process, we uncovered several further research questions to explore that are necessary considerations for implementations of this primitive including:

  • Who can hold tokens, participate and attest?
There are major questions around design choices in who should have access to, participate and benefit from an Alpha Bond economy. Under democratic and locality-based principles, ideally, those involved and local to the project would be signaling project progress, and would share in the fruits of the work being completed. To make this more concrete: What would the ramifications and ethical considerations be in the case of a European bank providing capital for an Indian-based educational improvement program, especially if the bank or other international financiers were allowed to attest and benefit?
  • Should there be an option to restart the curve?
Alpha Bonds are powerful for seed funding, but what are possible additional design choices for project completion? The seed stage provides the opportunity and data to demonstrate the feasibility of an “intervention” and often, once proved, needs continuing financing to gain traction, scale and make long lasting improvements. There could be a design to explore in giving an option to token holders to re-invest or “roll over” payouts in a next phase, or series of funding events, which could be enabled by additional RABC features.

To learn more and suggest your own research questions, check out the RABC model Github Repo, watch this presentation by Research Scientist Shruti Appiah and share your thoughts by commenting on this post. We look forward to collaborating on further research of Alpha Bonds and other Dynamic Bonding Curve designs to improve impact financing and sustainable development initiatives.


Dr. Shaun Conway, Founder & President, ixo Foundation
Jeff Emmett, Token Engineering Researcher, BlockScience
Jessica Zartler, Token Engineering Researcher, BlockScience
Harry T. Goodnight, Lead Executive Advisor, BlockScience

Research, Design, Modeling and Simulation:
Dr. Michael Zargham, CEO, BlockScience
Shruti Appiah, Research Scientist, BlockScience

With special thanks to Nick Hirannet, Kelsie Nabben, Peter Hacker, David Sisson, and Mathilda de Villiers for their feedback.

About ixo

ixo is leading the development of an Internet of Impact. The organization’s digital infrastructure is formed by interconnecting globally and locally distributed blockchain networks that implement the ixo protocol. Regenerative Finance (ReFi) and Impact Verification applications can be built and deployed at an Internet scale through this protocol. The ixo protocol applies the latest decentralised web (W3C) standards for linked-data (JSON-LD), decentralised identifiers (DIDs) and verifiable credentials (VCs). reFi and Impact Verification applications built on the Internet of Impact have the potential to fundamentally change the state of the world.

About Interchain Foundation

Interchain Foundation supports research and development for secure, scalable, open and decentralized networks by participating in research, development, product, community and social good initiatives that align with the ICF vision:

“We believe that open-source, cryptographic, consensus-driven, economic networks hold the key to an anti-fragile global economic system and equal opportunity for all.”

The foundation mandates and provides funding towards these projects. ICF’s current focus lies on the interoperable blockchain technology of the Cosmos Network.

About BlockScience

BlockScience® is a complex systems engineering, R&D, and analytics firm. Our goal is to combine academic-grade research with advanced mathematical and computational engineering to design safe and resilient socio-technical systems. We provide engineering, design, and analytics services to a wide range of clients, including for-profit, non-profit, academic, and government organizations, and contribute to open-source research and software development.

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