Risk-Adjusted Bonding Curves
Risk-Adjusted Bonding Curves
We need additional crypto-economic mechanisms for building more sustainable financing applications, such as tokenised impact bonds, that can dynamically adapt to changing risks over time within complex systems. Let’s begin this experimentation with a risk-adjusted token bonding curve pricing oracle.

First Published on Medium (20 June, 2019)

Are fixed token bonding curves broken?

Most current implementations of Token Bonding Curves only support fixed (invariant) pricing functions. Variant parameters are constrained to the token supply and point-in-time demand (order quantity).

This may reduce complexity, compared to multi-dimensional curves. However, this limitation comes at the cost of informational asymmetries.

…prices are an instrument of communication and guidance which embody more information than we directly have. (F.H. Hayek)

Uni-dimensional bonding curves might not be best suited to complex economies that could (or should?) internalise risks for the larger economy to be sustainable.

Current implementations of token bonding mechanisms cannot account for external systems changes over time, even when such changes can be calculated and have demonstrable probabilistic impacts or create emergent shifts in the economy. Buy and sell decisions are therefore only made on the basis of price which is constrained to unrealistic parameters. Prices can be artificially manipulated and token marketplaces can be shorted to benefit individuals who exploit information asymmetries, at the expense of other participants. Risks are externalised and must be paid for outside of the crypto-economic system. This can have negative impacts on the broader economy in which the crypto-economic system is operating and on which it is integrally dependant. This is not sustainable. The ICO marketplace demonstrated how messy this can get!

Engineering token prices

To-date most implementations of token bonding curves take prospective design decisions (best guesses) about which pricing function to use.
Token engineers make largely untested assumptions about how incentives will play out in the real-world.
This typically starts with sketching out a curve that represents the desired behaviour of the crypto-economic system.
Thereafter a function is identified that seems to best fit this behavioural pattern.

At best, these designs have been formally modelled. A great example is the engineering work on Augmented Bonding Curves by Michael Zargham and his Blockscience team. Computer-aided design for complex adaptive systems (cadCAD) enables us to model and identify the mechanisms and policies that will define the ‘safe space’ in which a given crypto-economic design can play out.
But this is an abstraction of complex adaptive systems that leaves open a large (even if bounded) uncontrollable space, within which there is no information feedback loop mechanism built into the system, other than market demand.

Solving real-world problems

To try fix this, let’s take a real-world example such as Impact Bonds.

The ixo foundation is researching a tokenised impact bond mechanism to provide next-generation financing for development outcomes.
This work is being done in the context of a very large institutionally-financed development impact bond for quality primary education in India.

Impact bonds transfer the operational risks of a development intervention to capital investors. In return, these investors receive financial returns as compensation for the risks. This only fully pays out if the bond delivers predetermined outcomes. The risk premium is accepted as an ‘impact’ contribution (hence the parochial term ‘impact investing’).
The mechanism can also reward intervention implementers with bonus payments for achieving outcomes targets. This could be an effective use of behavioural economics, when the incentive mechanism actually works in practice.

Traditional impact bonds — such as the Development Impact Bond (DIB) for education, typically have invariant terms for duration, coupon value and performance triggers.
Bonds are only issued after the full capital subscription has been realised. This can delay implementation of the intervention whilst capital is being formed.
It also requires ex-ante conviction that the operational risks will be contained within acceptable (predictable) bounds. Risks incur underwriting costs based on assumptions that may or may not be valid.

Life teaches us that prior expectations often don’t play out in complex real-world contexts.

Almost all interventions funded by instruments such as impact bonds could (or should?) be seen as start-up initiatives with unproven assumptions. This includes replicated interventions which are implemented in a different place, time or with any other untested variables.

A new financing mechanism

We need a financing mechanism that responds to new information and changes in risks over time. A financing mechanism that adapts to complex systems with dynamic, risk-adjusted pricing.

Ideally, this should enable startup (seed) capital to be raised to demonstrate the feasibility and promise of the intervention. After the startup phase, this mechanism should provide continuous funding (or a series of funding events) for the project to scale towards achieving its desired future-state outcomes.


We describe this adaptive impact financing mechanism as an alpha-bond.

The implementation requires a risk-adjusted bonding curve pricing curve signal, using a variant co-efficient (alpha) to statistically determine the probability of the bond achieving its targets.
In an ⍺Bond future-state outcomes programmatically trigger payouts to investors (and implementors) when milestones and targets have been reached.
Using this risk calculation at a given point in time could produce a risk-adjusted price for an ⍺Bond token by integrating the alpha coefficient as a modifier on the bonding curve.

If participation in a bond is liquid, investors can enter and exit the investment pool by trading their debt tokens (against an automated market-maker smart contracts, for instance), at a price that incorporates this risk information.

A novel pricing function

Variable power functions that are adjusted by an alpha coefficient could be a novel way of implementing Token Bonding Curves.

We want to build this as a trustless generic pricing oracle that can be called as a function by any application. The first software client will be developed and tested as a module in the Cosmos SDK, as an extension to our Cosmic Bonding module prototype. This will make the pricing oracle available to any application that implements the module in an application blockchain.

In a future article I will attempt to describe how risk can be deterministically calculated to derive the alpha coefficient by using the ixo protocol to measure and verify the performance of a project over time.