How Founders DAO reinvented the Bonding Curve?

What is a bonding curve?

A Bonding Curve or Token Bonding Curve (TBC) is a mathematical function defining the relationship between price and token supply.
This function is used to define the buying and selling price of a token making the bonding curve an automated market maker and provides an always available source of liquidity. Thus, the bonding curve sells tokens to users by calculating the average price of the token and minting them after payment.

The most fundamental advantage of bonding curves over traditional asset pricing mechanisms is that asset pricing is transparent, defined and immutable at all stages.

The bond curve can be defined by a multitude of mathematical functions to fit most situations. Here are four examples of bonding curves:

(Going from top left to bottom right) Sigmoid, quadratic curve, negative exponential curve, linear (non-increasing) curve (source: https://medium.com/linum-labs/intro-to-bonding-curves-and-shapes-bf326bc4e11a)

The first project to have proposed the use of a bonding curve is Bancor, the first Automated Market Maker built on smart contracts. The objective of the bonding curve was then to allow an immediate liquidity of the newly created tokens.

Many projects have followed Bancor’s example and have optimized/complexified their bonding curve to meet specific needs. For example, recently Uniswap modified its hyperbolic bonding curve to segment it into several straight lines concentrated around specific price ranges to achieve better capital efficiency for liquidity providers.

Bonding Curve: Pros and cons

The main advantages of the Bonding Curve can be summarized in 4 points:

• The first advantage of a Bonding Curve is the instant liquidity. Tokens can be bought and sold instantly, the bonding curve serving as an automated market maker.
• The second advantage is collateralization.The mint of the tokens by the bonding curve is produced against a predetermined collateralization. Indeed, each token is minted after payment, thus, all the tokens in circulation are linked to the available reserve. This relation is called Reserve Ratio (see section Intrinsic value of the $FNDR)
• The third advantage is the deterministic price. The buying and selling prices of the tokens go up and down according to the number of minted and burned tokens.
• Finally, the fourth advantage is the fairness for the whole community — During a token sale by TBC, there is no pre-sale allowing some people to buy the token at a reduced price thus avoiding arrangements between investors.

The biggest disadvantage of the classic bonding curve is the speculation effect. Indeed, the price of the token being linked to the number of tokens in circulation, the late buyers of the token take the risk that the early buyers of the token resell their tokens in the TBC making the price of the token fall. That is why the TBC does not protect the buyers from a fall in the price of the token and speculation is created on the timing of purchase and sale of the token in the TBC. This speculation is a real drawback creating a volatility of the token and limiting the trust of the investors.

Why is the FNDR Bonding Curve different?

The FNDR bonding curve is a combination of all the advantages of the classic bonding curves while eliminating their main drawback.

The Bonding Curve created by Founders DAO, ensures that each new token is more expensive than the previous token. Accordingly, each participant knows exactly how much each new token will cost at any given time. Since the new tokens have the lowest price at the lowest part of the curve (when supply is also low), early buyers have a considerable upside potential in comparison to later entrants to the market.
The bonding curve’s mathematical model advantage, over traditional asset pricing mechanisms, is that such asset pricing based on its supply is transparent, defined, and immutable at all stages.

The price of the FNDR token is fixed by the bonding curve F(x), where x indicates the number of FNDR :

The constant c indicates the initial value of the token. The rate of price increase is directed by the constant k. The constant a is the difference in price acceleration between phases 1 and 3, allowing to partially preserve a price increase on a more slowly increasing supply.
In its first phase, the bonding curve is a linear function. In its second phase, the rate of price increase is a squared function. Finally, in its third phase, the function decelerates and becomes again a linear function.

This bonding curve reflects 3 key stages of the protocol :

• The first phase corresponds to the installation of the protocole and a period of acquisition of the first user base.
• The second phase is an important growth phase allowing to move to a larger scale of financing for DAOs.
• The third phase is a stabilization linked to the maturity of the protocol.

The bonding curve can be represented by the following graph:

The bonding curve driving the FNDR minting price is composed of 3 distinct phases, allowing the FNDR price to experience different acceleration phases:

• The initial price of the FNDR is 0.01 USD.
• The first phase represents 1 billion USD in staking returns, equal to 2.5 billion FNDR minted. At the end of phase 1, the price of FNDR will be 0.79 USD.
• The second phase acceleration lasts for 9 billion USD of staking yield and stops at the mint of the 3,250,743,991th FNDR token. At this moment, the FNDR will have reached the price of 25.06 USD.
• Finally, the third phase has a directing coefficient 5 times higher than the first phase, which fixes the rate of price inflation.

The price increase de facto leads to FNDR increased value in the liquidity pools. It also helps to prevent pump and dump schemes.

Typical price evolution and yield reserve according to the number of FNDR tokens:

Intrinsic value of the FNDR

The value of the FNDR is assured by the existence of the corresponding capital that will be released for the DAOs.
So the minimum value of the FNDR corresponds to the following formula:

The minimum guaranteed value of the FNDR can then be represented by the following graph:

The intrinsic minimum value of FNDR obviously corresponds to a smoothed version of the Bonding Curve F(x) and is therefore also composed of the 3 phases with an acceleration phase after phase 1.

The minimum intrinsic value is therefore guaranteed. The intrinsic value of the FNDR can mathematically only grow. And the maximum value of FNDR is not bounded.

Simulation of the intrinsic value of the FNDR under three scenarios

Let’s simulate scenarios of the FNDR intrinsic value. In the figure below:

• The blue series represents the mint value of the FNDR token on the minted FNDR quantity. And the black series represents the minimum guaranteed value of the FNDR.
• Then, the red series represents the worst possible scenario. This scenario corresponds to a minimal investment in the DAOs (only the mandatory 20% of the mutualized investment pools) and no DeFi returns on all capital.
• The yellow series represents a medium scenario, corresponding to an average investment in DAOs (50–60% of FNDRs) and a low DeFi return on all capital (3%).
• Finally, the green series represents the best possible scenario, corresponding to a strong investment in DAOs (90+% of FNDRs) and a good DeFi return on all capital (15%).

Conclusion

By optimizing the Bonding Curve concept, Founders DAO helps create a fair and transparent investment system. Investors have control over their investments and can make accurate projections of their earnings while being assured of a known, lower purchase price of the token from the next investor. Accessible to everyone, from small holders to the wealthiest, in an equitable way, the Bonding Curve integrated into Founders DAO’s Tokenomics enables the creation of an ecosystem to finance and build the DAOs of tomorrow.

Let’s build the Web3 together!
For a greater decentralization of our economies, for a broader contribution from and back to our communities, for a positive ESG impact (Environmental, Social, Governance) on our societies and our Planet.

🌐Website: https://www.foundersdao.io
🐦Twitter: https://twitter.com/FoundersDAO_
👨‍🏫LinkedIn: https://www.linkedin.com/company/foundersdao/
💬Discord: Coming Soon!