Brinc: Decentralized Currency with Intrinsic Value

The Brinc Team

06.15.2021

1. Abstract

In this paper we will propose a BRC decentralized cryptocurrency managed by a bonding curve algorithmic smart contract where the price of a token is an increasing function of supply. The BRC token provides intrinsic value by holding a basket of on-chain cryptocurrency reserves with public market value which also provides redemption value and a lower bound on price; and sustainable economic incentives by distributing all protocol fees and staking rewards to token holders. The use case for the BRC token will be on emergent decentralized lending applications where both stability and intrinsic value is provided.

In this paper we will propose a BRC decentralized cryptocurrency managed by a bonding curve algorithmic smart contract where the price of a token is an increasing function of supply. The BRC token provides intrinsic value by holding a basket of on-chain cryptocurrency reserves with public market value which also provides redemption value and a lower bound on price; and sustainable economic incentives by distributing all protocol fees and staking rewards to token holders. The use case for the BRC token will be on emergent decentralized lending applications where both stability and intrinsic value is provided.

2. Introduction

Bitcoin is a peer-to-peer electronic system with a coin that was designed to operate as electronic cash. The extreme volatility in Bitcoin’s trading price on cryptocurrency exchanges has raised questions about its value and how to determine that value. The market value of Bitcoin can be viewed in its trading price and market capitalization, however, we need to determine whether or not there is actual intrinsic value¹ to support the publicly-available market value. Like, money or gold, Bitcoin does not have intrinsic value and its primary function is as a currency. However, money and currencies are mediums of exchange and must provide a store of value or the ability to maintain a relatively stable value over time. Bitcoin and most cryptocurrencies are weak stores of value as observed in their extreme price volatility. Cryptocurrencies do not have intrinsic value to justify their prices and are not a good form of money because of their price volatility. However, cryptocurrencies are a compelling currency option specifically because they do have a level of intrinsic value due to their blockchain technology and the fact that their integrity as a payments system can be trusted.

¹In financial analysis, intrinsic value is the inherent value of an asset and its cash flow, which is calculated using a valuation method as opposed to the publicly-traded fair market price of that asset.

There are now over a hundred stablecoins which have grown in popularity by seeking to solve crypto’s price volatility problem and these fall into three broad categories: 1) Asset-backed and stored off-chain; 2) Asset-backed with collateral stored on-chain; 3) Algorithmic with no collateral. 95% of stablecoins are asset backed and 65% of all stablecoins are backed by collateral and held off-chain. [1] The most popular choice is asset backed and pegged to the USD [2], but in reality, there are logistical and regulatory challenges with physically storing fiat currency at banks. Tether  has been successful in maintaining a price pegged to the US dollar and has gained user traction by surpassing Bitcoin in terms of transaction volume in 2019, however, management has refused to provide any documentation attesting to their actual reserve holdings of US dollars and recently claimed that only 67% of all USDT issued is backed by USD. [3] Fiat-pegged stablecoins may be a better form of electronic money, however, they rely on third-party financial institutions to process transactions and verify reserves, which contradicts the core principle of Bitcoin’s peer-to-peer trustless system. [4]

The U.S. Federal Reserve has invoked QE4 –the fourth round of quantitative easing measures and a zero interest rate policy resulting in higher levels of inflation. Therefore, any stablecoin that is pegged 1:1 to the USD will depreciate by 3.65% per year. [5] Furthermore, annual issuance of new coins/tokens on a blockchain network is a form of cryptocurrency inflation and is determined by the block time and block reward and is distributed to all the validators of transactions on these networks. Bitcoin currently has a mining inflation rate of 1.8% [6] and Ethereum with a rate of 4.1% [7], however, the latter is transitioning to a Proof-of-stake consensus mechanism and the expected rewards rate will launch at 20.3% and gradually decline to 4.6%. [8]  Staking has been gaining popularity as the barriers to entry are low and the reward payouts high; there are currently 120 yield-bearing assets with an average reward rate of 14.05%. [9] Staking is replacing mining and QE as a new form of inflation for cryptocurrencies at significantly higher rates. 

The BRC token offers price stability but reverses the inflation which is inherent in cryptocurrencies and stablecoins, by gradually increasing the price of the token via a bonding curve algorithm which sets price as an increasing function of supply. Further, all fees generated in the minting and burning of BRC tokens will be redistributed back to those holders in a sustainable staking rewards model. What makes the BRC token unique is that it provides intrinsic value as it bonds multiple cryptocurrencies into a reserve pool. The BRC token will minimize price volatility and provide a store of value as its price will be tied to the market value of the underlying asset reserves. 

3. Brinc - System Overview

BRC is a reserve-backed cryptocurrency that will be issued and backed in an equivalent amount and value of major cryptocurrencies: BTC, ETH, and DAI (“Reserve currencies”). The BRC token(s) will be minted by the protocol when BTC, ETH or DAI is deposited; alternatively, if a user wishes to sell their BRC token(s) they can return BRC to the protocol and select a reserve currency they would like to receive in return. The transactions are handled by Ethereum smart contracts and all reserves are also held in smart contracts so as to ensure decentralization and a trustless structure.

BRC will be an ERC-20 token issued on the Ethereum blockchain and will conform to the standard specifications as per the Ethereum Improvement Proposals. [10] All transactions will be conducted via smart contracts. Bitcoin, or BTC, coins will also be transacted on the Ethereum blockchain via wrapped BTC (WBTC). WBTC is an ERC-20 token that is backed 1:1 by Bitcoin held in custody. The “wrapping” standardizes Bitcoin to the ERC20 format which makes it possible to write smart contracts for transactions. [11]

Figure 1: BRC System Flowchart

4. Continuous Token Model

The BRC token will be issued as a continuous token which has a continuous price and minting function and a limitless supply. To buy a BRC token, a buyer sends an amount of reserve currency e.g. ETH to the bonding curve contract’s buy function which calculates the price of the token in ETH and issues an amount of BRC tokens. To sell BRC tokens, the contract will calculate the BRC token’s current selling price and will send the correct amount of ETH. Token prices are calculated by a bonding curve algorithm. [12] With the continuous token model, the cost to mint the token however increases as demand for the token increases. The cost decreases if people opt to withdraw their token from the supply and retrieve their ETH from the pool. Thus, depending on the current supply, the cost to mint the token is based on an algorithm set in the smart contract which has a primarily linear curve, combined with a logarithmic or exponential curve.

5. Bonding Curve

The token price and supply is managed by a bonding curve contract which is a smart contract based on a mathematical formula that defines a relationship between the price and token supply. [13] The bonding curve will be based on a curve where price increases as the supply of the token increases and the growth rate in price accelerates as the number of tokens minted increases. When a person has purchased the token, each subsequent buyer will have to pay a slightly higher price for each token, generating a potential profit for the earliest purchasers. As more tokens are purchased the value of each token gradually increases along the bonding curve. We can calculate both the price and quantity of new tokens minted on the bonding curve given the timing of when a reserve deposit of Ethereum is made. [14]

Figure 2: Bonding Curve

6. Token Price and Supply Calculations

A reserve ratio represents a fixed ratio between the token’s total value (total supply × price) and the value of its reserve token balance. This ratio will be held constant by a formula as both the reserve token balance and the token’s total value (i.e. market capitalization). Since each purchase or sale of a token results in an increase or decrease of both reserve tokens and the tokens, the price of the token with respect to its reserve tokens will continuously recalculate to maintain the configured reserve ratio between the two tokens. We can calculate the dynamically changing price of the token by applying a constant reserve ratio, which is based on the Bancor system formulas and are calculated as [15]:

(1)

Where: F is the reserve ratio of the token, R is the reserve token balance, S is the token supply, and P is the token price. The reserve ratio determines the price sensitivity of the continuous token and at different reserve ratios. A higher reserve ratio between the reserve currency balance and the token will result in lower price sensitivity, meaning that each buy and sell will have a smaller than overall effect on the token’s price movement. Alternatively, a lower ratio between the reserve currency’s balance and the token will result in higher price sensitivity, meaning that each buy or sell will have a larger effect on the token’s price movement. The current price can be determined through the formula above if given f, r, and s:

(2)

In order to calculate price when more than one token has been purchased requires integral calculus, as the price of each incremental token purchased is different and based on the bonding curve. Therefore, we need to compute the area under the bonding curve (Figure 2) that applies to the amount of tokens purchased. From the original formula, we can calculate: the total number of reserve tokens paid, Number of tokens received, the new price of token, and new token supply. When an infinitesimal amount of tokens, dS, are bought, the supply of tokens increases by this amount. The price in reserve currency for these tokens is P dS, which are added to the reserve, meaning dR = P dS. Also, since R = FSP, we have dR = d(FSP) = Fd(SP) = F(S dP + P dS), which can be solved to:

(3)

(4) above provides the price of the new token given a change in supply. If a user is buying more than one new token, T, then we can calculate the total amount paid, E, by applying integration as follows:

(4)

With the value for E, the total amount paid in reserve currency units, we can solve for T, which is the number of new tokens given E:

(5)

The BRC protocol will allow multiple reserve currencies that can be used to purchase BRC tokens. If there are m different reserve currencies, then for each currency i ∈ {1,2,…,m} we have an amount in reserve Ri, fractional reserve ratio Fi, and price Pi. Buying and selling tokens with one reserve currency i will affect the price of the BRC token while maintaining the same supply of the other reserve currencies. Given that there are R0 outstanding tokens and reserve ri0 of each currency i, we can solve for the supply of tokens s given multiple reserve currencies and the amount of T tokens received given R1, R2, R3,…m tokens paid can be solved as: [16]

(6)

(7)

A reserve ratio represents a fixed ratio between the token’s total value (total supply × price) and the value of its reserve token balance. This ratio will be held constant by a formula as both the reserve token balance and the token’s total value (i.e. market capitalization). Since each purchase or sale of a token results in an increase or decrease of both reserve tokens and the tokens, the price of the token with respect to its reserve tokens will continuously recalculate to maintain the configured reserve ratio between the two tokens. We can calculate the dynamically changing price of the token by applying a constant reserve ratio, which is based on the Bancor system formulas and are calculated as [15]:

(1)

Where: F is the reserve ratio of the token, R is the reserve token balance, S is the token supply, and P is the token price. The reserve ratio determines the price sensitivity of the continuous token and at different reserve ratios. A higher reserve ratio between the reserve currency balance and the token will result in lower price sensitivity, meaning that each buy and sell will have a smaller than overall effect on the token’s price movement. Alternatively, a lower ratio between the reserve currency’s balance and the token will result in higher price sensitivity, meaning that each buy or sell will have a larger effect on the token’s price movement. The current price can be determined through the formula above if given f, r, and s:

(2)

In order to calculate price when more than one token has been purchased requires integral calculus, as the price of each incremental token purchased is different and based on the bonding curve. Therefore, we need to compute the area under the bonding curve (Figure 2) that applies to the amount of tokens purchased. From the original formula, we can calculate: the total number of reserve tokens paid, Number of tokens received, the new price of token, and new token supply. When an infinitesimal amount of tokens, dS, are bought, the supply of tokens increases by this amount. The price in reserve currency for these tokens is P dS, which are added to the reserve, meaning dR = P dS. Also, since R = FSP, we have dR = d(FSP) = Fd(SP) = F(S dP + P dS), which can be solved to:

(3)

(4) above provides the price of the new token given a change in supply. If a user is buying more than one new token, T, then we can calculate the total amount paid, E, by applying integration as follows:

(4)

With the value for E, the total amount paid in reserve currency units, we can solve for T, which is the number of new tokens given E:

(5)

The BRC protocol will allow multiple reserve currencies that can be used to purchase BRC tokens. If there are m different reserve currencies, then for each currency i ∈ {1,2,…,m} we have an amount in reserve Ri, fractional reserve ratio Fi, and price Pi. Buying and selling tokens with one reserve currency i will affect the price of the BRC token while maintaining the same supply of the other reserve currencies. Given that there are R0 outstanding tokens and reserve ri0 of each currency i, we can solve for the supply of tokens s given multiple reserve currencies and the amount of T tokens received given R1, R2, R3,…m tokens paid can be solved as: [16]

(6)

(7)

7. BRC Bonding Curve Simulation Model

BRC will employ a different Reserve ratio approach by setting the total reserve ratio initially at 70%. This will allow for the value of the supermajority of reserve assets (BTC, DAI, et al.) to be reflected in the intrinsic value of the BRC token as the reserve assets can all be marked-to-market and the net asset values can be summed to calculate the value of a BRC Token while minimizing the effects on price slippage caused from the price elasticity of a lower reserve ratio.

In the example below, it was assumed that there was only one reserve token, DAI, with an initial supply of ten (10); the initial BRC token supply was 100,000 which results in a BRC token price of 0.000143 BRC/DAI. In the above simulation, ten (10) DAI are paid which mints 62,450 BRC tokens with an ending price of 0.000176. This represents a price increase of 23% and a supply increase of 62%. In the second scenario, 50,000 BRC tokens are sold and the bonding curve algorithm will return 6.2850 DAI with a new BRC token price of 0.000106. This represents a 21% decrease in the BRC token price and 50% decrease in token supply.

Table 1: Bonding Curve Pricing Algorithm

ParameterNotation 
Reserve currency (DAI)R0 
Token supply (BRC)S0 
Reserve ratioF 
Price of token (DAI)P 
Reserve supply (DAI)R 
New token price (BRC)P 
No. of tokens received (BRC)T 
Amt paid for tokens (DAI)E 
New token supply (BRC)S 
   
AssumptionsCalculationsDetails
Reserve supplyR1,000
Token supplyS1,000,000
Reserve ratioF = R / (S * P)70%
Current token priceP0  = R / (F * S)0.001429
   
Reserve paidE = R0 ((1 + T/S0)^1/F –1)10
Tokens receivedT = S0 ((1 + E/R0)^F – 1)6,990
New Token priceP1 = (S /S0)^1/F * P00.001433
%price incr.δP = (P – P0)/P00%
New Reserve amtR = R0 + E1,010
New Token supplyS = S0 (R /R0)^F1,006,990
% chg in supplyδS = (S – S0)/S01%
   
Selling Tokens  
Tokens paidT = S0 ((1 + E/R0)^F – 1)50,000 
Reserve currency receivedE = R0 (1 + T/S0)^1/F – 1)72.1867
New Reserve currency amtR = R0  –  E927.8133
Token priceP = (S/S0)^1/F * P00.001398
Change in token priceδP = (P – P0)/P0-2%
New token supplyS = S0 (R/R0)^F948,904
Change in supplyδS = (S – S0)/S0-5%

Figure 3: BRC Bonding Curve

8. Intrinsic Value

Underlying asset value

One of the core value propositions of the BRC token is that it provides for every token minted an equal value of one or more cryptocurrency assets in reserve. Therefore, the BRC tokens are backed by underlying cryptocurrency assets. This differs fundamentally from other cryptocurrencies which have no underlying asset values or cash flows. As the BRC protocol will hold 70% of the value of its BRC token market cap in the value of reserve currencies, it should maintain a minimum value at or near this minimum floor value.

The BRC currency is always equal to the sum of the values of the reserve currencies that are held in bond (reserve) in terms of quantity of currencies rather than the market value of the currencies. In order to obtain a market value for the BRC currency, V, the current market values, mpi, of the underlying reserve currencies, ri, could be marked-to-market and summed in order to obtain a current market price.

(8)

(9)

If the market price of one or more of the underlying reserve currencies increases then the intrinsic value of the BRC token price will rise; conversely, if the market price of one of more of the underlying reserve currencies decreases, the intrinsic value of BRC’s market value will fall.

Application Fees

The Brinc application will charge x% fees on the purchase transactions of BRC tokens, whereas 0 < x <1%. On the sale of BRC tokens, the fees charged will be y%, whereas y > x.  The fees will be deducted from the Seller’s return of reserve asset i.e. ETH which maintains the reserve balance and outstanding number of BRC tokens in supply. The protocol fees will be used for the operation of the BRC protocol and any remaining fees after the deduction of operating expenses will be distributed to token holders in the form of a staking reward or bonus dividend.

9. Governance

The BRC token will not mint a fixed number of tokens for sale in an ICO nor allocate and distribute any funds to founders.  All purchases of the BRC token will go directly into reserve smart contracts for the sole purpose of minting tokens and creating value directly for the BRC protocol.  Governance of the protocol and operations will be determined by holders of the BRC Governance token (gBRC) token and proposals and votes on all changes to the Brinc protocol will be initiated by any token holder, subject to certain minimum levels.  Proposals and periodic votes will occur in order to address issues that will help determine key decisions made for both the BRC price currency and the decentralized finance application: reserve ratio, inclusion/removal of reserve currencies, collateral requirements, interest rate policy changes, et al.

10. Application: Decentralized Finance

Decentralized lending is cheaper than traditional financing methods by eliminating fees charged by intermediaries. Other perceived benefits are: full custody users’ funds, lower set up costs/times, immutability and censorship resistance, transparency and efficiency, and capital mobility across platforms. [17] MakerDao pioneered the successful implementation of decentralized lending on the Ethereum blockchain through the use of smart contracts. This allowed users to borrow a cryptocurrency-backed DAI token by depositing ETH as collateral on loans.[18]  Whereas, MakerDao offers only one asset that can be borrowed, DAI, other leading lending protocols provide decentralized lending on multiple assets. 

Existing lending platforms appear to have overstated market sizes (i.e. supply of crypto assets) and the utilization rate of 16% on those assets are too low. This means that users are not borrowing and that the market size for defi lending is misleading. The BRC protocol will add a decentralized lending application which will allow anyone to create a loan market for ERC-20 tokens. The key features of the lending platform will be to make improvements on the borrower’s experience with a particular focus on overcollateralization of loans, collateral liquidations, greater economic incentives, and ease of use for both borrowers and lenders

11. Conclusion

The BRC currency allows for a cryptocurrency to have intrinsic value and increasing returns to scale, while maintaining the fundamental principle of decentralization and independence from financial intermediaries. The BRC token will provide: 1) price stability through redemption value as tokens can fully backed with collateral so as to create a lower bound on price; 2) Transparency of reserves by maintaining reserves on-chain at all times; 3) Liquidity of supply as buyers and sellers can continuously trade with the smart contract directly; 4) Intrinsic value of the underlying reserves and fee revenue from trades of the BRC token 5) Price appreciation inclination increasing returns to scale with increases in the supply, redistribution of all protocol fees, and incremental rewards from the launch of a defi application . 

BRC is a next generation token offering that solves for the underlying challenges and inefficiencies of competing cryptocurrency solutions while delivering a superior tool for defi applications. This blend of stability, transparency, liquidity and intrinsic value combine to deliver a cutting-edge, value-packed token that is poised to have a significant impact on the cryptocurrency market.

References

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 [13] Simon de la Rouviere, Tokens 2.0: Curved Token Bonding in Curation Markets, Nov. 21, 2017; https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5   

 [14] Slava Balansanov, Bonding Curves in Depth: Intuition and Parametrization, Dec 14, 2018; 

https://blog.relevant.community/bonding-curves-in-depth-intuition-parametrization-d3905a681e0a  

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