BOND tokens

BOND tokens are a variation on REP tokens which have slightly different powers. The primary purpose of issuing BOND tokens is to raise capital. Additionally BONDs can be constructed to incentivize and reward different behaviors, such as bounties for work, founder’s valuation, investment, and power revaluation. This page discusses these applications after detailing the general design and valuation of BOND tokens.

Overview

Suppose a DAO wishes to raise capital, say for the purpose of incentivizing improvement in one of the DAO’s smart contracts, by offering a bounty for development. Centralized companies in a traditional economy have several options. First, they can maintain a treasury of capital holdings for the purpose. This is suboptimal due to holding costs. A second option is to secure a loan, which is suboptimal because they would be paying an outside fee. Third, they can issue stocks, which carries the threat of diluting power, eroding faith in the company, and inevitably the market for stocks is not perfectly efficient. In some cases a fourth general option is ideal, to issue bonds. Bonds avoid some of the pitfalls of the previous three options. Like a loan, a bond can be constructed with a payout schedule which optimizes for the company’s current purpose, for instance paying out at a particular future time when the company expects a contract to close. Further, bonds do not have the same collateral security requirements. Finally, the most likely bond purchasers will be most familiar with the company, and will be more likely to have a predilection for improving the company so their bonds are secure, instead of harming it (by shorting the stock, e.g.). Thus bonds have the added advantage of building solidarity.

Many DAOs have implemented the obvious solution to raising capital, building a treasury. Many blockchain networks have amassed a treasury by setting aside ICO money, or by taxing their transactions with a fractional fee in order to build such a reserve to pay for future development or paying off early investors. The existence of a treasury gives the signal that the DAO is valuable, which is often used to attract more investment before the DAO begins to earn outside fees. However the holding costs of such a fund are entirely wasted, which betrays their unsophisticated design.

The already suboptimal solutions of loans and issuing equity are exacerbated in a decentralized environment. Traditional loans are fundamentally more difficult for a decentralized blockchain-based organization to secure than for a centralized company because of coordination problems with a group that is owned by a dynamically shifting multitude of international pseudonymous participants.

With the new technology of smart contracting, however, we have more tools available. A DAO can now make a type of internal loan. A DAO may arbitrarily choose to mint a new type of reputation token, called a BOND, that will algorithmically pay off their bounties later, through smart contracts.

There are several types of contracts that can be made in the attempt to match the BOND reward to the proposed bounty $b$. Assuming no treasury, the BONDs are paid out by the DAO’s REP salary as fees come in. The DAO is not in control of when outsider customers may choose to engage the DAO’s Work Smart Contract and pay the DAO fees. Therefore, without resorting to a treasury and its attendant holding costs, there is necessarily some variability in some aspect of any BOND, whether it be the rate of payout, the lifetime of the BOND, or the amount ultimately paid. However, BONDs can be designed which mitigate for any of these factors.

Mechanism design

We calculate the formulas for the lifetime $L_{B}$ and the quantity $q$ of BOND tokens needed to accurately match the cash value $\$b$ of the BOND given different payout schedules. The general theory that dictates these formulas is REP tokenomics.

Given the choice of one or more of these variables as random, we can solve for the formula that will determine the rule for the chosen BOND type. The rate of payout and the BOND lifetime $L_{B}$ are dependent on each other and constrained by the payout $\$b$. With those targets, the types of bonds break down as fixed-period or variable-period contracts.

Fixed Period, Risky Payout

Main page: Fixed-period BONDS

Given a fixed pay period $L_{B}$ the developer is given the number $q$ of BOND tokens that match $\$b$ based on the present value. This amounts to solving the equation $qPVf_{B}^{1}=b$ for $q$. Once $q$ and $L_{B}$ are fixed, the payout will be a random variable, with expected value $\$b$.

This solution leaves the ultimate value of a BOND token to chance, dependent on the random variables of the fee rate $f'$, the interest rate $r$, and the number $R$ of other BOND tokens that will be minted during the time $t<L_{B}$. The actual payout will depend on how accurate your estimates of these random variables are. However, the contract itself is deterministic (i.e., fixed). It performs algorithmically as promised, though the ultimate payout is a gamble.

Almost every traditional financial tool has similar risks. For example, even the instrument which seems like the most predictable contract possible, a long-term fixed-rate bond, actually carries the risk that the interest rates will grow higher than expected before the bond expires, which changes the bond’s ultimate valuation.  

However, there is an approach that eliminates even this risk:

Riskless Contracts

Main page: Riskless BONDs

An approach that can eliminate some or all of the randomness is to make the lifetime $L_{B}$ a stopping time. In this case, a smart contract is made to pay a certain quantity $q$ of artificially minted BOND tokens. In this case $q$ is directly related to the rate at which the BOND is paid off. Then the lifetime $L_{B}$ of a token is set to depend on the actual fees $f'$ the DAO brings in.

The technical terminology is that $L_{B}$ is a random variable, called a stopping time, which is determined by the stochastic process given by the incoming fees $f'$ and interest rate $r$ random variables.

There are two approaches to

a. (Fixed payout)

The lifetime can simply be set to end once  is matched in fees, then the rate will be of prime importance when deciding how valuable the BOND reward is. The rate depends on  and . Since  is a random variable, the stopping time  is a random variable. If  is large, then even though the contract is eventually guaranteed to pay out , the present value of this solution still depends on chance.

A better solution, one that does not depend on chance, is as follows:

b.      (Fixed present value payout)

To account for the time it takes to pay out  fees, we can include the present value calculation in the lifetime . This financial instrument uses the programmable contract to absorb all randomness (if you trust the oracle dictating the varying value of ). This solution gives a guaranteed payout of exactly  in present value calculated from the time the BOND was minted. In this case, the BOND pays out more than  in fee salaries over the course of its lifetime (assuming ) stopping only when the present value is reached. This is analogous in some ways to a floating rate bond, and in other ways to a student loan which has a predetermined payback schedule that depends on the student’s future salary.

In all these cases, besides the lifetime  the major consideration is the quantity  of BOND tokens minted for the reward . For a fixed reward, the quantity  will always be inversely related to the lifetime  that is set for the BOND tokens. The reason is that the quantity  is directly related to the rate of the fees that the rewarded BOND tokens earns, so larger  means smaller  is needed to match the value of any fixed  bounty.

To find the rules that implement these different types of BONDs, we use the REP valuation formulas derived above. We pick some basic types of BONDs that illustrate the method. Many other formulas can be derived using these tricks, such as when the DAO wishes to delay the BOND payout for an arbitrary period.

Fixed-period contracts

Suppose we pay a developer with  newly minted BOND tokens, which dilutes the total REP in the DAO as fees are now shared with the  tokens. The number  of tokens determines the rate of payout, as a larger  means a larger share of the REP salary. The exact rate of payout for  BOND token is proportional to the incoming fees as

1.1.1      Infinite lifetime

Under the assumption that REP lifetime is unbounded, , then the income stream  of one BOND token is the same as a REP token

In general, we have  The term  represents all the BONDs which are active at time .

Now suppose you want to find the lifetime  of a BOND that will give an expected payout of  for  tokens. We therefore hope to solve the equation

However, the terms  and  are complicated.  is a stopping time, and  is a stochastic process. Nevertheless, these terms behave relatively well, since we know the expected value of  will be an increasing function of , because  is increasing, because . Simply taking the expected value

setting it equal to  and solving for  gives you the desired stopping time . There is no simple formula for the expected values of fractions, so we make no further elaboration of the general case in this presentation. However, Jensen’s inequality allows us to give an estimate of the general case, and the following calculations give an upper limit.

Now assume the rate of fees is constant  and no further BOND tokens are minted during the lifetime . Then there is a minor change in the previous formulas

Therefore, to pay a developer  tokens that will have payout with value  at time  we solve the equation

for . We get

Further, we can find the present value of a single BOND token with arbitrary lifetime  under the assumption of constant fees is

Therefore we have the following solutions:

Proposition 5: Assume the rate of fees is constant  and that no further BOND tokens are minted during the lifetime .

Then  BOND tokens will have payout  by time  at a payout rate of  by setting the lifetime of a BOND to be

To pay a developer  BOND tokens with arbitrary predetermined lifetime  that will have present value worth  solve the equation for

Equation 7

Equation 7 has no elementary solution, but admits efficient solutions through standard numerical algorithms. However, next we assume the REP tokens have finite lifetimes which guarantees explicit elementary solutions.

1.1.2      Finite lifetime

Next, we consider the situation when there is a finite lifetime on all tokens. We make the further assumptions of constant minting ratio  and constant fees . We assume the BOND tokens are minted after the system reaches equilibrium. In this case, there are always  of the REP tokens in the system. Then diluting the system with  artificially minted BOND tokens at time  which have the same lifetime  gives

So

Therefore we solve the equation

for   to get

Proposition 6: Assume the rate of fees is constant  and the lifetime of all tokens is . To pay a bounty with present value worth  a DAO can mint  BOND tokens where

Similar calculations can be made to get the formula for the number  of BOND tokens when we choose the lifetime  independently of the lifetime  of the normal REP tokens.

The major problem with these formulas is that the assumption that the rate of fees  is constant is usually false. The above solutions make BONDs a gamble for both the developer and the DAO. If the rate of fees  increases during the lifetime  then the reward’s value will be greater than , and if the rate of fees decreases it will be worth less. However, as mentioned above, Jensen’s inequality gives us a bound, showing these results are conservative. Specifically, if the fees’ rate is not constant, but that the fees merely have expected value  then these formulas will be generous to the BOND holder. If however, the actual values of the fees have an average less than this expected value, the BOND holders can still end with less than  remuneration in present value.

We can eliminate those uncertainties with riskless contracts, discussed next.

1.2     Riskless contracts

Bonds issued by a government may be considered risk-free in the sense that they are guaranteed by force of law to pay out as they are advertised. DAOs can issue BONDs with similar contracts guaranteeing any fixed payout, which can be assured by self-executing smart contracts, as long as the DAO remains solvent. But such contracts, with pre-determined end dates and values still carry risk, in the sense that the interest rate may increase during the tenor of contract, so the fixed return on the bond may ultimately have a lower present value than expected.

In this section we eliminate even this type of risk, using the same basic REP tokenomics equations. We simply make the lifetime of a BOND token into a variable which is dependent on the actual fees the DAO earns, instead of the expected fees as before. The basic idea is that the variable lifetime   of a riskless BOND will grow if the fees shrink or the interest rate increases, and the lifetime will shrink if the fees grow or the interest rate decreases. Technically, a riskless contract makes the lifetime of the BOND  a stopping time of the stochastic process given by the fees. The smart contract governing the BOND tokens uses the record of fees to determine the expiration date dynamically, which guarantees the present value of the  BOND tokens at the time of issuance will be precisely .

Remember the income stream for a BOND token is

for time  The present value of a single BOND token is

We assume  tokens are minted to make a reward of value . We use  to denote the total number of BOND tokens that are earning reputational salaries in the DAO at any given time , which includes  and any other BOND tokens that have been minted during the relevant time period. Combining these facts gives the following result.

Proposition 7 To pay a bounty of  BOND tokens minted to have exact initial present value  make the stopping time  as the random variable that satisfies the formula

This formula works under general assumptions, as any of the terms may be variable. The result is not as deep as all the technical terminology might make it seem. The basic idea is simple. First, keep track of the random processes given by the fees , the new BOND tokens added , and the interest rate . That simply means we record the history of their values. Then the stopping time  is reached at the first time  that the above equation is satisfied. The stopping time is merely the moment we end the fees paid to the  BOND tokens. When programming the smart contract which controls this financial device, the integral simply becomes a sum, and the stopping condition is given by an IF THEN statement. The only variable that poses any difficulty in decentralized environments is the interest rate , which requires an oracle, since the other two variables,  and , are automatically recorded.

Proposition 7 gives a means for calculating the expected value and variance of the stopping time  under various assumptions on the parameters , , , and .

1.3     Bound on BONDs

In order for a BOND contract to be fully paid, the DAO must remain solvent, meaning the fees it earns must be great enough for the present value to be eventually realized. In the case of riskless BONDs the fees must satisfy the constraint

Equation 8

This gives a limit for how many bounties can be proposed, lest the BONDs cannot be paid if  is too small.  

For example let us assume that the lifetime of tokens is  and all the parameters are constant, such as the rate fees .  Assuming the group has reached REP equilibrium, we have  . Further simplify by assuming the only outstanding BONDs  are the  that are currently under consideration. Then the integral in Equation 8 may be solved to get

A DAO cannot repay a bounty that doesn’t satisfy this equation. The limit is

which is seen by letting , because, in that case, the DAO will use all its fees to pay back the  BONDs for eternity.

Proposition 8. A DAO cannot mint bonds of value in excess of .

Conversely, solving the above constraint for  shows the rate of fees must be large enough to satisfy

or else the DAO cannot ever repay the bounty, no matter how large the stopping time. Therefore, don’t seek a bounty  from a DAO unless you can expect their fee rate to eventually far exceed .

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In addition to raising capital, the BOND mechanism gives the DAO the power to “put their finger on the scale”. I.e., the DAO can mint and issue BONDs through governmental decision to redistribute power in order to serve their goals. As such a BOND can be seen as re-weighting the Forum’s WDAG through an act of DAO governance.

Alternatively, another use of the BOND mechanism is for DAO governance to resolve to issue a series of BONDs through an automated process, to serve a long-term goal. Especially, for example, when the DAO requests some specific work to be done on their behalf, such as software development. In this latter case, BONDs will follow the standard procedure for securing work: workers submit their ASCs. Some worker's ASC is randomly selected. That worker submits a WSC for validation. A BOND is issued in payment. This process gives the DAO, itself, the role of the public, as the DAO requests work from an appropriate bench. The only difference is that the BOND pays off later. ??

2       Applications

In this section we detail some basic applications of the tokenomics principles derived above.

First, we consider applications of BOND tokens. BONDs are simply financial instruments that pay out programmatically in the future, and so can be created for a variety of purposes. Major applications include incentivizing future work through bounties, attracting investors, or transparently broadcasting the future power of founders. BOND tokens can also be used to make algorithmically controlled stable coins. They are also the basis of decentralized markets in REP tokens, created to help workers exit a DAO gracefully, or to create a pillar for decentralized underwriting. ??

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To Do:

·      Make formula for Early Investor BONDs vs. Founder BONDs vs workers who take advantage of the DAO’s systems the Investors and Founders created.

o  Investors Tokens given above

o  Founders deserve some percentage of the profit and power created. This is transparently broadcast. The Founder BONDs

§ pay off at a certain later date

§ can be directly dependent on the amount of profits the DAO achieves

§ can be inversely dependent on the amount of further founder work that is done—meaning there could be a fixed percentage of Founder % of all future profits for a fixed period of time (possibly infinity, or it can attenuate)

o  Example, how do we give ourselves power in the DGF?

o    Workers receive

o  Governance tokens.

Controlling equity that has independent amounts of power in 1. the reputational salary, and 2. Governance decisions.

We may think of these tokens as “hegemony stocks” in the case that they are programmed to maintain power for their owners independently of how power is redistributed through other means. That is, hegemony stocks can be designed which maintain for their owners a fixed minimum percentage of governance power, with any programmed We may think of these as pure governance tokens

o  All these parameters can be subject to evolution. I.e., they are optimized across multiple DAOs, who all argue and experiment about what the best parameters are for fair reward of founder work. They want to give what is appropriate; not too much, not too little. But the answer will be dynamic and will obviously depend on the situation. E.g., a DAO that copies another DAO’s foundational structure, shouldn’t pay its founders as much, since they didn’t do as much foundational work. (That DAO should probably pay the other DAO’s founders some amount [smaller than the original DAO paid, though, all things being equal].)

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2.1     ??Investor BONDs

Since Ethereum started in 2016, there has been a new tool for investment using blockchain that has called into question many traditional concepts of securities regulation. With a short smart contract (which may be printed on enthusiasts’ t-shirts) called an Initial Coin Offering (ICO) and some embarrassingly simple marketing, many DAOs have been able to raise tens of millions in USD in the course of minutes. Investors receive digital tokens which they control with public-key digital signatures. Investor tokens can be as simple as a claim on future fees the DAO hopes to earn. But we can also make much more complicated rules by programming the smart contract to make tokens with a finite lifetime, variable returns, or other limits on their power. We explore some of these designs in this section with investor BONDs, or iBONDs.

Suppose our DAO wishes to raise  of investment, and we are willing to issue an iBOND which later pays  in present value. How do we determine how big  should be?  is called the return coefficient. This is related to the return on investment (ROI) through the formula

So the return coefficient is just ROI .

The DAO’s uncertainty is denoted by  which represents the probability the investment will not be fully returned. This can be captured with complicated probability tools to make a more accurate valuation. But for our first illustration we simply say  is the number  which gives the probability the DAO will fail, i.e., the probability that the iBOND will not be fully paid. This number is estimated for each organization based on every explicit factor available. DAOs have the advantage of being much more transparent than other types of company, so the estimation of  will likely be more accurate than for traditional startups.

Once we know the uncertainty  then the return coefficient  should satisfy the constraint

Constraint 9

To justify this formula, we imagine the example of a time series of investments. Say there are  investments of the same value , each one with the same risk , each one with the same  return coefficient. Over time, when  gets to be large, you would get back approximately . By the law of large numbers in probability theory, this formula becomes more accurate the more often you make investments over time, i.e., as . In order to attract rational investment, we need  to be big enough that the series will be profitable, meaning the ROI is positive. So we need

which gives Constraint 9.

Now to program an investment token we simply apply the previous BOND valuation rules to this constraint:

Proposition 9. Given an iBOND contract with price  minted at time  on a DAO with uncertainty  and  tokens minted, then the variable rate of return is , the correct expiration date is the stopping time  which satisfies the condition

This formula can be used to program the iBOND smart contract to expire dynamically once the discounted REP salary pays out , depending on all the variables, such as  and  which are usually not predictable.

However, Proposition 9 can also be used to give an estimate for the expiration date  if we make some accurate assumptions on the variables. For instance, in the simplest case, when  and  and  are assumed to be constant, and the lifetime of the REP tokens is . When the DAO is at equilibrium, we get as before constant . Then the integral is tractable analytically, and we get

? There are many factors that are used in traditional finance to estimate risk which are applicable to DAOs. We don’t explore these ideas further here, but merely point to a recently popular approach, called the Risk Factor Summation Method[3] as an initiation into the vast subject.

2.1.1      Floating commitment iBONDs

The expressiveness of programmable smart contracts allows investors great flexibility in designing their financial instruments. For example, an investor can dynamically choose their level of commitment with floating commitment (fc) iBONDs. This fciBOND dynamically re-evaluates the uncertainty . Then, assuming this time-dependent probability is accurate, Constraint 9 gives the formula for the present value of the investment in the company .

This allows an investor to keep their investments liquid. As opposed to iBONDs where an investor’s money  is statically committed until the stopping time is met or the DAO goes bankrupt, an owner of an fciBOND may dynamically remove their principle at any moment. However, as the uncertainty changes, their return coefficient will change. If risk increases, the reward should increase lest the investor pull out. If the investor hasn’t statically committed yet, by the time the DAO becomes more established, then their reward drops as the uncertainty decreases. At any point the investor can lock in their return coefficient by statically committing.  

To find the formula for fciBONDs we use Proposition 9.

Proposition 10 Suppose an fciBOND contract for an investment  at time  with uncertainty  and  tokens minted. Then the variable rate of return is  and its expiration date is a stopping time which is the first time  when

is met.

So the first moment  when the inequality is satisfied, the fciBOND expires, as the proper present value of the variable investment has been paid. Before the hitting time occurs, the part of the investment  that has not yet been paid out can be removed by the investor. This value is

at time . (The symbol  stands for commit or cull.) If you lose faith in your investment and remove what remains of your principle at time , then you will can demand . In that case, you will not receive the benefit of the  reward multiplier. Instead you receive what you would have gotten from a safe investment with floating interest (the first term in ), minus the amount you have already received from the REP salary (the second term). On the other hand, if you decide to statically commit your investment at time  then you receive an iBOND under the previous rules which continues the payout until stopping time  satisfies

Now, none of these considerations considers the DAO’s point of view. In order to have a large amount of liquid fciBOND investment and be able to use it, the DAO will need to make safeguards that are more complicated than the fciBOND rules that were derived above. Over the course of history, economists have found several regulations essential for healthy financial markets. With smart contracts we can include rules of any complexity. So the fciBONDs can have disclosures for precisely how they will execute in every eventuality. Then investors can monitor the transparent transactions to verify everything is executing as promised.

One basic consideration the DAO must make is how much of the liquid fciBOND cash can be used at any given time. This is similar to traditional banking’s reserves. For instance, in the US, banks are required to hold a certain percentage of their deposits in reserve, so that if an unusually large number of customers happen to request to withdraw their deposits at the same time, then the bank can cover the demand. If investors remove their investments from the fciBONDs en masse, and there is not enough liquid cash in reserve in the DAO, then there needs to be complicated rules in place to handle how the DAO will react to the inevitable loss of faith. Without explicitly exposing fciBOND investors to the greater risk, a DAO logically should be required to hold larger reserves relative to the amount of liquid fciBONDs. If we accurately estimate the uncertainty , which includes the amount of reserves relative to liquid deposits, we can make reasonable standards for such regulations. A well-established DAO with a history of stable fee rates typically requires less reserves than a newly proposed DAO, which typically shouldn’t use fciBONDs at all.

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[1] An Initial Coin Offering, similar to an IPO, is a smart-contract program created initially on the Ethereum network, which allows a DAO to mint new tokens to sell to investors in exchange for ether, the digital currency of Ethereum. This is the primary use of the Ethereum network as of this writing. The secondary use of Ethereum has been a second-order variation on ICOs, selling NFTs (non-fungible tokens), which represent further fractures of ownership in DAOs.

[2] We refer to these tokens orthographically as BONDs to compare these tokens to REP tokens. The general concept from traditional finance is written orthographically as bond.

[3] Damiano Montani, Daniele Gervasio, & Andrea Pulcini, “Startup Company Valuation: The State of Art and Future Trends”, International Business Research; Vol. 13, No. 9; 2020. Available online at

https://pdfs.semanticscholar.org/88d9/839fb8e7a2aa34b7ee28feb82005285a9ab4.pdf  Retrieved 12/12/22.

They break the risk factors down by 1. Risk of the management, 2. Stage of the business, 3. Political risk, 4. Supply chain or manufacturing risk, 5. Sales and marketing risk, 6. Capital raising risk, 7. Competition risk, 8. Risk of technology, 9. Risk of litigation, 10. International risk, 11. Risk of reputation, 12. Exit value risk.

Applications

Founder REP

If we start a centralized company, a major stage in its development is to valuate the founders’ worth before the company goes public or secures venture capital. This will also happen in any DAO. Founders must work before the DAO begins to generate profits. How do we make this explicit?

Assuming we accurately estimate the value of the DAO as  at the future time , and that we also estimate the percentage of that value that is due to a founder is , then how much REP do they deserve today?

Founders’ roles are similar to investors. Therefore the same considerations that helped us make the valuations of iBONDs help to measure the number and properties of the founder’s REP. The major difference is that in addition to the claims on the REP salary, founder’s REP should have normal REP properties—voting and policing and participation power in ASCs. Using Proposition 9 we get

Proposition 11. Given an fREP contract for  founder tokens minted at time  for a -founder in a DAO with future value estimated as  with uncertainty , then the variable rate of return is  The correct value is guaranteed by the expiration date given by the stopping time  which satisfies the condition

Similar to fciBONDs, a floating valuation of the DAO would allow much greater accuracy, and can be accounted for by allowing   to change in time and rederiving the above fREP contract. If we also make  a dynamic variable, this would allow the DAO to continually re-evaluate the founders’ importance in the group. Then we get

Proposition 12. Given an fREP contract for  founder tokens minted at time  for a -founder in a DAO with value estimated as  with uncertainty , then the variable rate of return is  The correct value for the  founder tokens is guaranteed by the expiration date  given by the first hitting time which satisfies the condition

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It is important to note, that this is not the only way to reward founders for their contributions. A more stable approach is given by ignoring such tokens and referencing the founders’ work with Forum references which is discussed in this other section [link] ??