Variable-period BOND

A variable-period BOND is a BOND token which expires after a variable lifetime $L_{B}$ which depends on the variable payout rate. This expiration date $L_{B}$ will change as the fees the DAO earns changes. This page details the design of the contracts which govern these tokens so their valuation is fair. The variables of payout rate, the expiration time, and the value of the BOND are dependent on each other. A DAO can choose two of the variables at will, then solve for the third to determine a fair contract using REP tokenomics theory. A variable-period BOND is called a riskless BOND when the period is chosen so that the token expires once the value is paid out.

The results and notation from the reputation tokenomics page are used here derive the formulas under the assumptions that a DAO's underlying REP tokens have infinite lifetime and when they have finite lifetime. We give estimates for $L_{B}$ under the further assumptions that the fees the DAO earns are constant.

Overview

Suppose we wish to pay a developer a bounty worth $\$b$. We can give them BOND tokens which pay out the same as a REP token would by participating in the REP salary. Our goal is to find formulas determining how large we should set the expiration date given the rate of payout and the value.

When we pay the developer with $q$ newly minted BOND tokens, which dilutes the total REP in the DAO as fees are now shared with the $q+R$ tokens. The number $q$ of tokens determines the rate of payout, as a larger $q$ means a larger share of the REP salary. The exact rate of payout for $q$ BOND token is proportional to the incoming fees as $f'q/(q+R)$.

Depending on whether the REP token design of the DAO has REP tokens with finite or infinite lifetime we get different formulas for how to program the lifetime $L_{B}$ for a variable-period BOND.

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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.

We can eliminate even this type of risk, using the 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. ??

See Also

• Riskless BONDs