Editing BOND tokens (section)

== Mechanism design ==
The BOND token design we detail here is a variation on a REP token, which pays out similarly through the [[Reputation#REP Salary Mechanism|REP salary]].<ref>A DAO may choose to give the BONDs priority access to incoming fees over REP tokens, so that BOND payout is more secure and predictable. However, we do not make that assumption in this analysis, as that introduces unfairness in the payouts of REP tokens depending on when they were minted within the lifetime cycle <math>[t,t+L]</math>.</ref>

We calculate the formulas for the lifetime <math>L_B</math> and the quantity <math>q</math> of BOND tokens needed to accurately match the cash value <math>$b</math> of BONDs with various different payout schedules. The general theory that dictates these formulas is [[Reputation tokenomics|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 <math>L_B</math> are dependent on each other and constrained by the payout <math>$b</math>. With those targets, the types of bonds break down as fixed-period or variable-period contracts.

=== '''Fixed Period, Risky Payout''' ===
''Main page: [[Fixed-period BOND|Fixed-period BONDS]]''

Given a fixed pay period <math>L_B</math> the developer is given the number <math>q</math> of BOND tokens that match <math>$b</math> based on the present value. This amounts to solving the equation <math>qPVf_B^1=b</math> for <math>q</math>. Once <math>q</math> and <math>L_B</math> are fixed, the payout will be a random variable, with expected value <math>$b</math>. 

This solution leaves the ultimate value of a BOND token to chance, dependent on the random variables of the fee rate <math>f'</math>, the interest rate <math>r</math>, and the number <math>R</math> of other BOND tokens that will be minted during the time <math>t<L_B</math>. 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: [[Variable-period BOND|Riskless BONDs]]''

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

The technical terminology is that <math>L_B</math> is a random variable, called a stopping time, which is determined by the stochastic process given by the incoming fees <math>f'</math> and interest rate <math>r</math> random variables.

There are two approaches to riskless contract design are to make fixed payouts or the more complicated fixed present value payout. 

==== Fixed payout ====
The lifetime <math>L_B</math> of the BOND can simply be set to end once <math>$b</math> is matched in fees by stopping the first time the constraint <math>qf_B^1(L_B)=b</math> is satisfied. In this case, the rate <math>q</math> will be of prime importance when deciding how valuable the BOND reward is. The rate of payout depends on <math>q</math> and <math>f'</math>. Since <math>f'</math> is a random variable, the stopping time <math>L_B</math> is a random variable. If <math>L_B</math> is large, then even though the contract is eventually guaranteed to pay out <math>$b</math> as long as the DAO continues to earn fees, the present value of this solution still depends on chance. 

A better solution, one that does ''not'' depend on chance, is the following:

==== Fixed present value payout ====
To account for the time it takes to pay out <math>$b</math> fees for a BOND contract, we can include the present value calculation in the lifetime <math>L_B</math>. In this case we treat the left hand side of the equation <math>q_0PVf_B^1=b</math> as a variable that depends on the variable lifetime of the <math>q_0</math> BOND tokens minted at time <math>t_0=0</math>. This financial instrument uses the programmable contract to absorb all randomness (if you trust the oracle dictating the varying value of <math>r</math>). This solution gives a guaranteed payout of exactly <math>$b</math> in present value calculated from the time the BOND was minted. In this case, the BOND pays out more than <math>$b</math> in fee salaries over the course of its lifetime (assuming <math>r>0</math>) stopping only when the desired discounted 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 <math>L_B</math> the major consideration is the quantity <math>q</math> of BOND tokens minted for the reward. For a fixed reward <math>$b</math>, the quantity <math>q</math> will always be inversely related to the lifetime <math>L_B</math> that obtains for the BOND tokens. The reason is that the quantity <math>q</math> is directly related to the rate of the fees <math>f'</math> that the rewarded BOND tokens share, so larger <math>q</math> means smaller <math>L_B</math> is needed to match the value of any fixed bounty <math>$b</math>.