Editing BOND tokens (section)

=== '''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>.