Investor BONDs

Investor bonds, or iBONDs, are a type of BOND token which is designed to raise capital in a DAO by issuing a token which pays off in the future by sharing a fraction of the fees the DAO earns. There are many types of contracts which can be written for different purposes by DAOs at different business stages, such as founding, early adoption, mature, and senescent businesses. We use the theory of reputation tokenomics to find the rigorous formulas for valuating iBONDs.

??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.