Stake is a unique investment instrument that allows one to benefit from the growth of the underlying asset: Cash. It has many of the advantages of classical instruments that are equity or debt based, while avoiding their substantive shortcomings.
Stake has an intrinsic value as it receives a cash-flow, from a fraction of the interest generated by Cash. There is a maximum of 1 million units of Stake in existence, and each new unit is only created when it is bought for a price higher than the last. So that the amount of Stake in existence grows only when it trades above its high water mark.
Due to reserves, the market value of Cash in circulation is rigidly tied to the demand for Cash. Naturally, the cash-flow paid across all Stake is an increasing function of the value of Cash in circulation. Together with the restrained Stake issuance, this makes the value of Stake exceptionally well tied to fundamentals, ie. the demand for Cash.
The prices and quantities at which Stake is issued correspond to offers on a limit order book, where Stake is created for each set of offers lifted. In this representation, there are one thousand units of Stake offered within each one cent increment in price from 0 to 10 US Dollars.
Compared to selling Stake through an auction, early investors can buy at much lower prices - indeed offer prices start all the way down from zero.
Compared to the classical venture capital funding round model, the valuation for newly issued Stake is predetermined (with no down round). This removes the friction of negotiating valuation, ensures all parties receive the same terms, and makes arbitrary dilution impossible.
The total Cash paid out to Stake holders is per year, where is the amount of Cash in circulation, is the Stake rate. The Stake rate varies as follows:
|Value of Cash in circulation||Stake rate|
|1mm (106 )||1% (10-2 )|
|1bn (109 )||0.1% (10-3 )|
|1tr (1012 )||0.01% (10-4 )|
In general, is calculated as the value of Cash in circulation (in units of US$) to the power of , bounded to stay between 0.01 (ie. 1%) and 10-4 (1 basis point). The quantity is time varying, therefore at each point in time measures flow of Cash, and the total Cash paid in a year is the time average of over the year.
Having a payout which is a predetermined increasing function of fundamentals (the demand for Cash) is superior to both equity and debt, as equity does not ensure any cash-flow, while debt cash-flows only have a known cap, with no prospect of growth.
At any point in time, defining the high water mark as the highest traded price of Stake (in US$), capped at 10, the amount of Stake in existence at that time is . The flow of Cash to a holder of one Stake unit is then at a rate of per year. This Cash is paid in exchange for Stake, and the rate at which Stake is exchanged for Cash is 9% of each Stake unit per year.
As such, the Stake cash-flow acts like a bond principal repayment or share buyback, where the number of instruments in circulation is reduced with a cash payout. It is unlike a share dividend or bond coupon, where the price of the instrument drops by an amount equal to the cash-flow, in response to an upcoming payment. Reducing circulation is preferable because it specifies a time horizon over which the future demand for Cash determines the value of Stake today.
A benefit of the Stake instrument is that it converts into Cash in a formulaic manner. This implies it can be priced in terms of discounted cash-flows. The expected value of these cash-flows informs the Stake market price, while market price moves can drive issuance, which impacts the cash-flow per unit of Stake. It is possible nonetheless to unravel this cycle, and compute a lower bound for the present value of Stake, valid under any market price action.
This calculation is laid out in the next section. The resulting lower bounds for the present value of Stake are shown in the tool below. There are two models considered: the target size model supposes that the Cash market capitalisation (in US$) exceeds beyond years after the Stake purchase; the reference asset model supposes that Cash market capitalisation follows the same trajectory as a chosen crypto asset.
This section requires knowledge of financial mathematics.
Let be defined as the value in Dai of all Cash in circulation at time (also known as the Cash market capitalisation). Let be the total value (in Dai) of Cash flowing to all Stake holders, instantaneously at time . So , where is the Stake rate at time . By definition then
It is assumed throughout that the price of Dai is exactly $1, so that represents the cash-flows in USD terms.
Let be the last trade price of Stake at time , then the high water mark is defined as
The stochastic processes and are adapted to a filtration . Time is in units of years (by definition equal to 365.2425 days), and by convention time refers to the present.
Let be the USD discount factor to time , ie. the present value of receiving $1 in years from now.
The present value of holding one unit of Stake is then
where is the first time Cash will enter circulation, or if this has already happened.
Obtaining a better lower bound would require to remain below a known level (other than 10) while Stake is held. A strategy which maintains an offer for the full Stake held, at some limit price , can achieve this. With such a strategy, the present value of Stake is
where is the time at which Stake is sold. As such, , with partial order fills represented such that whenever a fraction of the order is filled at times , then equals with probability for each .
General lower bound
so that , meaning this limit strategy has an expected return at least that of the holding strategy.
If then, using the fact that for all (proof below), also
which does not depend on . Alternatively if , then , which during the initial issuance from pre-orders implies , and then bound holds anyway.
Assuming non-negative forward rates at time zero, so that is decreasing in , then
In case moreover a deterministic model is used for , this last bound equals
On the other hand, if then so that and . In this case so that it is not profitable to invest in Stake now with this strategy.
Proof that for all , whenever :
For have so one of or must hold.
and for all
Target size model
Suppose for all then define and set be the constant
Assuming the yield curve is normal at time zero, so that whenever , implies
for all . If for all , as holds during the initial issuance from pre-orders, then
Using a simple bound on as in , the top strategy can be defined satisfying
In the case this is simply , and the term measures the duration (as in bond duration) of the Stake cash-flow schedule.