Living on “the Bitcoin standard” has been a dream for many in the Bitcoin community since its inception. While much progress has been made to make this possible, few real world transactions are priced in BTC today. Restaurants do not price menus in BTC. Workers do not price their labor in BTC. And business do not denominate contracts or debts in BTC. Even in the rare instance where such transactions are settled in BTC, they are almost always priced in a unit of account like USD.

Some argue that this is okay and that eventually the volatility of Bitcoin’s purchasing power will subside, but I’m skeptical. Even in a world where Bitcoin is the least risky asset on earth and the only form of money, demand for it will rise and fall with changing economic conditions. During a panic or recession, demand will rise, increasing its purchasing power, and during an economic boom, demand will fall, because people will prefer to invest their capital elsewhere. This is not how an ideal unit of account should behave.

For this reason, I believe it is necessary to build a new unit of account, defined in terms of BTC, that can compete with traditional monetary standards like USD. If we could define 1 BTC to be worth 10 “units” today but create a dynamic P2P mechanism to reach consensus on how many “units” 1 BTC is worth tomorrow, we could create a unit of account that people prefer over USD but which still settles in BTC.

The question of course is how to reach consensus on that unit of account. Who determines the rate of growth in “units”? When should the quantity of “units” fall by 5% and when by 10%? How should “purchasing power” be defined? Can a P2P protocol actually exist to reach consensus on such a thing?

Rather than trying to explicitly measure purchasing power, which is a fairly ambiguous concept, I would suggest we try to measure bitcoin’s expected real rate of return. While not perfectly correlated, bitcoin’s purchasing power is tied to the rate of return the market expects. Bitcoin today has a lower expected rate of return than Bitcoin five years ago, and Bitcoin five years ago had a lower expected rate of return than Bitcoin five years before that.

Why should Bitcoin’s expected rate of return be correlated with Bitcoin’s purchasing power? Bitcoin’s expected rate of return reflects the rate of return the market requires given its perceived riskiness. As Bitcoin becomes considered a less risky investment, the required rate of return naturally falls, and demand for it rises.

There are many ways to think about Bitcoin as an asset. One way to think of Bitcoin is as a perpetual bond that continuously reinvests in itself. The value of a perpetual bond is inversely proportional to its discount rate, which reflects the market’s required rate of return. Thus, if Bitcoin is like a perpetual bond, its purchasing power should rise when its expected rate of return falls, and vice versa. Meanwhile, we would expect Bitcoin’s purchasing power to grow at its expected real rate of return.

We might therefore derive the following equation for the number of “units” per BTC at time t, U(t), as a function of its expected real rate of return per unit time, r(t):

F(0) = 1 F(t+1) = F(t) * [1 + r(t)] U(t) = F(t) / r(t)

Of course, this model isn’t perfect. If demand for BTC suddenly rises but the expected rate of return does not change, the purchasing power of 1 “unit” will increase, and vice versa. As Bitcoin matures, however, we would expect the number of “units” per BTC to closely track changes in its purchasing power.

The question now is how to reach consensus on r(t). One possible way to do so is to introduce two new tokens on Bitcoin and use their relative quantity to determine r(t). We might call one TIGHTEN and the other EASE, and we would allow holders to convert between them according to a constant sum-of-squares invariant:

A^2 + B^2 = K^2

Where A and B are the outstanding quantity of TIGHTEN and EASE, respectively, and K is some constant.

We might then define the annualized interest rate r(t) to be equal to some ratio, such as (A - B) / (A + B), so that it is zero when the two tokens are at parity.

With this design, as long as (50+r)% of the collective value of TIGHTEN and EASE is “honest,” holders can convert and correctly set r(t). Since their holdings only have value if the unit of account they control is useful, there is a strong incentivize for holders to convert optimally.

This has the nice property that anyone can influence monetary policy by buying or selling TIGHTEN or EASE. Changing the relative price of the two tokens indirectly affects the interest rate, since it creates an opportunity for someone to convert and realize arbitrage.

Of course, we wouldn’t want to use the latest point estimate of r(t) in practice. Instead, we would want to use the median over the last 10-100 blocks where r(t) is positive. This would ensure that the conversion rate accurately reflects the relative price of the two tokens and that r(t) is always well defined.

What are your thoughts on this proposal? I realize that this design is incomplete and there are probably multiple unanswered questions, but I’m hoping this might spark an interesting conversation. Do you think Bitcoin could benefit from a more dynamic unit of account like this? Would appreciate any feedback!