### On Bitcoin (BTC)’s Convergence: Simplified, part 1 – AJC

On Bitcoin (BTC)’s Convergence: Simplified, part 1 – AJC

You all remember this picture, right?

If you don’t then you can go read about it on Plan B’s page: PlanB. If you do know what it is, let’s move on.

Plan B made that chart with Bitcoin monthly data. The same chart can be made using daily data:

Again, this is the same plot as Plan B’s, but it is for all days since August 17th, 2010. Now, notice that the data is spread out on the lower left corner, and it is clustered in the upper right. Here, I’ve circled this:

Interesting. Another thing that can be done is to show the same data as a multiple of the stock to flow model. So, for points above the horizontal line, they would have a multiple >1.0, and for points below the horizontal line they would have a multiple < 1.0 and greater than 0. We can also show the data with the x-axis as time, instead of x-axis as S/F ratio. So, that’s this chart here:

Now the data points are ordered chronologically, and they are shown as a multiple of the stock-to-flow model. So, the linear regression line is now the middle horizontal line at the y-axis level of 1.0.

Do you see a pattern? Here, let me highlight some things:

Now the dates of the halvings are shown as vertical orange lines. Also, the all-time-highs and all-time-lows are circled. The circles are getting closer and closer with time to the middle line of 1.0, which is the S/F model. This is why the data points in figure 2 are spread out at the bottom left and are bunched closer to the linear fit at the top right. The value is converging toward the stock-to-flow model.

That convergence can be visually presented with some curves, like so:

The details of all the math in this story are presented in the full version of this story, here: https://medium.com/@AJC241469/on-the-apparent-convergence-of-bitcoins-usd-market-value-toward-the-stock-to-flow-valuation-model-7a9275ac2206

Now, how do these converging lines appear on the Bitcoin price chart? This is how they appear:

Notice that these converging lines are disconnected and they are not smooth. That’s because they now depend explicitly on the S/F ratio, whereas before they were just a fit to the price data that was already transformed into a multiple of the S/F model. They are disconnected to highlight the effect of the halving, which dramatically increases the S/F ratio. One thing to note about this picture is that the converging lines that correspond with dates after October 25th 2019 are simulated approximations.

If this is a little confusing, the figure below may help. It is color coded to demonstrate what is what:

Hopefully this demonstrates that this is all the same data, it’s just two different ways of expressing the data — either 1) as a multiple of the S/F model, where the market value data is irregular and the converging lines are smooth, or 2) as a price where the market value data is smooth and the converging lines are irregular.

Looking to the future, one might ask, “how must the price move such that the market value maintains its pattern of converging to the S/F model?” To answer that question, we look at the figure below:

In this figure, the “corners” of the converging lines are circled. These represent the end-points of what is called the “narrow halving window,” which is the range of prices through which Bitcoin must pass in order to maintain its pattern of converging to the S/F model. Noticeably, these circles get closer and closer. Therefore, if Bitcoin’s market value is to continue its pattern of converging to the S/F model, the price of one bitcoin must pass through a very narrow range in May of 2020 — approximately \$14000 to \$20000. We will know very shortly if this pattern of convergence will be continued into the next halving cycle.

Published at Sat, 09 Nov 2019 06:07:45 +0000

{flickr|100|campaign}