Bitcoin Pricing Models
This week I wanted to talk about some Bitcoin pricing models. But first, we should talk about what a model is in the abstract. A model is an attempt to capture some underlying truth. Generally it starts with some relationship that can be quantified, and ends up with something that’s easier to understand, like a chart. Models are necessarily built from data in the past, from which we try to extrapolate or predict what might happen in the future given a similar set of circumstances.
However, with Bitcoin (and markets in general) the price of something is ultimately determined by the buying and selling behavior in the market. That behavior can change over time, and as I’m sure we’ve all observed, human behavior can be unpredictable. Therefore, the old axiom that all models are flawed, but some are useful, is worth restating.
With that being said let’s start with the MvRv model, or Market Value to Realized Value.
The concept of “realized value” was first introduced by Coinmetrics in 2018. Realized value is the price of each Bitcoin the last time it was moved. Contrast this with the concept of market value (or market cap), which is the assumption that each BTC is worth whatever the last price paid was. It’s a very different approach.
To illustrate this point, consider the following chart that shows the Realized value and Market value over time. Realized value and Market value are both arrived at by adding up the “value” of each coin and then presented as a total value for the entire network.
CHART 1
You may have noticed that there are times when the Realized value and the Market value intersect. There are also some rare time periods when the Realized value of the Bitcoin network was greater than the Market value. But in general, the Market value tends to be higher than the Realized value.
Now if we take the Mv and simply divide it by the Rv, we get the MvRv ratio - first proposed by David Puell and Murad Mahmudov. When we do this, what we end up with is something that looks like an oscillator with decreasing magnitude. The peaks and troughs tend to highlight another aspect of the Bitcoin price, which is that it does appear to have a cyclical nature with upward trajectory and decreasing volatility.
CHART 2
The MvRv ratio is one approach we can use to enhance our understanding of cycle timing and possible future outcomes. But of course no approach is sufficient by itself. For example, consider the dynamics between the mining hash power of the Bitcoin network and the price of Bitcoin.
CHART 3
Source: Coinmetrics Pro
In the chart above, we are looking at the price of Bitcoin on the X-axis (orange), and the hash power of the network on the Y-axis (blue). The general observation that most people pick up right away is that the dots seem to align from the bottom left to the top right of the chart. This is a positive linear relationship in log scale.
In other words, if the price is higher, the hash rate tends to be higher and vice versa. Simple enough, but why does this matter? After all, doesn’t a higher Bitcoin price simply attract more miners? Sure, but let me bend your brain for a minute.
CHART 4
Source: Coinmetric Pro
In the chart above, I’ve taken the rank of the Bitcoin price and the rank of the hash power. That is to say, a higher number results in a lower rank. Consequently if values increase over time, they tend to go down and to the right (decreasing rank over time). The red dots represent the hash power of the network and the purple dots represent the price. If you look at the pink box in the top left corner, you may notice that there is a period of time where there are no purple dots. This was the period of time before Bitcoin had a price, immediately after the network was launched but before there were any exchanges or any reliable way to determine what the price was or if the network had any value at all.
Now, notice that before the price showed up, the hash power chopped around for a bit but then suddenly started to move down and to the right. Let’s look at this using raw values from Coinmetrics again.
CHART 5
Source: Coinmetric Pro
Here the hash power is in red, and the price is in green. Notice that the hash power increases for several months before any price has been determined, and then even after a price first arises around $0.06 and doesn’t do much from July to September of 2010. But the hash rate is going parabolic, why? Even in that short period of time the hash power of the Bitcoin network increased by a factor of ten.
I’m going to suggest that it was the increase in the mining activity that bolstered confidence in the network itself in two ways.
1) When miners invest in the mining process, they put their money where their mouth is by burning power which they have to pay for each month and dedicating hardware to perform the calculations.
2) With a greater distribution of miners, it became more and more difficult to use a brute force attack on the network.
I think the increase in mining activity in the early days was a critical factor in the success of Bitcoin. If that hadn’t happened, we might not be talking about BTC at all today. Fast forward many years and the situation is more complicated. Capital expenditures are long-term commitments that corporations make with the expectation of generating positive returns over time. Additionally, the market price of Bitcoin incentivizes increased mining participation up until profits return to the marginal level. Recall that we visualized this relationship by putting hash power and price on two different axes and creating a scatter plot. But is this information useful for investing purposes?
A naive approach is to take the log-scale values and run a linear regression model. Now we can “predict” the price using hash rate, or the hash rate using the price.
CHART 6
Source: Coinmetrics Pro
But can we say that the Bitcoin cycle timing problem has been solved? And if so, why did I say this model was naive? Well by doing a linear regression on non-normal time-series data we have violated many rules of statistics and we must be burned at the stake. What can we do instead?
One thing we can do is to employ a technique called Spearman’s Rho, in which we convert the raw values into rank values and then use that data for the model instead. Let’s give it a try.
CHART 7
Source: Coinmetrics Pro
In the chart above, the red line is the hash power rank, the purple line is the price rank (higher value is a higher rank), and the green area represents the difference between the rank we expect and the rank we actually observe.
Once again, we see that the market does appear to have a cyclical nature, but viewed from the lens of nonparametric statistics the issue of declining cycles tops and bottoms seems to be less of a factor.
Thank you,