A reliable equation for mining bitcoin? – Recently, I introduced you to the work of Arthur Hayes on the cost of producing a bitcoin. Hayes was a pioneer with his research into the relationship between the price of a bitcoin and its cost of production. Since then, many authors have been inspired by his model. One can quote in particular Arun which takes again the work of Hayes and adapts it to an investment objective. So I will present this model to you. We will also discuss how I used it to determine a floor price for Bitcoin.
In the continuity of Hayes
We saw in the previous article how a miner can determine the cost of producing bitcoin based on their equipment. However, what interests me now is the investment, not the actual mining.
So I looked for an iteration of the cost of production model that can be used to invest in Bitcoin. After a few hours on Medium, I found several relevant adaptations of this model. Among these, we have that of Charles Edwards and that of Vikram Arun which I will present to you today.
Arun took Hayes’s model and reworked the equation so that he no longer had to worry about the computing power deployed by a miner. The equation for the cost of producing a bitcoin is reformulated as follows:
β the reward per mined block expressed in bitcoin (BTC).
δ the difficulty expressed in hash.
time constant sec of the number of seconds in an hour (3600).
232 constant of the probability of mining a block with one hash per second.
Put simply, this equation divides the energy cost of mining a block by the block reward per block mined. Once my equation was in my pocket, I set out to establish a satisfactory dataset to solve it. To make this calculation, we need the price of electricity and the energy efficiency of the mining devices in circulation.
The study carried out by Coinshare in 2019 shows that the distribution of mining is mainly between China, the United States and a few countries in Europe. I therefore recovered the prices of industrial electricity in the countries mentioned.
Electricity price in dollars per kWh
Low fork High fork
China $ 0.04 $ 0.08
USA $ 0.05 $ 0.12
Canada $ 0.06 $ 0.11
Sweden $ 0.08 $ 0.09
Iceland $ 0.06 $ 0.06
Estonia $ 0.04 $ 0.09
Average $ 0.06 $ 0.10
The daily difficulty value and the daily bitcoin price are taken from Coinmetrics. Finally, average energy efficiency is modeled based on Edwards’s research.
Edwards’ freely accessible dataset brings together the energy characteristics of all mining devices to establish a fairly weighted average of the energy efficiency of the entire Bitcoin network. With the dataset ending in mid-2019, I supplemented it with the specifications of mining devices released since then. Each device has an average lifespan of one and a half years before being replaced (this is of course an average, to be taken with the pinch of salt). This lifespan is estimated from the Coinshare mining industry study.
Buy Bitcoin according to its production cost?
Once all my data had been collected, I compiled them in an Excel spreadsheet in order to model a range of production cost per bitcoin. The result of this modeling is presented below.
The upper end of the price bracket materializes the cost of producing a unit of bitcoin for miners with the most expensive electricity. The lower terminal represents the production cost for miners with the cheapest electricity.
The choice to use a heterogeneous set of electricity prices makes it possible to capture certain ancillary costs such as wages or machine cooling which are more difficult to quantify.
The cost of production serves as a floor value and the price seldom drops below. The only notable exception is the second half of 2014 when the price of bitcoin is moving around 60% below its cost of production.
This irregularity can be partially explained by the bursting of a bubble in 2014. This bubble was almost as large as that of 2017. However, its magnitude is less visible on the graph due to the logarithmic scale.
We notice the effect of certain events on the cost of production. At the end of 2012, the cost of production suddenly increased before being followed by the market price. This increase in production cost corresponds to the halving that took place in 2012.
The drastic drop in the cost of production in 2013 corresponds to the introduction of ASICs (Application-Specific Integrated Circuit) in the mining market. These machines dedicated specifically to mining, replacing the graphics processors, reduced the cost of production until the network difficulty adjusted.
Modeling an energy price bracket is highly relevant in an investment decision. The computing power and energy cost variables are data that any investor can relate to.
They represent the effort expended to produce a unit of digital asset and the dollar value of that effort, respectively. In an efficient and competitive market, the price of the mined asset should not drop below its production price bracket.
Miners who are no longer profitable would have to mine another asset or stop production. This practice observed among miners is similar to the production interruptions resorted to by oil-producing countries in the event of a drop in prices allowing available reserves to be reduced and prices to rise. The production cost of an asset therefore does not determine a fair value for the asset, but rather a floor value for the asset studied.
If you want to use this model for investing, you can like me build your own chart according to your research and beliefs. You can also refer to the Bitcoin Production Cost indicator, programmed by Edwards following his research.
The cost of production modeling and the resulting analyzes can be transposed to other proof of work assets, such as Litecoin or derivatives of Bitcoin, Bitcoin Cash and Bitcoin SV.