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assumptions:

assumptions:

The fair value of Bitcoin is a constant function of energy consumption (Energy Input), supply growth rate (Supply Growth Rate) and the fiat currency coefficient f representing energy.

in:

• Energy consumption (unit: watts) = hash rate (GH/s) * mining efficiency (J/GH)

• Supply growth rate (unit: s-1) = annual growth rate of bitcoin circulation, which is equal to the reciprocal of the reserve-to-production model (S2F). Calculated based on the annual rate of change of Bitcoin (unit: year-1), and then converted to seconds

• Fiat Factor (USD/Joule) = a constant conversion factor to account for the fiat value of energy

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3. Calculation: Energy Value of Bitcoin

To test this theory, all input data, except mining energy efficiency, is from: blockchain.info.

The most challenging part is the accurate assessment of the energy efficiency of Bitcoin mining at different points in time.

3.1 Evaluating the Energy Efficiency of Bitcoin Mining (J/GH)

The energy consumption of Bitcoin mining is related to two factors: the hash rate of the SHA-256 algorithm and the energy efficiency of the mining machine itself.

In the early days, Bitcoin was mined using energy-intensive CPUs and GPUs.

However, the mining efficiency of ASIC mining machines is more than 100,000 times higher than that of the mining machines used in 2009. This means that a relatively high portion of the average electricity cost of a miner today has been translated into effective hashing power.

To assess the historical profile of the energy efficiency of Bitcoin miners, I calculated the energy efficiency of 150 Bitcoin miners from Cambridge (ASICs only), BitcoinWiki (FPGAs) and Bitcoin.it (ASICs, CPUs and GPUs). All ASICs, FPGAs, and Intel, AMD, and Nvidia hardware for energy efficiency (J/GH) are considered, and an approximate time to market for the miner is found. The common models were grouped and the average energy efficiency of the models was calculated on the basis of equal weight.

The daily energy efficiency of the Bitcoin network is then calculated as a weighted average of all hardware within two years of CPU/GPU/FPGA release, and within 1.5 years of ASIC release.

• CPU and GPU miners typically last for years

• Bitcoin mining is usually not competitive in the early days

• Other studies have also shown that in recent years, ASICs have typically depreciated over a period of 1.5 years

Finally, a 1-month moving average of energy efficiency was calculated for a phased phase-out of model types.

In fact, some miners are more versatile and have a longer lifespan. However, due to the risk of adding historical error in the energy value model, and trying to obtain an unbiased result, we did not exclude these miners, data cleaning or other data manipulation.

During the above process, Bitcoin energy efficiency (J/GH) formed the following trend over time.

An S-curve (representing a gradual decrease in J/GH over time) as Bitcoin mining efficiency increases. Note that mining efficiency has increased dramatically since the introduction of ASIC-based mining machines in 2013-2014.

3.2 Calculation of fiat currency coefficient (USD/joule)

The fiat factor is a constant that converts energy consumption units (joules) into fiat currency (dollars). It simply expresses how serious "we" are about energy.

According to the above energy efficiency curve, the legal currency coefficient obtained is:

2.0E-15

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4. Conclusion: The energy value is consistent with the historical currency price

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Bitcoin energy value 10-year chart

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5. Market forces - building a bridge between supply and demand

The first question is:

Is Bitcoin's Energy Value Model Logical?

In the article "Bitcoin Value Modeled Using Scarcity", Plan B found that the market price has a strong relationship with the scarcity of assets such as Bitcoin. We can assume that this represents the basic relationship of human "demand" for long-term "hard currency" and value-preserving assets.

Not all scarce assets have or maintain broad market values. For example, there are about 3,000 cryptocurrencies with a market capitalization below $500. Many of these tokens have a "limited" supply model, yet the market still sees them as having no fundamental value. Scarce, but worthless. Scarce assets that are easily obtained or copied have a lower market value.

Sustained, high levels of human effort are often associated with demand.

When putting energy (energy) into an event, the provider of energy (the worker) expects others to demand their effort. When suppliers see the fruits of their labor, demand for workers grows, and workers work harder for greater rewards. However, suppliers may stop committing to the event if their demand for labor declines, or if workers can earn better returns elsewhere.

This can both explain Bitcoin’s computing power struggle and serve as an argument for Bitcoin’s energy value model.

Continuous mining input represents a balance between supply and demand. The rising bitcoin price encourages miners to increase mining investment through computing power growth and technological improvement, thereby improving energy efficiency. Therefore, a large increase in the market price usually promotes an increase in mining input and therefore increases the energy value of Bitcoin. However, when speculation causes prices to skyrocket, without a corresponding increase in energy consumption, historically, prices plummet back to energy values.

It represents a phenomenon of mean reversion, as would be expected from fundamentally driven intrinsic value valuations.

Bitcoin's price and energy value are interlinked, as tightly as magnets. Although there may be deviations between the two, they ultimately fit together. Although the energy value of Bitcoin is mathematically independent of transaction price and transaction volume, the "invisible hand" of the market connects them.

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6. Measuring: the effectiveness of the energy value model

Based on daily data from January 2010, the R2 of the "energy value" formula is 80% of the actual bitcoin price (the higher the R2, the more realistic the model). In comparison, the R2 for the reserves-to-production model under the same data is 88%.

While 8% lower than the RPM model, there are a few things to consider:

But here's the problem.

• The energy value of Bitcoin is highly dependent on our estimated mining efficiency. In this analysis, a total of 150 detailed information of Bitcoin mining machines were manually sorted out, and there is a possibility of data omission or data error. Depreciation periods are an approximation of actual conditions. Efficiency may also vary based on changes in operating conditions and overclocking. It is impossible to perfectly represent the hardware used by every Bitcoin miner at every point in history. Therefore, some errors may occur here.

• If all miners stopped mining bitcoins suddenly, the price of bitcoin would reach infinity, as predicted by the reserves-to-production model. The energy value is predicted to be zero. If all miners abandon Bitcoin (such as a catastrophic event occurs: the collapse of the SHA-256 algorithm, a better way to store wealth), no new blocks will be generated, no transactions will be sent, and the blockchain network will tantamount to paralysis. In such a case, using only the reserve-to-yield model (0.4 *SF³) would consider Bitcoin to have infinite value. The energy value model says: If all miners stopped mining Bitcoin tomorrow, then the electricity input would be zero and Bitcoin would be worthless.

• Reserves production model The model is a fitted power law. The price of Bitcoin has had an exponential performance and the reserve-to-production model has been specifically chosen to match it. By optimizing the parameters, better Bitcoin price fitting accuracy is obtained. Energy values ​​have no curve fitting parameters, only a fixed constant that allows conversion of pure energy into dollars. In fact, the exponential increase in the mining efficiency of miners and the increase in hash rate may explain the exponential relationship between reserves and production.

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Bitcoin's energy value model and reserve production model

From the chart above, we can see that inflection points and large gaps between Bitcoin price and fair value indicate great times to buy or sell Bitcoin.

A sharp drop in energy consumption often means a good time to exit the market, while a strong increase in energy consumption represents a great time to buy.

The energy value formula says Bitcoin's current (December 12, 2019) fair value is around $11,500, which is 50% above its current trading price.

This suggests that Bitcoin will have a huge risk reward in early December 2019. The energy value oscillating chart below also gives a positive sign.

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8. Enlightenment brought by the energy value model

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Historically, it is unwise to buy when the hash rate is falling, and the risk reward is much higher to buy when the hash rate is recovering.