Forecasting Bitcoin price using quantitative models, Part 4


An intellectual attempt to estimate Bitcoin’s price, corrected according to the hash rate metric.

This is Part Four of a multipart series that aims to answer the following question: What is the “fundamental value” of Bitcoin? Part One is about the value of scarcity, Part Two — the market moves in bubbles, Part Three — the rate of adoption, and Part Four — the hash rate and the estimated price of Bitcoin.

Hash rate and the estimated price of Bitcoin

In data mining, the term “hash rate” is a security metric. The greater the hashing power, the greater its safety and resistance to external attacks. It’s one thing for a hacker to attack your home computer, but it’s another when a hacker tries to attack tens of thousands of computers around the world at the same time.

The hash rate growth is due to the ever-increasing computing power of mining servers, which also means increasing costs to mine Bitcoin (BTC). A simple rule tells us that a given activity must have economic convenience in order for it to be sustainable over time. Those who extract oil from the ground must sell it at a cost greater than the cost of extraction, those who produce electricity must sell it at a cost greater than the cost of production, and so on.

The same rule applies to Bitcoin mining, whereby the cost of electricity, the amortization of increasingly powerful servers, etc., must be lower than the revenues generated by receiving Bitcoin for the activity carried out.

Related: Is Bitcoin a waste of energy? Pros and cons of Bitcoin mining

Therefore, the growing difficulty of mining Bitcoin must be matched by economic convenience.

In the first months of 2010, Bitcoin paid miners about $10,000 per month. Today, thanks to the growth in the price of Bitcoin, the network of miners in the world are distributed a wealth of over $500 million per month — and this value is destined to grow.

The figure is enormous, even if partially commensurate with the consumption of electricity, but it allows us to understand the generation of wealth that this “social experiment” is able to create. As we can see from the graph, the growth of the hash rate is higher than the growth of monthly remuneration. Therefore, in order to estimate the correct price of Bitcoin based on hash rate, it is first necessary to understand the trend of remuneration for each unit of hash over time.

As we can see, the dollar remuneration of the hash rate is in sharp decline. This means that security increases almost exponentially over time, but the cost of security drops considerably over that time.

For a better understanding, while the remuneration for each block grows — despite or thanks to the halving that increases scarcity — the difficulty of undermining a new block increases much more quickly, at least for now. Therefore, the price/hash rate ratio goes down because the denominator goes up more substantially than the numerator.

So, to estimate the (non-linear) trend of decline in remuneration for hash rate, the function that best represents this trend is, as always, the power law function, as shown in the following figure.

Once we obtain this function by multiplying the two functions of hash rate growth and payment by a single hash rate, it is possible to obtain the function that approximates the monthly remuneration in U.S. dollars over time.

This result does not approximate the value of the price of a single Bitcoin but of the monthly remuneration that is growing over time, as can be seen on the previous graph.

To estimate the Bitcoin price, corrected according to this hash rate metric, it is necessary to divide this value by the average number of Bitcoin that is mined in a given month. By doing so, we obtain the typical stepped trend of the stock-to-flow model described earlier.


We can conclude that even in the face of strong volatility and apparently incomprehensible price movements, the principal three factors that move the price of Bitcoin — the scarcity, the demand and the cost of production — can be really useful to understand the dynamics of Bitcoin price movements.

We can argue that there are long-term fundamental value trends that can help to consider Bitcoin a “strategic asset class” of investment.

This article was co-authored by Ruggero Bertelli and Daniele Bernardi.

This article does not contain investment advice or recommendations. Every investment and trading move involves risk, and readers should conduct their own research when making a decision. The views, thoughts and opinions expressed here are the authors’ alone and do not necessarily reflect or represent the views and opinions of Cointelegraph.

Ruggero Bertelli is a professor of financial intermediaries economics at the University of Siena. He teaches banking management, credit risk management and financial risk management. Bertelli is a board member of Euregio Minibond, an Italian fund specializing in regional SME bonds, and a board member and vice president of the Italian bank Prader Bank. He is also an asset management, risk management and asset allocation adviser for institutional investors. As a behavioral finance scholar, Bertelli is involved in national financial education programs. In December 2020, he published La Collina dei Ciliegi, a book about behavioral finance and the crisis of financial markets.
Daniele Bernardi is a serial entrepreneur constantly searching for innovation. He is the founder of Diaman, a group dedicated to the development of profitable investment strategies that recently successfully issued the PHI Token, a digital currency with the goal of merging traditional finance with crypto assets. Bernardi’s work is oriented toward mathematical model development, which simplifies investors’ and family offices’ decision-making processes for risk reduction. Bernardi is also the chairman of investors’ magazine Italia SRL and Diaman Tech SRL, and is the CEO of asset management firm Diaman Partners. In addition, he is the manager of a crypto hedge fund. He is the author of The Genesis of Crypto Assets, a book about crypto assets. He was recognized as an “inventor” by the European Patent Office for his European and Russian patents related to the mobile payments field.

This article has been successfully submitted to the World Finance Conference.

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