“Fair market value of bitcoin: halving effect”

The purpose of this article is to analyze the effect that halving has on the fair market value of bitcoins. The main hypothesis of the study is that the decline in the cost of min-ers’ remuneration for mining is a significant factor that affects the price of cryptocur- rencies. The article examines the factors that regulate the issuing process. The significance of a limited supply of bitcoin is detailed in the article, as well as the mechanism for the implementation of the issue of new bitcoins. The study compares the historical inflation data of the US dollar and the projected data on the inflation of bitcoin. The article analyzes the main technical element of cryptocurrency – halving – when the miner’s reward is halved. This analysis includes the mathematical methods of statisti- cal data processing. Research results show that reducing remuneration by half every four years leads to an increased market value of the cryptocurrency. This relationship is clearly illustrated by the Kendall rank correlation method.The results of the study can have a significant impact on the fundamental assessment of bitcoin and can also enable investors to assess any of the existing and operating cryptocurrencies according to this method.


INTRODUCTION
Many significant problems in the global financial system were exposed in the 2008 economic crisis. The recession also gave incentives to create an alternative structure for the world economy. Thus, changes were made, and new economic tools and technologies began to be used.
Bitcoin has been attracting more and more attention from economists, politicians, and traders since its introduction in 2009. In particular, the cryptocurrency started to dominate in the financial press, due to its phenomenal growth in market value and the number of transactions made.
Bitcoin's success has inspired many cryptocurrency projects based on various Blockchain technologies. Since the beginning of 2017, leading cryptocurrencies, such as litecoin, dash, monero, have gone up in price by several thousand percent, resulting in a substantial increase in trading volumes. By 2018, cryptocurrency market capitalization has increased from 18 to 830 billion US dollars. In addition, daily trading volume with various cryptocurrencies has increased from several thousand to hundreds of thousands of dollars, and sometimes even to millions of US dollars.
Therefore, an intriguing question arises: what is the fundamental reason for price changes of crypto assets in the long run? This issue is crucial for two reasons. Firstly, there is no suitable model for assessing the impact that bitcoin emission has on its price. Secondly, the majority of cryptocurrency market participants use technical analysis as their

LITERATURE REVIEW AND THEORETICAL BASIS
In their works, Mba, Pindza, and Koumba (2018) and Briere, Oosterlinck, and Szafarz (2015) consider the possibility of further diversifying cryptocurrency-based investment portfolios for private and institutional investors. For example, if an investor who had 100 thousand US dollars at the beginning of 2011 decided to invest 1% of his funds in bitcoins, he would have earned an average annual yield of 298.64% for 8 years, and his total capital would have increased from 100 thousand US dollars to 7.06 million US dollars 1 .
Many scientists have been studying bitcoin from multiple perspectives ever since it appeared. Corbet, Lucey, Urquhart, and Yarovaya (2018) and Dierksmeier and Seele (2018) addressed the issue of classifying cryptocurrencies, determining whether they are a medium of exchange and payment or just a speculative investment.
Yi, Xu, and Wang (2018) conducted a study related to the correlation between cryptocurrencies and traditional assets and assessed whether cryptocurrencies could be used as a hedging or diversification asset.
The vast majority of economic literature concerning bitcoin and cryptocurrencies, in general, is dedicated to studying economic factors, such as the market power of supply and demand, production cost of cryptocurrencies, the influence of the public interest through mass media. Chaim and Laurini (2018), Balcilar, Bouri, and Gupta (2017) emphasized price volatility and opportunities in trading correlation strategies. However, little research has been done on the effects that technical elements of a separate cryptocurrency have on its market value.
Supporters of the traditional theory believe that investors should look for investment and hedging opportunities on a certain market by evaluating the effectiveness of other markets. However, such strategies are not beneficial in the current state of the cryptocurrency market. This is due to the difference between cryptocurrencies' underlying technologies along with its market environment and traditional financial assets (stocks, bonds, etc.). Dorfleitner and Lung (2018) give a more detailed discussion on this topic in their work.
Bitcoin operates on blockchain technology, which involves the formation of blocks containing information about transactions users carry out within a network. Each new block generated by a network is built into a chain of blocks, which contains information not only about new transactions, but also all previously conducted operations (Brühl, 2017). This technology allows for a structured database, leaving it in the public domain. Moreover, this technology of distributed registries excludes spoofing, identity theft, data deletion, and it does not allow interested persons to violate the property rights of the owners.
It is worth noting, however, that the primary purpose of Bitcoin is to create an alternative method of making transactions. This approach essentially eliminates intermediaries out of the money-flow chain (like banks and other financial institutions) between buyers and sellers, as well as the need for government bodies to control and regulate activities of financial organizations. As stated by Nakamoto (2008), the structure of peer-to-peer data transport is based on the idea of equality of all participants in a network. This eliminates the need to drag and synchronize special servers, decreasing the odds of performance deterioration of any given system. The result is that every network participant is both its client and server for storing data. This process allows bitcoin to have full independence in network connectivity.
Bitcoin's key ideas include, as previously discussed, independence from intermediaries and regulators and the autonomy of the network functioning. However, bitcoin's intent, according to its creator (or creators), was to eliminate the chief, in their opinion, the disadvantage of modern money equivalents -inflation. The idea of perfect money, which in the long run does not lose its value, was fully realized in this cryptocurrency and significantly contributed to its success. Therefore, in order to prevent inflation, the code of cryptocurrency originally had several basic regulating principles: 1) limited issue; 2) increase/decrease in complexity of mining; 3) remuneration halving for the generated block.
Let us examine the three factors in further detail: In a decentralized monetary system, human intervention in the process of currency issuance is reduced to zero. However, the release of new bitcoins into circulation is totally under control of a special cryptographic algorithm, which follows the rules of peer-to-peer networks. This algorithm determines the frequency, time, and amount of issued monetary units (Sauer, 2016). Any attempts to modify the amount of issuance of new monetary units will be cryptographically rejected (Nelson, 2018;Mikhaylov, 2018b).
The creation of bitcoin units epitomizes the issuance of legal-tender coins on a predetermined algorithm. The algorithm's imposed limit on the maximum possible amount of bitcoins is 21 million coins (Nakamoto, 2008).
The issuance of new bitcoins follows the completion of forming new blocks of transactions. The frequency, with which the blocks are generated, is constant: six blocks per hour. The amount of mined coins by bitcoin network gets reduced in a geometric progression: every 210 thousand mined bitcoin blocks, the amount of mined bitcoin blocks next cycle will be reduced by 50%, which corresponds to a four-year issue cycle. As a result, the algorithm determining bitcoin issuance develops a clear timetable, according to which the number of issued bitcoins will never exceed more than 21 million coins (Table 1).
2. The rate of complexity is essential to the process of cryptocurrency production. Aside from the fact that this indicator helps miners determine which equipment must be used for the extraction of cryptocurrency and what power it needs to possess, the complexity of mining regulates the pace at which bitcoins are issued.
Every 2016 blocks found in the bitcoin network, the difficulty of mining is recalculated. If miners found one block of transactions every 10 minutes, as the developer (developers) of the network originally intended, in order to maintain the planned issuance of 21 million coins, locating this quota of blocks would take two weeks. When new members connect their equipment to the network, they increase the computing power, which leads to a reduction of the amount of time it takes to find a transaction block. Thus, we can make the following conclusion: the higher the hash rate of the network, the greater the number of miners involved in the extraction of cryptocurrency, and hence, the less time it takes to find a transaction block. All this leads to an increase in the complexity of mining. On the contrary, the reduction of hash rate indicates that fewer miners are involved in the process of mining, which means that the time to find a transaction block increases, and the complexity of the network decreases (Nyangarika, Mikhaylov, & Richter, 2019b).
3. As was mentioned previously, the total output of bitcoins is limited to 21 million coins. When the last block out of the 210 thousand limit set by the system is found, the reward for the next found block, according to the plan, is halved. The reward for finding a block of transactions has decreased two times in the ten years that bitcoin has existed.
So, on November 28, 2012, the number of new bitcoins that the network generates had reached its limit, and the reward was reduced from 50 BTC to 25 BTC and in early July of 2016 -from 25 BTC to 12,5 BTC.
The following reduction of remuneration (halving) is estimated to take place in May of the year 2020.
In addition to influencing the overall earnings of miners, halving that occurs once every four years significantly affects the process of issuing new bitcoins (Table 1). This directly affects the market val- ue of cryptocurrency. So, participants of the bitcoin network who mined 100 BTC per month, and then sold them to offset their production costs, begin to produce two times fewer coins after remuneration halving, which leads to a decrease in the supply of the "new" bitcoins in the market. With the same level of demand and twice-decreased supply side, the market starts to react by increasing the market value of cryptocurrency. The same opinion is shared by Kroll, Davey, and Felten (2013) and Nair and Cachanosky (2017). They write that at the same level of demand and twice-decreased supply side, the market starts to react by increasing the market value of cryptocurrency.

METHODS
The period from November 1, 2010 to December 31, 2018 (98 months) was taken in order to analyze the impact of halving on the value of bitcoin. This time frame was divided into weekly intervals indicating the historical opening and closing prices.
In order to reduce the impact of price volatility and improve the quality of the obtained results, the following method of estimation did not include the weekly maximum and minimum price values for the selected period. This kind of search data helped reduce the impact of high price volatility that the cryptocurrency market is prone to. A characteristic feature of bitcoin that distinguishes it from government-issued fiat currencies is its limited issuance. The maximum possible amount of bitcoins that may exist will never exceed the mark of 21 million cryptocurrency units (Nakamoto, 2008).
A miner gets rewarded for each found transaction unit/block (blocks are generated every 10 minutes). The amount of remuneration is fixed and occurs after 210 thousand transaction blocks are found. The process of remuneration reduction will continue forever. However, by the year 2140, bitcoin supply would peak, and the overall supply will total 21 million cryptocurrency units. After that, miners, whose computer power will be used to locate blocks of transactions, will be receiving remuneration only from the commission or fees paid by the members of the system when making payments in cryptocurrency. The process of issuing new bitcoins units will stop (Figure 1).
With limited issuing of cryptocurrency, the inflation level of a bitcoin invariably falls with every passing year. This is because the algorithm of remuneration halving (twofold payment reduction) is embedded in the foundation of the system. The presence of this algorithm within the system of bitcoins gives way for the progressive decrease in the level of remuneration, which results in a smaller supply of coins (Table 2).
Bitcoin issuance can be easily predicted since the system is algorithmic, and nobody will ever be able to influence the results of emission.
Constant reduction of bitcoin issuance by 50 percent every four years leads to the reduction of bitcoin inflation. Therefore, by 2025, the level of inflation will be less than 1% and will amount to 0.83% per year. And by 2037, it will be less than 0.1%. By the year 2053, the inflation rate would drop to a level that will be completely invisible.
If we make a comparative analysis with fiat currencies that are prone to inflation, the advantage of bitcoins becomes so evident, that it is undeniable.
The US dollar was taken for the comparative analysis of inflation levels during the period from 1914 to 2014 (100 years). Bitcoin inflation data are taken from Table 2.  The fundamental differences between these inflationary indicators are noticeable when conducting comparative analysis (Figures 2, 3). The US dollar, representing government-issued fiat currencies, shows moderate inflation for over 100 years. However, the inflation rate exceeded 10% three times in the period of 1968-1983 (Brown, 2017). Deflation can also be observed, but it occurred at a time when the gold standard was used. Deflation had not occurred after the gold standard was canceled by President Nixon in 1971 (Fratianni & Hauskrecht, 1998).
Bitcoin data are more predictable. Inflation shows a steady downward trend with every passing year.
As mentioned earlier, the rate of remuneration within the bitcoin network is directly influenced by halving (twofold reduction of remuneration). It is hard to imagine that halving is the technical element that exerts a significant influence on the market value of bitcoins.
The first halving in the bitcoin system occurred in the middle of November in 2012. The number of new units generated by the network when finding a transaction block was reduced from 50 BTC to 25 BTC, which greatly affected the supply of bitcoins in the market. When halving happened, the market price was $12.5 for a bitcoin. A year later, a new price maximum was set at $1150 for a bitcoin. Since halving oc-      This indicator illustrates the historical results of bitcoin price changes within a weekly interval, its positive and negative price data, and price scale.
It is vital to weekly group intervals into periods, which are equal or approximately equal to one month to conduct a successful analysis. When taking historical data into account, we have 425 time intervals (weeks), which equals to 98 periods (months).
In order to achieve results, the next step is to find the average price values x for each period grouped earlier, i.e., the sum of all the values for each selected period, divided by the number of values in the selected period. Finding data of average price values helps maximize reverse pungent speculative growth and decline of the value of bitcoins in the market. Thus, the effects that halving has on the market value of bitcoins is evident (Table 3).
Having obtained data for average price values, it is possible to build graphs for the visual assessment of halving's influence on the value of bitcoin. For an accurate estimation, two graphs have been presented, because market prices of bitcoin for the period of 2015-2018 are considerably higher than the prices over the period of 2011-2015.
Throughout 2011-2015 ( Figure 5) the price peak was reached after 12 periods (12 months) and amounted to $1,150 per BTC. After that, a price correction began.
Throughout 2015-2018 (Figure 6), the price maximum was reached after 16 periods (16 months) and amounted to $19,500 for a BTC. Then price correction started again.   According to the data obtained, it is easy to see that after halving, the price over the next four periods was still at the previous levels in both cases.
With the onset of the fifth period, price volatility started to increase. Either way, the market needed an interim period of five months for the onset of reactions to halving.
To validate the impact of halving on the value of bitcoins, the rank correlation coefficient by Kendall was analyzed.
Kendall rank correlation coefficient is calculated by the following principles: 1) comparing each characteristic feature according to their sequence number (ascending, descending); 2) defining differences between ranks; 3) calculating the coefficient correlation according to the formula: where P -the amount of coincidences, Q -the amount of inversions, N -the number of periods; 4) calculating the critical point according to the following formula: ( ) ( ) 22 5 , 91 kp kp n Tz nn where n -the sample size, kp z -the critical point of the bilateral area, which can be calculated using the following Laplace function table: It is possible to execute the following calculations using the Laplace function

DISCUSSION
Judging from the presented data, bitcoin is fundamentally a more attractive asset than fiat currency. Being an asset, which is less prone to inflation, and assuming that the current price volatility decreases, bitcoin has a chance to become an asset, which the population will use as a storage of value, without the fear of money devaluation through inflation.
Today, or tomorrow, or in 10 years' time, the number of bitcoins in circulation cannot exceed 21 million units. Therefore, over time, the cost of bitcoin, ceteris paribus, should increase by at least the amount of the depreciation of the traditional currencies.
Having an algorithm of remuneration halving in its programme code, the bitcoin system creates a limited supply of new coins, which allows the production of cryptocurrency up to the year 2140, without exceeding the maximum supply of 21 million coins (Nakamoto, 2008).

CONCLUSION
Halving is a technical element, which has a direct impact on the market supply of new coins. Reducing remuneration every four years for each found transaction block, halving simultaneously reduces the overall issuance of new bitcoins twofold, which leads to an increase in the market value of cryptocurrency. Analysis of the effect that halving Bitcoin issuance has for the periods of 2011-2015 and 2015-2018 clearly shows that in both cases, it took the cryptocurrency five months to properly react to the halving that had occurred. The correlation between the level of remuneration from mining and the market price is confirmed by the Kendall rank correlation method. The correlation coefficient (τ = 0.27) is greater than the critical point (T_kp = 0.13), which suggests that the rank correlation between the level of remuneration and the market price is significant. The Kendall method can be used to conduct a comparative analysis of remuneration and market value of other cryptocurrencies.
Although bitcoin was established as a payment system, eliminating intermediaries from the money relationship chain, it is unlikely to become popular among the population as an instrument of payment (Hong, 2016;Ciaian, Rajcaniova, & Kancs, 2016). However, bitcoin is not subject to depreciation as the national currency is, it also does not depend on the control and regulating public bodies. All this makes it a good tool for savings.
The program code of the bitcoin system features an algorithm that cuts the reward from mining in half (halving). Moreover, it creates such a limited supply of new coins that cryptocurrency mining will be possible up until the year 2140, whilst still not exceeding the maximum supply of 21 million coins.