1 Security and scarcity: the dual feedback loop of Bitcoin.

The beauty of Bitcoin is that its security and scarcity work together to form a set of self-reinforcing collaborative feedback loops. The following figure shows:

Three models value Bitcoin: how do security and scarcity designs drive value? Figure 1: the scarcity and security of Bitcoin enhances its value, creating a double feedback loop.

Between halving, bitcoins have become more scarce as a proportion of the amount of money dug up in each block (currently about 18 million bitcoins) is diminishing.

With production regularly halved, the scarcity of Bitcoin has become increasingly apparent. It halves every 210000 blocks over a period of about four years, halving block awards and bringing Bitcoin’s long-term inflation rate closer to zero.

Note: the halving of mining reward is a long-term mechanism specially designed to restrain the inflation of encrypted digital currency and prolong the mining ecology.

The circular chart at the top right above shows that each new bitcoin accounts for a smaller and smaller proportion of circulation and has less and less impact on the market. This growing scarcity has pushed up prices.

The circular chart at the bottom left above shows that the rise in prices has encouraged the enthusiasm for mining.

The increase in computing power has improved the security of Bitcoin, and the strengthening of security measures will also push up prices. As a result, scarcity increases security, and increasing security and scarcity will increase the price of bitcoin in the long run.

2 time base: Bitcoin calendar system.

When studying price, market capitalization, hash rate, difficulty, transaction value, stock, and other variables related to time, I suggest using the bitcoin blockchain calendar as a basis to examine correlation and the relationship between these factors and time variables. will be more natural, appropriate and accurate.

After completing the analysis, these results can be easily converted to regular Gregorian calendar time for demonstration and further analysis. In the Bitcoin calendar system, the “Block year” (Block Year) is 52500 blocks, while the four-year “Block Age” (Block Era) is 210000 blocks. (see “living with Satoshi Nakamoto” for more details.).

The value of Bitcoin comes from its security and scarcity. Let’s take a look at the following three models.

Model 1: mining difficulty to obtain safety.

The existence of hash rate (computing power) ensures the security of bitcoin to some extent, but it turns out that the curve of hash rate is a relatively smooth curve because the hash rate is adjusted every 2016 blocks.

The hash rate is not a fixed value, and it will be adjusted continuously with the change of mining difficulty.

3.1 Model establishment.

In fact, in the life cycle of Bitcoin, the hash rate and difficulty increase with the block time to the 12th power.

In the article “Cryptography breaks Moore’s Law”, we study the increase of hash rate in the past 9.5 “block years” and find that it has been increasing to the 12th power of the block time (or equivalent, the height of the block).

The basic algorithmic driver of the hash rate is the difficulty of adjusting bitcoin. Adjustments occur every two “block weeks” (every 2016 blocks). The difficulty curve is much smoother than the average hash rate or even the average hash rate per week. If the production speed of the block is faster (slower) than the average of 10 minutes, the difficulty of the next two weeks will be increased (reduced). The average time (seconds) for miners to dig out a block is: time = difficulty * 232 / hash rate.

Three models value Bitcoin: how do security and scarcity designs drive value? Figure 2: relationship between difficulty logarithm and block year (regression relative to block year logarithm).

Let’s take a look at the regression diagram of block time and mining difficulty.

Figure 2 shows the logarithm of the block chain year and difficulty (with a base of 10) in quarterly intervals. In the 4th and 5th years, due to the popularization and application of ASICS mining machine, the form of GPU mining has been replaced, which makes mining more difficult.

The following table refers to half a year’s data, but the regression analysis uses quarterly data.

Three models value Bitcoin: how do security and scarcity designs drive value?

All the data in the logarithmic range (difficulty logarithm and block annual logarithm) are analyzed by linear regression, and the power law relationship with index 12.38 can be found. However, if we limit the data to year 6 and beyond (after the advent of the ASICS mining machine), the power law index will become 10.51 (R ²= 0.975). The difficulty of mining seems to be closely related to the height or year of the block.

The price of Bitcoin and the difficulty of mining have been in a positive cycle for a long time. Higher prices will attract more miners to enter the market, thus increasing the hash rate and making it more difficult again, keeping the block time at about 10 minutes. The progress of mining machine technology not only improves the profit margin of miners, but also increases the hash rate, which increases the difficulty.

3.2 the relationship between price and difficulty.

So what does price have to do with difficulty?

Woobull likes to study a Bitcoin difficulty ribbon made up of multiple moving averages of difficulty. This chart shows intuitively that a strong price correction will cause the difficulty of the index to flatten over a period of time, perhaps as long as a year. This could be a buying opportunity because weaker miners have been forced out, restoring market stability.

Three models value Bitcoin: how do security and scarcity designs drive value?

This may also be the time when we are closest to the balance of supply and demand, because the supply of bitcoin has little response to the price, except for a very short period of time-the hash rate automatically modifies the block time to 10 minutes. so the supply release rate is basically fixed.

If we use quarterly data to regress the difficulty logarithm of the price logarithm starting from the sixth block year, we find that the slope is 0.646 ~ R ²= 0.919. Using difficulty as a security agent, we can use the relationship between difficulty and block year (power law with index 10.51) and price-difficulty relationship (power law with index 0.646) to obtain the following price forecasts:

Three models value Bitcoin: how do security and scarcity designs drive value?

For the logarithmic price forecast from Block 6 to Block 11.5, the standard deviation in the error term is 0.289, and the price change of one σ is 1.95.

Therefore, if the relationship between block year and price and difficulty persists, there is a 68 per cent probability that Bitcoin prices will be in the range of $8000 to $30300 near Block 12 (2020) and between $36400 and $138,000 around Block 15 (2023).

3.3 regression and cointegration.

The R ²values generated by regression between non-normally distributed processes must be handled carefully, as false correlations may occur.

In historical price data, both difficulty and price have increased strongly over time. In order to have an effective power law regression between price and difficulty, it is important to look at the order of the processes being compared. How many times does it take to differentiate a variable to get a stable normal distribution?

Fortunately, both logarithmic difficulty and logarithmic price seem to be second-order processes. For logarithmic difficulty, the average value of the first-order (second-order) increment is 0.2306 (- 0.0129), of which 5.1% (57.9%) is negative. The first-order difference does not seem to be close to the normal value, but the second-order difference looks normal.

For the price logarithm, the average value of the first order (second order) is 0.114, the negative value of the first order (second order) difference is 33.3% (43.4%), and the first order differential does not seem to be normal. The second-order differential seems relatively normal. Therefore, the co-integration between difficulty and price looks feasible, because both seem to be second-order processes.

Model 2: scarcity and reserve-production (S2F) model.

The most famous bitcoin value analysis model is Plan B’s reserve-production model (scarcity model). Note: Plan B is a well-known cryptographic asset analyst on Twitter.

Three models value Bitcoin: how do security and scarcity designs drive value?

The expression of this model is very simple, that is, scarcity gives value. PlanB points out that this applies to precious metals, including gold, silver and platinum; even diamonds follow the same ordinary power-law curve with an index of 2.2 (note that in a later article, PlanB revised the inventory flow of silver to a lower value and increased platinum and diamonds, and basically all had the same curve).

Using the evolution of Bitcoin relative to its growing reserves-production (recording reserves versus production at logarithmic prices), he found that Bitcoin followed a steeper power law than precious metals, about 3.3.

Note: the Stock-to-Flow (S2F) ratio model (i.e. reserves-production model) refers to the number of available assets or reserve assets divided by the quantity produced each year. The Stock-to-Flow ratio is an important indicator because the higher index value in S2F reflects the decrease in the annual inflation rate of assets.

Perhaps one of the reasons why the Bitcoin power law index is 50% steeper than the gold and precious metals index is the increasing security / difficulty of bitcoin. As Bitcoin becomes more and more scarce, it is also more and more secure, while the scarcity and security of gold are basically static.

Reserves-production is inversely proportional to the rate of inflation and is measured by the amount of circulation divided by one year’s production, including recovery and any reduction in reserves. In the case of gold, the reserve-to-production ratio (S2F) is 55, an inflation rate of about 1.8 per cent. This is a relatively stable figure in recent years.

In terms of block time, Bitcoin has a fully predictable inventory. There are some changes that differ from the calendar time, but the block year is very close to the calendar year and is currently shortened by a few weeks.

The article “Bitcoin’s non-inflationary monetary policy” accurately illustrates how S2F grows over time. S2F = 4 x (2 ^ E-2) at each half, where E is the block age. At present, we are in the third era, which begins when the value of S2F ratio is 24. In the process of halving twice, the value of S2F increases gradually, and then increases greatly when it is halved.

The next half of Bitcoin is expected in May 2020, when it will enter the fourth era of Bitcoin (after the third halving), and the S2F value is expected to jump to 56. Its scarcity will also be further magnified.

At that time, the S2F value of Bitcoin will match gold for the first time in history, and the inflation rate will fall to 1.8%. Bitcoin will become more scarce than gold. By 2024, S2F will reach 120 and inflation will fall to 0.83%.

Never before in history has there been such a tough and absolutely scarce currency.

Using the quarterly data in the block calendar system, I find that the power law relation price ~ S2F ^ 3.25 is similar to the result of Plan B. In this analysis, I used the midpoint inventory flow (looking back and looking forward for half a year), rather than a fully forward-looking or only backward option to measure traffic. The regression R ²of this power law is 0.926.

Three models value Bitcoin: how do security and scarcity designs drive value?

A more detailed study of the cointegration of two non-stationary processes (price and reserve-production) shows that this relationship is effective. A frequently used analogy is that reserve-production is a dog that leads its owner home in a deliberate way (closer to a higher price), while a drunk chained to a dog moves either way in a constrained random walk.

In fact, concerns about false correlations seem to be linked to excess inventory. After all, the reserve production within the block time is not a random process, but a completely predetermined calculation. For each halving, the forward inventory is given by the above halving formula, and then increased by 1.0 units per block year until the next halving (because constant flow of one year is added to the reserves), until the next halving (because the constant flow of one year is added to the inventory). Therefore, reserves can be used as a basic vector to measure other more derived processes, such as price, difficulty, and hash.

The uncertainty of price prediction is very large. In the price logarithm, the standard deviation of the prediction error of the reserve-production model is 0.325, or the coefficient in any direction is 2.11.

You might ask, what about the bifurcation of the main bitcoin chain? BCH and BSV are the biggest forks of the original bitcoin and nominally have the same scarcity attribute, but because their security is greatly reduced and they are not really decentralized, the market doubts whether they will strictly abide by the core Bitcoin supply algorithm. Obviously, they are much less secure, with BCH being 36 times less secure at the time of this writing, and BSV even less difficult.

Three models value Bitcoin: how do security and scarcity designs drive value?

Model 3: price and block time.

Some people, such as HC Burger, even like to directly simulate and speculate the price of bitcoin based on regular calendar time. Using block time, one can find a fairly reasonable power law. Price~ Byr ^ 5.42, where Byr is the number of years of the block (you can also use the height of the block). The resulting R ²value is 0.916, which is slightly lower than the stock flow model. The standard deviation of the logarithm of the price is 0.350, or 2.24 times.

In an article written by Burgercrypto (Burger and Burgercrytpo, which are two different platforms, he raised the question of using the logarithm of time. What he is worried about is: “if two time series may be cointegrated, then these time series must be integrated in the same order.”

But time is not a time series! It is a completely predetermined basis vector that is used to map other data. The only question is: if you use Gregorian time, what should be used as the zero point. The most obvious is January 9, 2009 (or January 3, 2009), but sometimes people use other arbitrary starting points, which seems suspicious.

In fact, Burgercrypto points out that time is a relative concept and discusses various options for startup time. If you use chunk time, then this is not a problem, because in this case, there is an absolutely defined starting point. At least in the case of block time and reserve production, we do have a completely predetermined basis vector. Using the logarithm of block time is just a deformation of a fully predefined basis vector.

6 comparison of three models.

We summarize these three predictions in Table 5 and plot them in figure 3. For each forecast, the standard deviation is about twice the forecast price on both sides of the price.

Three models value Bitcoin: how do security and scarcity designs drive value?

The reserve-production model is the most long-term and forward-looking model, and also shows the fastest price response, as expected for shocks or shock flows. We can call it “shock flow”. Unlike the strong shock wave in physics, which causes a four-fold increase in shock wave density, the supply “shock stream” increases prices by about tenfold.

We can regard the reserve-production model as a leading indicator and the price-based model as a lagging or backward indicator. The difficulty model is a coincident model, and like inventory flow, it has an identifiable driver.

The S2F model has a clear price driver, that is, the impulse or large change provided when S2F is inevitably pushed to new highs every four block years. This is a steep model, the price is the power law of S2F, and S2F is the index of block time. It is not surprising, therefore, that its forecasts for future prices are very aggressive. Obviously, this is also the most forward-looking model, because the halving effect is known between now and 2140 years ago.

For calendar time or block time, the only direct driver is persistence, or something similar to the Lindy effect. (note: the Lindy effect means that for something that does not die naturally, such as a technology or an idea, their life expectancy is proportional to the time they already exist. The Bitcoin network is considered to have stronger persistence and growth potential because its life cycle has been extended by another block year. Of course, with the passage of time, the difficulty and inventory flow will increase with the passage of time.

Three models value Bitcoin: how do security and scarcity designs drive value? Figure 3: price forecasts for block time, inventory, and inventory outflows in the 15th year (March 2023). The next halving will take place in Block 12 (May 2020)

Safety (difficulty) and scarcity (reserves-production) provide the basic drivers of value. Security makes things more valuable, or at least protects value. People want what’s in the vault. Scarcity certainly makes things more valuable. Although diamonds are more carbon than coal, diamonds are more valuable than coal.

All of these are models, and they will have reference value until they fail. Useful, but not the ultimate truth. We are still learning how the highly dynamic Bitcoin network has evolved, and it has a lot of complexity.

The difficulty model arises from the observation that price and difficulty are related to a moderate power law, and the difficulty itself has increased sharply over time.

In terms of difficulty, given the limitations of electricity price and availability, one cannot help but ask whether it can grow at such a fast rate. In Bitcoin Power consumption: is it worth it? In the article, I found that the electricity consumption of bitcoin mining has more than doubled every year over the past few years. This may lead to rationing or price rationing for miners.

Over the next year or two, we will track price behavior and have some understanding of how much special coins are worth from security (difficulty) and how much value comes from scarcity (inventory flow). Perhaps someone will develop a compound model that takes these two factors into account. Interestingly, in the next 3.5 block years, the difficulty and inventory flow model will eventually predict a price of around $70,000.

Because there is no “quantum pulse” effect produced by halving the forcing function, the difficulty lags behind. Since the miners knew in advance what would happen, they would take measures to phase out the old equipment and upgrade to the new equipment to adapt to the environment after the output was halved.

When you see the results of these models and the high standard deviation, whether using predictions based on difficulty, reserves-production, or block time, it reminds us that when the price of bitcoin moves $1000 or $3000 in the opposite direction, people really shouldn’t panic. Because this is a small offset from the typical volatility of Bitcoin.

Writing this article allowed me to introduce another model, a difficulty-based price model, but deepened my common belief in Plan B’s reserve-production model. I think both models are worth tracking. The difficulty analysis may provide some explanation for why bifurcations such as BCH and BSV have similar reserves-production to Bitcoin but are worth so little relative to Bitcoin.

I also encourage the use of block time as the basis for regression and cointegration analysis: this is the natural rhythm of bitcoin.

7 the genius of Satoshi Nakamoto.

Halving the block reward algorithm seems to be Satoshi Nakamoto’s genius. For example, he could have proposed the release of 500,000 bitcoins a year for 42 years.

He chose to halve four block years as cycles, providing a “shock stream”, suggesting that he has an advanced sense that the technology cycle, and perhaps the monetary and business cycle, will have a full impact on mining and the Bitcoin economy as a whole.

Mining hardware is destined to improve faster than Moore’s Law. If Bitcoin succeeds, rising prices will attract more miners into the industry.

For S2F, although it has a strong basic principle, by 2024, when S2F will be equal to 120 (inflation rate is less than 1%), the model will enter unknown territory. This will be the scarcity of monetary assets we have never seen before. At some point, the power law will be broken, but will it be when the market value of Bitcoin is equal to the market value of all gold ($8 trillion), or equal to the global M2 money supply ($90 trillion), or some other level?

The reserve production model quantifies the relationship between the future market value of Bitcoin and the money supply, and suggests that the price of Bitcoin will slow.

Remember, it is not only the money supply that matters, but also the speed of money circulation. At present, Bitcoin circulates much faster than the dollar. Higher speeds support larger economies, but they are less stable. The speed of Bitcoin is expected to decline as it becomes more valuable and becomes a more stable asset.

After 2024, once the inflation rate of bitcoin is less than 1%, what does it matter if it is 0.4% or 0.1%? By 2080, all but the last 100 bitcoins will be mined. Before that, the reserve-production model may break through a less steep power law. Perhaps the increased security due to increasing difficulty can also support the current steep power law; it is also hoped that Bitcoin’s young, vibrant nature and its ever-changing inventory is one of the reasons.

The power-law index of precious metals is about 2.2, so this could be a transitional phase, as Bitcoin is likely to move on the same curve as gold and silver if two, three or four new supply shocks are halved in the future.

The total global wealth is about $300 trillion, but people do not need the same amount of base currency, that is, the unit of account. 2/3 of the world’s wealth is in real estate, and if Bitcoin becomes the base currency of the future monetary system, it can be revalued in bitcoin. Then there may be decentralized Bitcoin banks in the future.

Before we reach this stage, we are likely to see central banks add bitcoin to their reserve balances to defend the monopoly of their institutions and banking systems. Bitcoin seriously challenges the idea of a French coin-based reserve bank, so there may be many changes, but it is hard to predict.