Bitcoin Математика



More than hacker intrusion, the real loss risk with bitcoin revolves around not backing up a wallet with a fail-safe copy. There is an important .dat file that is updated every time bitcoins are received or sent, so this .dat file should be copied and stored as a duplicate backup every day.

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How to Determine Bitcoin Value, and Other Cryptocurrencies
Now that we’ve established what cryptocurrencies are and why they are difficult to value, we can finally get into a few methods to approach how to determine their value.

Remember, price is what you pay, value is what you get. A stock can have a higher or lower price than what its value is truly worth, and a cryptocurrency can as well. What is a realistic Bitcoin value?

There’s no way to determine a precise inherent Bitcoin value, but there are certain back-of-the-envelope calculations that can give us a reasonable magnitude estimate for the value of bitcoins or other cryptocurrencies based on certain assumptions.

The trick, of course, is coming up with reasonable assumptions. 😉

Method 1) Quantity Theory of Money
Editor’s Note: I no longer consider this particularly applicable to Bitcoin because its usage has primarily shifted to being a store of value rather than medium of exchange, but back in 2017, it was one of my frameworks for analyzing it when it was less clear that it would shift in that direction. This approach mainly values it as a medium of exchange, which still makes it worthwhile to be familiar with.

The century-old equation to value money that anyone who ever took a macroeconomics class has learned is:

MV = PT

Where:

M is the money supply
V is the velocity of money in a given time period
P is the price level
T is the transaction volume in a given time period
If you double the money supply of an economy, and V and T remain constant, then the price P of everything should theoretically double, and therefore the value of each individual unit of currency has been cut in half.

The majority of mainstream economists accept the equation as valid over the long-term, with the caveat being that there’s a lag between changes in money supply or velocity and the resulting price changes, meaning it’s not necessarily true in the short-term. But the long-term is what this article focuses on.

If you know any three of the variables, you can solve for the final one. In other words, we can rearrange it into:

P = (M*V)/T

From that point, P will give us the inverse ratio of Bitcoin to whatever currency we use for our T variable. In other words:

Bitcoin Value = 1/P = T/(M*V)

The total number of bitcoins in existence (M) is a little under 19 million, and it will max out at under 21 million over the next several years based on its algorithm. That’s the easy part.

Now we have to come up with estimates for V and T, which is the hard part.

Let’s start with a velocity example. Suppose you had a town of just two people, a farmer and a carpenter. The only money in the town is that the carpenter has $50. If, in the course of the year, the carpenter buys $30 in carrots and $20 in tomatoes from the farmer, and then the farmer pays the same $50 to the carpenter to build a fence around her property to keep pests out, then a total of $100 in transaction volume (economic activity) has occurred. The money supply is $50, and the velocity of money is 2.

The velocity of the United States M1 (highly liquid) money supply (shown here) hit a high of over 10 in 2007 and is now around 4.

The velocity of the United States M2 (moderately liquid) money supply (shown here) hit a high of 2.2 in 1997 and is currently at less than 1.5.

Currently, the velocity of Bitcoin is much higher on average, but the problem is that a large portion of this velocity is just trading volume, not spending volume. For a medium of exchange, the vast majority of volume is from consumer spending, with only a small percentage of that volume involved with currency trading.

Bitcoin however has a significant percentage of it just being moved around by speculators, rather than people going down to their coffee shop and buying a cup of coffee with some Bitcoin fractions. There’s no way to know what percentage is moved around for spending compared to what percentage is moved around for trading/speculation.

But anyway, we have actual velocity, even if the number itself is questionable, and we have what the typical velocity range of a major fiat currency is. When I value Bitcoin, I will use a range for the velocity value to imagine a few different scenarios.

The final (and hardest) part is T. This is the variable that represents the actual value of goods traded in bitcoins per year.

Let’s start with criminal activity, since that was one of Bitcoin’s original applications. Editor’s note: This example became less and less relevant over time because as it became easier to track, Bitcoin’s use-case for illegal activity has diminished.

PwC estimates that global money laundering is $1-$2 trillion per year.

According to CNBC, the United Nations estimates that the global drug trade is worth $400-$500 billion per year, and that organized crime in general clocks in at $800-$900 billion, with much of that figure coming from their drug trafficking.

Most broadly of all, this research paper estimates that the global black market is equal to about 20% of global GDP, or about $15 trillion annually.

If we imagine right now that 10% of the global black market economic activity occurs in Bitcoin and nobody else uses Bitcoin, it would mean $1.5 trillion in goods/services is exchanged Bitcoin per year, which would be immense.

Going back to the Bitcoin = T/(M*V) equation, if M is 17 million bitcoins in existence, and we use V as 10, and T is $1.5 trillion, then each bitcoin should be worth about $8,800. Let’s call that an unrealistic high end estimate.

If T is $500 billion and V is 10, then each bitcoin is worth under $3,000.
If T is $100 billion and V is 10, then each bitcoin is worth under $600.
If T is $10 billion and V is 10, then each bitcoin is worth under $60.
I’m going to argue in my next section that the transaction volume of Bitcoin is on the bottom end of that range. It’s nowhere near $1.5 trillion, and probably not even a tenth of that.

Now, black market activities aren’t the only use of Bitcoin. A variety of companies accept Bitcoin like Microsoft, Overstock, Expedia, Newegg, plus other companies listed here. But it still seems more of a novelty at this point.

Besides estimating the current value of bitcoins, we can estimate the future value of bitcoins.

Suppose that cryptocurrencies really take off, and in ten years, 10% of global GDP trades hands in cryptocurrencies, with half of that being in Bitcoin. At about 2% GDP growth per year, the global GDP in ten years will be about $90 trillion USD, which means $9 trillion in cryptocurrency transactions including $4.5 trillion in Bitcoin transactions per year.

If T is $4.5 trillion, M is 20 million bitcoins in existence by then, and V is 10, then due to the Bitcoin = T/(M*V) equation, each bitcoin should be worth $22,500 by then.

And here’s a bearish scenario. If Bitcoin drops in market share to just 10% of cryptocurrency usage, and cryptocurrencies only account for 1% of GDP in ten years, and M is 20 million and V is 10, then each bitcoin will be worth about $450.

And I mean, it could drop to zero if its usage totally collapses for one reason or another, either because cryptocurrencies never gain traction or Bitcoin loses market share to other cryptocurrencies.

As you can see, there’s a huge range for what bitcoins should be worth in the coming decade or so, depending on how much economic activity they eventually become used for and what the velocity of the coins is.

If you stick to a velocity of 5 or 10 and look down those columns, you can then just focus on what level of economic activity you expect Bitcoin to be used for in the next decade, which will give you a rough idea of what it might be worth at that time.

Method 2) National Currency Comparisons
Note: This is a second medium-of-exchange calculation that is worthwhile to know, but in my opinion no longer a key way to think about cryptocurrency valuation.

Now, let’s keep it a bit simpler by not worrying about monetary velocity. Let’s just compare cryptocurrency adoption compared to fiat currencies as a rough order of magnitude sanity check.

Trading Economics has a list of the size of the M2 money supply of each country, converted to USD. The United States has over $18 trillion.

Right now, Bitcoin is worth worth $250 to $400 billion. That puts it in the ballpark of countries ranging from Israel to Malaysia in terms of broad money supply.

This chart gives an idea of the active user base of Bitcoin, since the ledger is public. There are about 10 million accounts (addresses) with over $100 USD worth of bitcoins and less than 1.5 million with over $10,000 USD worth of bitcoins. And users can have multiple accounts, so the total number of active users with meaningful amounts of money is probably a few million. For reference, the Bitcoin subreddit has about 1.8 million subscribers.

And then we’re back at the question of how much economic activity (the equivalent of GDP) that actually occurs in Bitcoin from these million or fewer active users. How much of the $400 billion+ global annual drug traffic market uses bitcoins? Or how much of the $15 trillion global black market? How much legal economic activity is occurring in bitcoins? It’s difficult to say.

Considering there are fewer active Bitcoin users than Israel citizens, the average Israeli citizen is quite well off, and most Bitcoin users probably only do a tiny portion if any of their economic activity in Bitcoin, there’s nowhere near as much economic activity in Bitcoin as Israel’s GDP.

But it could be a tenth as much, which means the value of all bitcoins together could be about a tenth as much as Israel’s money supply. That implies Bitcoin is heavily overvalued right now.

If 500,000 people do an average of $10,000 in Bitcoin economic activity per year (not trading, just actual spending), that would only be $5 billion in actual Bitcoin economic activity. That’s a tiny fraction of Israel’s nearly $400 billion economy, and Bitcoin’s total value would be a tiny fraction of Israel’s money supply (therefore just a few billion dollars worth), meaning each bitcoin should be worth like a hundred bucks and it’s currently grossly overvalued in tulip territory.

However, one argument for why Bitcoin is worth more now than it should be based on its estimated current economic activity, is because some people expect its adoption rate to go up quickly.

Suppose for example that within 10 years, Bitcoin surpasses Canadian dollars in terms of economic activity to become a top-ten world currency. Canada has 38 million people and a GDP of $1.8 trillion and their M2 money supply is worth over $1.5 trillion.

If there are 8 billion people in the world in ten years, and 5% of them use Bitcoin, that’ll be 400 million Bitcoin users. If the average Bitcoin user does only 10% of their economic activity in Bitcoin and 90% of their economic activity in typical currencies, then that’s the equivalent of 40 million people using Bitcoin for 100% of their economic activity, or roughly the size of the Canadian economy assuming similar average per-capita economic activity.

If Bitcoin’s reasonable market cap becomes worth, say, $1.5 trillion in that scenario (comparable to Canada’s M2 money supply), and there are 20 million bitcoins in existence by then, each bitcoin would be worth $75,000. That’s a bullish scenario, but not impossible. It explains why some people are willing to pay several thousand dollars per bitcoin today.

Method 3) Pure Store of Value: Percent of Net Worth
Note: For Bitcoin in particular, these are the types of models that I consider to be more valuable at the current time. Bitcoin’s usage has shifted primarily to being an alternate store of value rather than primarily being used as a medium of exchange.

Lastly, let’s compare Bitcoin value to gold value.

As the years go by, cryptocurrency adoption and payment rates are not really increasing by much. Not many businesses accept them and most people don’t seem to care about paying with them. Bitcoin’s usage in particular has shifted more towards being a store of value and a network that allows users to transmit value, rather than as a day-to-day medium of exchange.

Similarly, people buy gold not because they want to spend with it, but because they know it has permanent storage value for its utility. So, let’s assume Bitcoin has shifted to that status, and that it never takes off as an actual form of payment but instead just serves as a store of value for some people. Since Satoshi released the blockchain technology to all, Bitcoin has no unique claim to the underlying technology. Instead, it merely relies on network effects as the first mover in the cryptocurrency space, and money tends to be a “winner take all” game.

The world has about $400 trillion in wealth if translated to U.S. dollars. This consists mainly of stocks, bonds, real estate, business equity, and cash.

All the gold in the world is worth maybe $10 trillion, based on the World Gold Council’s estimate of how much gold has been mined and what the per-ounce price is. In other words, maybe 2-3% of global net worth consists of gold.

This is one way that analysts speculate about potential price movements in gold in a fundamental sense- they ask what if more people want to own gold in their net worth, due to various factors such as currency depreciation? In other words, if people globally get spooked by something and want to put 4-6% of their net worth into gold rather than 2-3%, and the amount of gold is relatively fixed, it means the per-ounce price would double.

If Bitcoin’s total market capitalization achieves half of the global value of gold ($5 trillion, or about 1-2% of global net worth) and the number of bitcoins at that time is 20 million, then each bitcoin would be valued at $250,000

If Bitcoin only achieves 10% as much global value as gold (well under 1% of global net worth), then each bitcoin would be worth about $50,000

If Bitcoin only achieves 5% as much global value as gold, then each bitcoin would be $25,000.

If Bitcoin collectively is only worth 1-2% of gold, then each one is down to $5,000 to $10,000.

Stock to Flow

Each commodity has a stock-to-flow ratio, which is a measure of how much is mined or produced per year compared to how much is stored.

Agricultural commodities, oil, copper, iron, and other industrial commodities generally have stock-to-flow ratios that are below 1x, meaning that the amount of them that is stored is equal to less than one year’s worth of production. Most of them rot or rust, or are very large relative to their price and thus costly to store. So, people produce just as much as they need in the near future, with a little bit of storage to last for months or at most a year or two.

Silver, being a bit more of a monetary metal and thus stored as coins, bullion, and silverware, has a stock-to-flow ratio of over 20x. This means that people collectively have over twenty time’s silver’s annual production ounces stored throughout the world.

Gold, being primarily a monetary metal, has a stock-to-flow ratio of 50-60x, meaning that there is 50-60 years’ worth of production stored in vaults and other places around the world.

When Bitcoin began in 2009, it had a low stock-to-flow ratio, but as more coins have come into existence while the number of new coins produced every 10 minutes has decreased due to its three pre-programmed halving events, its stock-to-flow ratio has kept increasing, and now roughly equals that of gold. Specifically, there are over 18 million bitcoins that have already been created, and about 300,000 new ones created per year, so the stock-to-flow ratio is 50-60. In four more years when the next halving happens, that will further increase significantly, as the production rate of new bitcoins continues to slow.

PlanB has put forth a stock-to-flow model that, as a backtest, does a solid job of categorizing and explaining Bitcoin’s rise in price since inception by matching it to its increasing stock-to-flow ratio over time. The line is the model and the red dots are the price of bitcoin over time. Note that the chart is exponential.

The model predicts a six-figure price in the coming years. Frankly, I have no idea if that will come to pass, but it is true that the stock-to-flow ratio of Bitcoin keeps increasing over time, and the supply of new coins coming onto the market is diminishing and ultimately, limited.

With this model, after each halving event every four years (where the number of new bitcoins created every 10 minutes decreases by half), the price of bitcoin eventually shoots up, hits a period of euphoria, and then comes back down to a choppy sideways level. Each of those sideways levels is a plateau that is far above the previous one. The recent level has been fluctuating around the $5,000-$15,000 region, and now it’s moving into the next level, according to that method of analysis.

Final Thoughts
Many people prefer precious metals to cryptocurrencies when it comes to alternative investments.

They have thousands of years of reliable history, and each precious metal has scarcity and inherent usefulness. They are all chemically unique, especially gold, and there are a very small number of precious metals that exist.

Cryptocurrencies on the other hand, while each one does have scarcity, are infinite in terms of how many total cryptocurrencies can be created. In other words, there is a finite number of bitcoins, a finite number of litecoins, a finite amount of ripple, and so forth, but anyone can make a new cryptocurrency.

What this means is that even if cryptocurrencies become popular in usage, they could become so heavily diluted by the sheer number of cryptocurrencies that any given cryptocurrency only has a tiny market share, and thus not much value per unit. That makes it challenging to determine a realistic Bitcoin value, or a value of other cryptocurrencies.

Right now, Bitcoin, Ethereum, and a few other systems have most of the market share. If cryptocurrencies take off in usage worldwide, and a small number of cryptocurrencies continue to make up most of the cryptocurrency market share, then it will likely be the case that the leading cryptocurrencies remain valuable, especially if you hold onto all coins when hard forks (currency splits) occur.

In that sense, the value of Bitcoin or any other cryptocurrency is based purely on its network effect, which is a type of economic moat. It lacks industrial value and could one day go to zero, but as long as enough people consider it a store of value, it can maintain or grow its value. As bitcoins become harder to mine, their individual value can increase as long as enough investors remain interested in storing value in the network.

Blockchains are an extremely novel technology, and cryptocurrencies based on blockchain technology do have a lot of reputable applications as a means of global exchange and store of value. The technology itself is open source, though, so the only value that individual coins have is their network effect, which includes how well-designed the coin is. Bitcoin was the first one, and is beautifully designed.

The engineering method of problem-solving is to break a difficult problem into several small parts and then solve them individually, or realize that certain parts are unsolvable and to identify which assumptions need to be made. The benefit of this article is that it quantitatively shows which assumptions are necessary to justify various cryptocurrency valuations.

Here’s what it takes to come up with a reasonable forward-looking valuation estimate for a given cryptocurrency:

Understand the numbers and growth rates of how many units can exist in that cryptocurrency. That’s easy.
Estimate how much economic activity or value storage will occur in total blockchain cryptocurrencies in 5-10 years. That’s hard.
Estimate how a given cryptocurrency will change or retain market share of total cryptocurrency usage. That’s hard.
Over time, my views on those second two questions have become more bullish in favor of Bitcoin, compared to my initial neutral opinion. Bitcoin now has over a decade of existence, and continues to have dominant market share of the cryptocurrency space (about 2/3rds of all cryptocurrency value is Bitcoin). Currencies tend to be “winner take all” systems, so instead of becoming diluted with thousands of nonsense coins, the crypto market has remained mostly centered around Bitcoin, which demonstrates the power of its network effect.

Similarly, the software to start a social media platform is easy and well-known at this point. However, actually making a social media company is extremely difficult, because you need tons of users to make it worthwhile, and only when you get enough users does it become self-perpetuating. Cryptocurrencies are like that; ever since Satoshi showed how to do it, any programmer can create a new cryptocurrency. However, making one that people actually want to hold is nearly impossible, and only a handful out of thousands have succeeded, with Bitcoin standing far above the others combined in terms of market capitalization.

Bitcoin prices could go up by a lot, or they could fall to nothing, and it mostly comes down to how much and how fast Bitcoin or any of these cryptocurrencies can maintain and grow their network effect to be seen as either a permanent store of value or a medium of exchange. As a medium of exchange, they are failing to take off. As a store of value, Bitcoin alone seems to be succeeding. Purely as a store of value, bitcoins have considerable upside. If the Bitcoin network earns even a quarter or half as much market share as gold, the upside per bitcoin is tremendous.

Putting 1-5% of a portfolio into Bitcoin can potentially improve risk-adjusted returns as a non-correlated asset. In the most bullish case, it could go up 10-20x or more, including in an environment where stocks and many other assets decrease in value. In a bearish case, it could lose value or even go to zero.



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