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The fundamentals of bitcoin as an asset exist and they are stupider than you can imagine

tldr; tldr; Hodling is deflationary and all those wild price swings from bitcoin are changes in the fundamental value of bitcoin. Really.
tldr; Imagine there is a market where $100 worth of goods are sold every day using 100 bitcoins which cycle around. Then each bitcoin would be worth $1. Now suppose that 50 of the bitcoins were being held in anticipation of growing in value so only 50 bitcoins were cycling each day. For all the goods in the market to be sold every day each bitcoin will now be worth $2.
Introduction There has been a lot of discussion about what the fundamental value of bitcoin is. The consensus view in this subreddit is that the fundamental value is zero. I argue in this post that the fundamental value of bitcoin is whatever the price is right now, or a something close to it. This is because the fundamentals of bitcoin are stupid. Unimaginably stupid.
Bitcoin as Currency Bitcoin is a terrible currency compared to normal statist filthy fiat. Bitcoins are often permanently lost due to hacking or easily made mistakes. Transactions take considerable time to be confirmed. The price is highly volatile. But this post isn’t going into those issues in depth.
There is little evidence for mainstream Bitcoin use. A report by Morgan Stanley on the acceptance of Bitcoin from online retailers found that only 3 out of the 500 online retailers tracked accepted Bitcoin payments, a decrease from 5 in the previous year. The report concluded: “Bitcoin acceptance is virtually zero and shrinking”.
The number of transaction on darknet markets is large. On darknet markets users buy illegal products using cryptocurrencies (not just Bitcoin). Due to their illegal nature, it is impossible to know the exact value of transactions that take place on them. Between February 2011 and July 2013 the darknet market Silk Road had 1,229,465 transactions comprising 9,519,644 bitcoins in revenue. Darknet markets, along with ransomware payments are the only uses where there is evidence of a substantial number of bitcoin transactions taking place.
To work at scale darknet markets require cryptocurrency to pay for goods on sale. The anonymous nature of cryptocurrency allows transactions to take place without the buyer or the seller knowing anything about each other (although if a buyer has drugs mailed to them the seller will know who they are). If darknet markets used another form of payment then law enforcement could buy something and then track both the money going to the seller and the commission paid to the darknet market. It isn’t true as many people have claimed that nothing backs bitcoin. Bitcoin is backed by darknet markets.
There are a few kinds of people who buy bitcoin and want to spend it. They include drug buyers, those who need to pay off ransomware, money launders, fraudsters, and a few others but for simplicity’s sake I will just call them drug buyers. Likewise, there are a few types of people who sell products for bitcoin but again for simplicity’s sake I will call them drug sellers.
Non-circularity Bitcoin is a currency with a property that I call non-circularity. With Actual Money, when I buy something in a shop, the money I paid with goes towards the wages of the staff, rent and the products themselves among other expenses. This money then flows on to others. When a drug seller receives bitcoin in exchange for their drugs they can’t use the bitcoin to pay for their groceries or to pay their rent. They must exchange the bitcoin for filthy fiat to buy food. The inability to use bitcoin for further purchases means it is a non-circular currency. Bitcoin is a medium of a medium of exchange.
A full bitcoin transaction thus consists of three parts:
  1. A drug buyer goes to a bitcoin exchange to get bitcoin in exchange for filthy fiat
  2. The drug buyer goes to the DNM to exchange bitcoin for drugs from the drug seller
  3. The drug seller goes to the bitcoin exchange to get filthy fiat in exchange for bitcoin
An exchange is any place which matches buyers and sellers of bitcoin. This includes online exchanges like Coinbase as well as LocalBitcoins which matches people for face to face transactions. As nobody receives bitcoin for payment except drug dealers, the only place for drug buyers to get bitcoin is an exchange. The extreme volatility of bitcoin means that drug buyers and sellers try to complete the process as quickly as possible and avoid holding onto bitcoin.
Perfect Price Unstickiness For normal currencies prices are sticky. That means that nominal prices do not respond quickly to changing economic conditions. In contrast bitcoin has what I call perfect price unstickiness so the price of goods in bitcoin changes almost perfectly to changes in the value of bitcoin.
This is because prices for items which can be bought with bitcoin are never actually set in bitcoin, probably due to the high volatility. Instead they are set in fiat. The amount in fiat can either be listed directly, so $US50 for these drugs, or the price can be listed in the converted amount of bitcoin, 0.005BTC if 1 BTC = $US10,000. Changes in the price of bitcoin on exchanges are instantly reflected in the prices of drugs in bitcoins on darknet markets.
Hodling Another feature of bitcoin that should be considered is that people hodl bitcoin. The word comes from a typo of ‘hold’. Bitcoin is often bought on exchanges not for use as a currency to buy drugs, but as an asset in expectation of a price rise. Hodlers are the third type of user of bitcoin along with drug buyers and drug sellers. Although they don’t use it.
What’s the difference between an asset that is held and one that is hodled? This is admittedly vague, but an asset is hodled if it is being held, it can be held for long periods at low costs, it can but isn’t generating any income and there are no plans to generate income from it soon.
Cash under the mattress is being hodled, cash in my wallet that I am going to buy stuff with soon is not. Money in my bank account is generating income and so is not hodled. Bitcoin held in anticipation of price rises is being hodled. Bitcoin bought to buy drugs but which has not been used yet is not. Gold stored in a vault is being hodled, gold used for electronics purposes is not (jewellery is a harder case). A vacant block of land with no plans to develop it or use it for anything is being hodled but one that is soon going to have an apartment block built on it is not.
Commodities can be held and do not generate income until sold but it is expensive to hold most commodities for long periods of time. This prevents most commodities from being hodled.
Velocity The velocity of money is the average number of times a unit of fiat changes hands in a period. You can skip the next three paragraphs as they are a little annoying and you can get by without them. Just know that I am defining the velocity of bitcoin as what the velocity of bitcoin would be if no bitcoin was being hodled.
Due to hodling, the velocity of bitcoin under the conventional definition can vary wildly. Consider two cases. Both have 100 bitcoins, 100 transactions a day and all non-hodled bitcoins are spent each day. The first has no hodled bitcoins, the second 50 hodled bitcoins. The first has a velocity of bitcoin of 1 transaction per day, the second is 0.5 per day.
I want a definition of velocity of bitcoin that is not impacted by changes in hodling. I did consider doing this analysis through changes in velocity but the final formula is easier to understand if we find a definition of velocity of bitcoin that is independent of the level of hodling.
The definition that achieves this is (Length of Time)/(Average length of time to complete transaction). When there is no hodling the two definitions agree but the new definition is unchanged by any rise or fall in the level of hodling, which is what we need. From this point on when I refer to the velocity of bitcoin I am referring to the second definition.
The actual time to complete a bitcoin transaction seems to be over a week. In an interview one vendor claimed that it took one week for the bitcoin to be released from escrow and longer to convert it to actual money.
Intuitive argument Assume that the amount of drugs sold on darknet markets changes little from week to week. If the price of bitcoin doubles over the week then the number of bitcoins flowing through the darknet markets will halve. So where have the bitcoins gone? Drug buyers and sellers don’t have them. The only option is hodlers. In fact, it was the hodlers buying the bitcoins that caused the price to change.
Formula The conventional formula for the relationship between velocity of money (V), nominal amount of money (M), price level (P) and real economic activity (Q) is
V*M = P*Q
I am going to change that equation slightly so it now concerns the velocity of bitcoin (V), the total number of bitcoins (M), the price level of bitcoin (P), the total value in fiat of all economic transactions (Q) and the proportion of bitcoins that are hodled (h). If h*M bitcoins are being hodled then there are (1-h)*M bitcoins being used in economic transactions. The new equation is
V*(1-h)*M = P*Q
Next we isolate P:
P = V*(1-h)*M/Q
If the price level changes from 1 to 1.1 that means that there has been 10% inflation over the period and that the value of bitcoin has fallen. To find the value of a single bitcoin we have to take the reciprocal of P and that gives a formula for the true value of bitcoin:
1/P = Q/[V*(1-h)*M]
In the rest of the post when I write the price of bitcoin I mean the price bitcoin sells for on exchanges. I establish in the next section that this price must be close to the true value of bitcoin.
Equilibrium This section uses the flow of bitcoin model established earlier. We assume no activity from hodlers and that economic users do not hodl bitcoin (not true but it simplifies and does not hurt the model). Furthermore, we assume that all activity on the bitcoin exchanges happens, then all activity on the darknet markets happens. Drug sellers sell their bitcoin to drug buyers, then drug buyers use the bitcoin to buy drugs on the darknet markets. Neither the exchanges or the darknet markets charge commissions. I use specific numbers but my reasoning is easily generalizable.
To establish why the equation is true we must consider what happens if the actual price is higher or lower than the price given by the formula. First let us suppose that the price is lower than the price predicted by the formula. Over the time period of a day suppose that Q = 100 (so $100 worth of transactions a day), V = 1 (transactions take a day), M = 100 (100 bitcoins) and h = 0.5 (50 bitcoins are hodled). This gives a predicted price of $2. Suppose the price is instead $1.
Every day there are $100 worth of drugs available to be sold and buyers willing to buy $100 worth of drugs. At a price of $1 and with only 50 bitcoins available for economic use each day that means that only $50 worth of drugs can be sold. This would drop Q to 50 and immediately correct the equation.
However, there are buyers and sellers who want more drug dealing than that. Some buyers are not going to be able to get their drugs given the current price. Some of them will be willing to pay higher prices for bitcoin to guarantee they can have their drugs. Suppose that the drug sellers have 50 bitcoins (hodlers also have 50). They want to sell their 50 bitcoins to drug buyers on an exchange. Some drug buyers then bid the price of bitcoin up to $1.10 (for example). This benefits other drug buyers as now $55 worth of drug transactions can take place each day. In this way, the price will be bid up to $2, the equilibrium price.
If the price is $1 and the drug buyers have the 50 bitcoins then they will spend the bitcoins to buy $50 worth of drugs and then we are in the situation above.
Now suppose the reverse happens and the actual price is higher than the predicted price. Let the actual price be $4, with all the same example values from the previous example, so the predicted price is $2. On the exchange drug sellers have 50 bitcoins worth $200 to sell. Drug buyers want to buy $100 worth of bitcoin. At this price only 25 bitcoins are sold. To ensure they sell more of their bitcoin, drug buyers bid down the price. If the price does not immediately reach $2 then the left-over bitcoins will be held by the drug sellers until the next day when the price will be bid down again.
The drug sellers holding bitcoin for a few extra days is not the same as hodling because they are actively trying to sell them on an exchange but they haven’t because the price isn’t in equilibrium. They could instead decide to sell only 25 bitcoins and hodl the other 25. This would raise h to 0.75 and the price would be in equilibrium again.
Now suppose that the drug buyers have 50 bitcoins and the price is $4. Then $100 worth of drugs are bought with 25 bitcoins. The drug sellers will not be able to sell their bitcoin as drug buyers already have enough bitcoin to buy the next round of drugs they want. The drug buyers spend their last 25 bitcoin and drug sellers now have 50 bitcoins and the situation is as above.
In conclusion, the price of Bitcoin is fundamentally determined by speculators and brought into equilibrium by criminals.
Inflows and Outflows of Hodling The previous section treated the level of hodling as constant, except when drug buyers or sellers decide to hodl extra bitcoins that are in their possession. Now we will treat the amount of hodled bitcoins as changing. The next topic to consider is the relationship between filthy fiat spent to hodl bitcoins and the bitcoin price.
To calculate how much it costs to raise the hodl ratio from 0 to h we assume that the bitcoins are bought continuously. We integrate the function Q/[M*V*(1-t/M)] between 0 and h*M. The result is (Q/V)ln[1/(1-h)].
To double the price of bitcoin by taking h from 0 to 0.5 will cost (Q/V)ln(2). In fact, it will always cost this amount to double the price of bitcoin as we can see by finding the difference between the total value of hodled bitcoin when we consider hodling levels of h and (h+1)/2.
This means that the price of bitcoin rises exponentially when a constant amount of new money buys bitcoin to hodl. I would illustrate this with a log-scale graph but I don’t know where to find one. It also means that the market capitalisation of a cryptocurrency gives very little idea about how much the cryptocurrency is worth. It is an impossibility for all hodlers to receive the Actual Money that they think their bitcoin is worth.
Volatility People hoping to get rich and their buying and selling bitcoin is what causes bitcoin’s extreme volatility. Theoretically this could be stopped if there was a bank where hodlers could deposit their bitcoins and earn interest. However, for this to work would require the existence of a bitcoin bank which is not a Ponzi which seems like an unlikely outcome.
Hodling Gold A quick digression into gold, but I suspect someone has already thought of what follows. We can consider gold like a conventional commodity with conventional supply and demand curves (the real world for all commodities is more complicated but this is going to be quick). But people also hodl gold. If hodlers decide to buy $100 million worth of gold produced in the year, then that will change the equilibrium price. The new price is such that the difference between the quantity demanded by non-hodlers and the quantity supplied at that price multiplied by the price is 100 million.
If the overall level of hodling declines then the reverse happens. The hodlers sell an amount of gold, that amount is the difference between the amount supplied and demanded. The hodlers earn that amount multiplied by the new lower price. (I assumed people bought a fiat amount of gold and sold a volume of gold to make things easier).
Without another hodler to take on the gold or an improvement in market conditions, the hodlers are guaranteed a loss. To make a profit hodling gold you need there to be hodlers to sell it on to (or an improvement in the underlying factors). It follows that all the gold hodled in the world today cannot be sold without causing the fundamentals of gold to collapse. With 40% of the gold produced in 2017 being hodled this will eventually become a significant issue.
Full Reserve Banking Another place where we can consider the impact of hodling is full reserve banking. It is a form of banking where banks are required to have cash on hand equal to the full amount in all demand deposit accounts. The bank does not lend this money. This contrasts with the present system where banks are only required to have a certain fraction of this amount on hand, called fractional reserve banking. Money in a fractional reserve bank account is not being hodled (or is, but to a more limited degree) as it is being lent on to other people and it is generating income for the depositor.
Deposits under full reserve banking are hodling. They are like cash stuffed under a mattress but have better security. In a recession people increase their saving rates. Much of this additional saving will be in liquid assets because of fears of economic trouble. This rise in deposits under full reserve is an increase in hodled cash which then causes deflation. This is a big problem in a recession. (Somebody else has probably already made this observation).
Velocity and Value Consider the equation of bitcoin’s value again. Notice that the value increases when V decreases. Which means that the length of time to complete a transaction has increased. Bitcoin is an asset and a currency and its value as an asset increases as the length of time it takes to complete a transaction increases. This is a minor bit of stupidity which surprised me but seems obvious in retrospect as if bitcoins take longer to be processed then they must be worth more so that all transactions can happen. (This is assuming that a decrease in V does not also cause a decrease in Q which might be caused by drug buyers and sellers switching to a different cryptocurrency).
Hodler Behavior With one exception which I might make in another post I make no assumptions about hodler behaviour. I think they are buying and selling with no rational basis. But there are two rational reasons why someone would expect the price of bitcoin to rise: increased economic activity using the cryptocurrency in the darknet markets or an increased level of hodling in the future. The DNM is an actual economic activity but due to its illegality knowing anything about the amounts involved is impossible for almost everyone as is predicting their trends. Future hodling levels are also impossible to predict, unless you run a pump and dump. We can’t expect any sort of rational behavior from hodlers.
Nakamoto Scheme Preston Byrne developed the concept of a Nakamoto Scheme to describe cryptocurrencies because of how they differed from Ponzis and pyramid schemes. While bitcoin has been frequently called a Ponzi or pyramid scheme it is clearly something different. There are no “dividends” paid or any sort of organised structure. There are similarities, notably early adopters make their money at the expense of later adopters. Like in pyramid schemes hodlers try to convince new people to join in.
It is best to consider bitcoin as a type of asset which is uniquely suited for a pump and dump. When hodlers buy bitcoin, and encourage others to do the same (the pump) the fundamental price of bitcoin really is raised by these actions which helps the pump.
To add to Byrne’s work, we should put the properties of cryptocurrency assets at the centre of the scheme. A Nakamoto scheme works like this: first create a cryptocurrency and keep most of it for yourself. Then release it and try to get as many other people hodling as possible and try to get the darknet markets to adopt it (I’m looking at you Monero). This increases the fundamental value of the asset. Then dump your hodlings. Pocket the actual money. This is probably legal right now. But I’m not a law-knowing person.
For the hodler the Nakamoto scheme is like going to a party. You arrive and leave later on. If there are more people at the party when you leave compared to when you arrived then you’ve made a profit. There is also drug dealing going on at the party. The change in the level of drug dealing also impacts your profits. You have to try and get more people to come to the party and be careful of everyone else at the party who have the exact same incentives as you. It is a weird new form of scam.
Lower bound on price While the price of bitcoin can theoretically be infinitely high there is a lower bound on the price when the hodling ratio is zero. For given levels of Q, V and M the value of bitcoin can never go below Q/[V*M] (the highest possible price for bitcoin is when 1 satoshi is equal to the value of a transaction).
Some bitcoins have been permanently lost due to people losing their wallet keys or bitcoins being sent to the wrong address. If we suppose that H is the proportion of coins that have been permanently lost then the actual lower bound is Q/[V*(1-H)*M]. Note that a hodler losing their coins does not change the present fundamental value of bitcoin.
What could cause bitcoin’s price to go lower? Besides a mass hodler sell-off the obvious reason is a permanent decline in Q. What could cause this? Law enforcement have successfully shut down many darknet markets but others have replaced them quickly. What could really hurt darknet markets is increased government scrutiny of exchanges. When governments realise that bitcoin has no use beyond criminal transactions and speculation they might decide to treat every bitcoin transaction as inherently suspicious and regulate exchanges heavily. This will make bitcoin much harder to use for criminal transactions and thus greatly decrease Q and the value of bitcoin.
Previous work This post is not entirely original. Satoshi himself said that if a bitcoin user wanted to give a donation to everyone else then they should delete the keys to their wallet and increase the value of everybody else’s bitcoins. I realised that someone who hodled a bitcoin would temporarily have the same effect.
More significantly Joseph C Wang came up with a formula very similar to mine. A significant difference is that he thought increased economic activity with bitcoin would not cause an increase in bitcoin’s value but an increase in its velocity. My model has nominal prices of drugs in bitcoin falling when Q increases. Wang has prices remaining the same and the velocity of bitcoin increasing to handle the extra transactions. I developed my formula before I became aware of Wang’s work.
Further Topics This post is over 4000 words so I have not gone into depth on a few subjects like the costs of block rewards (higher than you think), shocks like darknet market shutdowns, why bitcoin can’t fall to a liquidity trap, how to value a cryptocurrency that isn’t being used for economic transactions and why it makes sense that bitcoin and bcash had a higher combined value at the time of the fork compared to bitcoin alone. If there is demand I’ll put together a second post which will cover these issues.
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