Background: A lot of the discussion on bitcoin value is IMO lacking in a proper analytical grounding. People throw out random numbers, or say you should look at the market cap of visa etc, without providing any rationale. I'm not an academic, but I studied economics and spend my day valuing companies so I have a degree of expertise. I also did a bit of research to understand better the dynamics of other currencies to which I compare certain attributes, e.g., velocity. Note that this is over a year old so the numbers are a bit out of date but that shouldn't make much difference to the basic analysis. The link to the article on scribd is here... http://www.scribd.com/doc/217902157/Valuing-Bitcoin
... and I've inserted the full text here (I guess the formatting will not be great)..
Summary: I use a very simple model of transaction value, bitcoin velocity and the number of bitcoins in use to derive a fair value for a bitcoin today. Rather than trying to analyse in detail the likelihood of and means by which bitcoin may become more widely adopted, I use a scenario analysis that allows us to take a ‘finger in the air’ approach to estimating the likelihood of Bitcoin’s success or failure. Taking this approach we can back-calculate to work out what is implied in the current valuation of bitcoins in terms of likelihood of adoption, or other key variables.
This is primarily a simplified framework to help elucidate the fundamentals that drive the value of bitcoins. The assumptions herein are very ‘back of the envelope’ and are principally for exposition.
- First principles
The value of a single bitcoin is related to the value and velocity of transactions made using bitcoin, and the volume of bitcoins in use.
The value of transactions made with bitcoin. Let’s say we assume that bitcoin will succeed in becoming the payment choice for US$100bn of transactions per year. Let’s also first assume that this US$100bn takes the form of one single transaction – say to buy all of the outstanding stock of Facebook. In order for this to be possible, the entire market value of Bitcoin would need to be at least US$100bn. For argument’s sake, let’s say someone managed to accumulate all of the bitcoins in existence (ca.12.5 million today) and used them to make this transaction, then we can infer that the value of a single bitcoin, when this transaction happens, is $8,000.
The velocity of transactions made with bitcoin. Let’s take the same example above, but this time let’s assume that rather than one transaction, it takes the form of two transactions – let’s say to buy ‘whataspp’ and ‘wechat’, for the equivalent of US$50bn each. Let’s further assume that the seller of whatsapp, uses the US$50bn of bitcoins he has received, to buy wechat. How much does Bitcoin need to be worth to facilitate this series of transactions? Hopefully one can see that at the very least, it needs to be worth $4,000, half of the example above, because the same bitcoins could be used twice. Therefore, the same ‘value’ of transactions has been facilitated, US$100bn, but depending on the number of times the same bitcoin can be used the implied value of bitcoin can differ.
The volume of bitcoins in use. The previous two examples have assumed that the whole outstanding stock of bitcoins is being used to facilitate the transactions. This is unlikely to be true. It is very likely that a good number of bitcoins have been ‘lost’ – ie., stuck on hard drives thrown into landfills, etc. Let’s assume there are 2.5 million lost bitcoins – the value in our first example would then have to be US$10,000. Moreover, clearly a lot of people today hold bitcoins as a store of value, or perhaps more accurately, as a speculative investment. The number of bitcoins genuinely in circulation, therefore falls still further.
- Arriving at a formula to determine the value of a bitcoin
Using the basic principles outlined above, we can generate a simple formula to describe the value of a bitcoin as such:
1 btc = T/V/U
Where T = transaction value V = velocity U = no. of bitcoins in use
This is obviously a simplification, so we need to explore each aspect in greater detail to understand how to use it properly.
2.1 Transaction value (T)
How do we determine transaction value in the real economy? The obvious place to look is GDP, the most widely used measure of economic activity. It measures the value of all final goods and services consumed in an economy. Does this equate to the value of transactions in the economy? No – because before a good is finally consumed there are typically many other transactions going on to facilitate its transformation from raw material, to intermediate good, to finished good, to consumption by end consumer. The advantage of GDP, however, is that it is relatively easy to measure. Estimating the value of all transactions, on the other hand, is very hard and is a problem economist have recognized for a long time. That is not to say there aren’t estimates: a September 2013 white paper by Mastercard estimated the total value of transactions globally in 2011 as $592 trillion, compared to global consumer payments / GDP of $63 trillion. This may well be a good ballpark figure, however for our purposes we can probably just stick to measures of GDP. Why? Because, faced with this measurement issue, economists have worked around it to base their analyses on GDP, and therefore as we try to compare bitcoin value versus, say, the USD, it makes sense to use the framework most commonly used.
It is important to understand, however, that because of this framework only bitcoin transactions that are used in the final consumption of goods and services count towards our measure of ‘T’. Trading of bitcoins, or international remittances, for instance, do not count.
2.2 Velocity (V)
Given the difficulty in measuring the value and volume of transactions in an economy, it is quite difficult to measure velocity directly, in an accurate or meaningful way. To get round this problem economists take a different approach, which is quite useful for our purposes. Rather than measure velocity (V), we measure the ratio (k) of all cash balances in the economy (coins, notes, bank deposits – M1 money) to a measure of transaction volume, in this case GDP. By means of illustration, this ratio for the US today is about 14%. This means that to support the USA’s GDP of $16 trillion, roughly $2.3 trillion needs, at any one time, to be sat in bank accounts, in people’s wallets or under the mattress. Put simply this measures how much people and businesses like to keep on hand for everyday consumption. The rest of their savings can go into non-cash savings vehicles, like a house, or the stock market.
The velocity of money V can be seen as the inverse of k – i.e, each dollar of that $2.3 trillion would need to be spent around 7 times in the year to generate the $16 trillion in GDP. This in reality is a simplification, but we can work with it to come up with comparable assumptions for bitcoin.
2.3 Bitcoins in Use / Money supply (U)
In order to work out the velocity of money in the US economy, economists need to know the money supply. Figuring out the money supply in fiat currencies is more complex than for bitcoin – this is because there are different types of fiat money – it can be in the form of coins and notes, or in basic bank current accounts, savings accounts, fixed deposits, etc. In the example above we calculated the velocity of M1 money – that is coins, notes and demand deposit bank accounts.
Bitcoin is just bitcoin, and we know there have been ca. 12.5m bitcoins mined. That being said, it is not so straightforward to determine bitcoins ‘in use’. For one, there are all the lost coins. In the analysis herein I have assumed 2.5m have been lost (or, more accurately, private keys lost). There is also the question of how to treat those bitcoins that are being held for investment purposes. M1 is sort of a measure of ‘ready cash’ – a description that does not really apply to most bitcoins. In reality, most bitcoin holders probably treat some portion of their stockpile as ‘ready cash’, and the rest as investment. It is this ‘ready cash’ proportion that is of interest in calculating U.
- Estimating a value for bitcoin
With the above analysis in place, it is easy to start understanding the implications for the value of bitcoin. For example, if the US were to switch to a pure bitcoin economy today, and the velocity of bitcoin was the same as for the dollar, then we can say the value of a single bitcoin would need to be:
Btc = T/V/U = 16 trillion / 7 / 12.5 million = $183,000
3.1 The value of bitcoin based on today’s usage
Estimating T, V and U:
T. It is quite hard to estimate what T is today. We know the total transaction value from the blockchain, but most of this is exchanging bitcoin for other currencies or transfers between accounts. This doesn’t count in our estimate of bitcoin ‘GDP’. We do know it must be quite low – the most well known retailer accepting bitcoin, Overstock.com, takes in about $1m in bitcoin sales per month, so $12m per year. Let’s estimate, finger in the air, that total real world goods and services transactions in bitcoin are $1bn per year – this may well still be high.
V. It is very difficult to estimate velocity for those bitcoins that are in use as ‘currency’. It seems a fair assumption, however, that the velocity is slower than for USD, since there are simply not many bitcoiners out there buying and selling stuff. Again, with a finger in the air, let’s assume velocity of bitcoin today is 1 (compared to around 7 for the USD).
U. we know there have been around 12.5 million bitcoins ever mined – but are they in use? Certainly, some have been lost, so we should definitely remove them from our calculation of U. What about coins that are being used for speculative investment? Are they in use, but just very slow moving? We could choose to look at it that way, but I would rather assume that people using bitcoin see some of their stockpile as being ‘for investment’, and some as for everyday spending. Those that are for investment are really more like houses or stocks and bonds, and therefore not really part of U. Over time, as bitcoin approaches its long term price we would expect that people would hold bitcoin less as an investment, and therefore bitcoins in use would rise. For now though it seems clear that most bitcoins are being held for investment. Again, it is impossible to say what proportion, but I think it is high – say at least 80%. If we assume that 2.5 million bitcoins are lost, and that 80% are for investment, that means that only 2 million are ‘in use’.
These finger in the air assumptions give us the following as a minimum value required to support the value of btc transactions in the economy today:
Btc = T/V/U = 1bn / 1/ 2mn = $500.
Of course, we know the value of bitcoin today (ca $422 as of 12 April 2014), so we could back calculate the value of an individual variable. Since the average value of bitcoin over the last year or so is in the $500 range, these assumptions look plausible.
The true, fair, value of bitcoin today, however, given that most people are holding it as an investment, is clearly based on future expectations of its adoption and usage. Below, therefore, I build up some basic assumptions about what that could look like, to derive a very rough, back of the envelope type calculation for the real value of one bitcoin.
3.2 Estimating a fair value for bitcoin
Obviously, it is very unlikely that bitcoin will replace the US dollar, so we need to arrive at some sort of reasonable assumptions for what might happen.
For the purposes of this exposition, I will focus on where bitcoin could be in 5 years time. This is a close enough time frame to feel comfortable making some sort of prediction. Of course, the full potential of bitcoin may not be realized for 10 or 20 years or more, however in order to be conservative and to keep the assumptions at a level where people can have a good gut feel for whether they are realistic or not, let’s stick to 5 years.
I’m going to use three scenarios: 1. Crash and burn – where bitcoin is dead in 5 years – no one is using it at all – it just didn’t live up to the hype, there are a couple more gox like scandals and the original evangelists have moved onto new things 2. Nice but boring – bitcoin continues its slow but steady rise, but there is no exponential take off and usage remains confined to online payments by the relatively tech-savvy and libertarian 3. To the moon – bitcoin reaches critical mass, usage becomes easy, widely accepted and the wider population starts to understand it better. In developed markets it takes meaningful market share in online transactions and is beginning to make meaningful inroads in offline payments. In some emerging markets it is trusted more than the local currency, and adoption rates are soaring.
Basic considerations on U
I don’t know the answer to this, someone probably does, but let’s assume that in 2019 there have now been 15 million bitcoins mined. Let’s assume 2.5 million are still lost, so there are 12.5 million bitcoins, either being used as an investment or as currency.
Scenario 1 – Crash and burn
In our equation T = 0 (or very close to 0) therefore:
1 btc = 0/V/U = $0
Scenario 2 – Nice but boring
Let’s say that bitcoin takes 1% of online spending, and basically zero offline spending. E-commerce in 2019 is expected to be valued at around $3 trillion. Therefore we assume T = $30bn. Remember we estimated that T today is around $1bn.
Since there is a material amount of spending happening now, let’s assume that V has doubled to equal 2.
In this scenario it is likely that most people are still holding bitcoin as an investment, hopeful of future price increases, however it has been almost 10 years since bitcoin was founded, bitcoin are a lot easier to spend and after holding for so long people are now more willing to spend them. There are probably a decent number of second stage adopters using bitcoin just as an online payment vehicle, not for investment. So let’s assume that just 70% of bitcoins are held as an investment, and therefore there are 3.75m being used for transactions. Therefore:
1btc = 30bn/2/3.75m = $4,000
Scenario 3 – To the moon!
In this scenario bitcoin has really taken hold, particularly online, where 20% of transactions now use bitcoin. Offline uptake is slower, but gaining traction. Let’s say 1% of offline transactions in developed markets use bitcoin. In emerging markets, where currencies are volatile, and where a lot of people have been receiving remittances in bitcoin from relatives abroad, offline uptake is greater, let’s say 2%.
Online transactions – 20% x $3 trn = $600bn Developed world offline – 1% x $45trn = $450bn Developing world offline – 2% x $30trn = $600bn
T = $1,450bn
In this scenario spending has really taken off, so let’s assume velocity (V) has now reached 5.
Of the 12.5 million coins in existence now, a good chunk are actually being used for real world transactions, so let’s say only 50% now are being held for investment – i.e., U = 6.25m.
1 btc = $1450bn / 5 / 6.25m = $46,400
Probability of occurrence
To estimate our bitcoin value, we take a weighted average of the values produced by each scenario, based on an assumption about the likelihood of each coming to pass.
Scenario Btc value Likelihood Weighted value 1. Crash and burn $0 50% $0 2. Nice but boring $4,000 45% $1,800 3. To the moon $46,400 5% $2,320 100% $4,120
Therefore, if you accept the assumptions above, and the probability attributed to each scenario, the probability weighted value of a single bitcoin in 5 years time will need to be $4,120.
Time value of money
To reach a valuation for a bitcoin today, we need to discount backwards from the value in 5 years time. This is very simple, since we do not need to discount heavily as we have already considered the ‘risk’ within our scenario analysis. The only discounting we need to do is therefore at the risk free rate, which is usually taken to be the yield you would get if you held a US Treasury bond of similar duration. Let’s say this is 3%. Discounting $4,120 back to today we therefore arrive at our final ‘finger in the air’ value for one bitcoin today:
1 bitcoin = $3,554
- Implications of the current btc value
As of April 12 2014, the value of one bitcoin is around $420. We can take this value and, holding other assumptions as they are, solve for a single variable to see what might be happening.
For instance, perhaps I am being unfair in treating some bitcoins as out of use. If we solve for U, taking $422 as the value of one bitcoin, the implied number of bitcoins in use is 43 million – an impossible number. Let’s assume that in 2019 all 15 million bitcoins ever mined are ‘in use’, and that the velocity of transactions stays the same. If so, the value of 1 bitcoin today ought to be $1,222.
If we solve for the probability of scenario 1 happening (keeping the ratio of the likelihood of scenario 2 and 3 the same), we discover that today’s $422 valuation implies a likelihood of bitcoin ‘crashing and burning’ of 94.06%.
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