Is Bitcoin a bubble? Many posts suggest that Bitcoin is a bubble and compare it with the Dutch tulips bubble and dotcom bubble from the past. Some posts argue that Bitcoin is not a bubble and list all advantages of cryptocurrencies and features of this new technology. Few posts try to capture the intrinsic (or fundamental) value of Bitcoin. As mathematicians, we believe in hard numbers instead of subjective arguments. In this post we suggest a way to quantify the intrinsic value by estimating how much money has been invested in Bitcoin.

Why Bitcoin?

Why are we looking at Bitcoin, while there are more than a thousand cryptocurrencies out there?
A few reasons are that

  • Bitcoin has the largest market capitalisation which is nearly 50% of the total cryptocurrencies market share
  • most of the time you need Bitcoin in order to buy other cryptocurrencies

Apart from the intrinsic value, Bitcoin has a bunch of subjective added values that are impossible to quantify:

  • decentralisation – no more intermediate between you and the money, no centralised manipulation.
  • security – you can store Bitcoins on an offline computer/harddrive/USB (as a protection agains hackers), and still will be able to perform transactions online with just a signature.
  • transparency – all transactions are publicly published in the blockchain.
  • evolution – open source and public contribution make Bitcoin evolve with the current needs.
  • availability – cross-borders transactions 24/7.

The added value specifically for us as mathematicians is that the markets for crypto currencies are  not regulated. This is a big opportunity for machine learning algorithms: the raw data is “clean” (compared to a regular stock: no merges, no acquisitions, no dividend payments and other steps you need to calculate before you could actually see what is going on with the stock price).

 Market cap is not the right value estimator

How much value is in Bitcoin? This is a hot topic for every one who is trading cryptocurrencies. This question is impossible to answer, since the value of Bitcoin is determined by the trust and belief in the new technology. How do you estimate value of trust? Most of the articles I could find on the value of  Bitcoin are building up on the market capitalisation of Bitcoin.

Market capitalisation (or shortly: market cap) of Bitcoin is the total amount of circulating Bitcoins multiplied by the price of Bitcoin

At the time of writing this article the market cap for Bitcoin is just above 66 billion USD, which is larger than the CocaCola brand (55.6 billion USD).  The amount on Bitcoins in the circulation almost reached 80% of the 21 millions possible mined Bitcoins.

There are some calculations that “in 10 years Bitcoin’s market capitalization would be 10 times the average daily volume, giving a figure of $1.75 trillion for the market cap. In 10 years, the analyst thinks that there will be 17 million Bitcoin in circulation, up from the current 16.3 million figure. If the potential 17 million of Bitcoins in supply is divided by the $1.75 trillion market cap estimate, then each Bitcoin would be worth just over $100,000“.

There is a problem with the value of Bitcoin that is based only on market capitalisation. It only reflects the value at a given moment in time, with no reference to the price developments in the past. Moreover, it is nearly impossible to predict market cap in the future.

Comparison with gold and world money

Bitcoin is a currency with the fixed limit of total supply, which is 21,000,000 Bitcoins. Assuming the mining power stays constant, the last Bitcoin will be mined in 2140. Because of this property, Bitcoin is often compared to the gold.

The gold market is estimated at 8.7 trillions USD. If we assume that gold will be replaced by Bitcoins, then one Bitcoin should be worth ~414 thousands USD, which is 100 times more than the current price of Bitcoin.

The same calculations can be done with the world’s money that is estimated at 5.2 trillions of USD. If we assume that eventually Bitcoin will replace all the fiat money, then 1 Bitcoin will be worth ~247 thousands USD, which is 60 times more than the current price of Bitcoin.

If you do believe that Bitcoin will replace money or gold, then there is definitely room for growth. However, this is based on a belief. How can we quantify the value of a Bitcoin?

Calculating invested money in Bitcoin

We thought that the only value we could possibly estimate is the amount of invested money. At least this will give us a lower boundary for the intrinsic or fundamental value of Bitcoin.

“The intrinsic value is the actual value of a company or an asset based on an underlying perception of its true value including all aspects of the business, in terms of both tangible and intangible factors. This value may or may not be the same as the current market value. Additionally, intrinsic value is primarily used in options pricing to indicate the amount an option is in the money.” Investopedia

Unfortunately, also in this case we can not just read the invested amounts from the blockchain. So here is a way how to estimate them.

We know that several transactions are validated and combined in a block during Bitcoin mining. For this the miner gets a reward: 12,5 Bitcoins plus transaction fees. The amount of Bitcoins per block is halving every 4 years. Currently it is 12,5 Bitcoins, in 2020 it will be 6,25. Since transaction fees are negligible compared to the 12,5 bitcoins, we skip them in our calculations. Basically, every Bitcoin block “costs” 12,5 Bitcoins. If we assume, that the miner sells mined Bitcoins shortly after they are mined, then we can estimate the invested money for 1 block.

Investment per mined block = (the “cost” of the block) * (the Bitcoin price at the time the block was mined)

Now we take cumulative sum over all mined blocks and we get an amount of injected/invested money in the Bitcoin blockchain.

The rate of block creation is predetermined: about 6 blocks per hour. It is adjusted every two weeks, so that for our exercise we can assume it is constant over time. That means 144 block within a day. Note, that crypto markets are functioning 24/7 continuously. If we multiply the number of blocks per day by the investment per the block then we arrive at the investment per day.

Investment per day = (investment per mined block) * (number of blocks per day)

Summing up over all days of Bitcoin life, we finally obtain the cumulative injected money in the Bitcoin chain.

Of course, not all of the mined Bitcoins are sold shortly after they were mined. Because the blockchain does not contain information about it, we make an assumption to get an estimate.

To get the daily Bitcoin price, we use cryptocompare API and Python. This post describes nicely how to do it. The cryptocompare API provides the prices from 2010-07-17. To get earlier cumulative prices we consult blockchain.

The estimated injected dollars in the Bitcoin blockchain is about 3 billion USD (the final date is 2017-09-20). The market cap, however, at 2017-09-20 is just above 66 billion USD. For the prices this means that on average the Bitcoin community has paid about 200 USD for one Bitcoin, whereas the current price is just above 4100 USD.

How big is the bubble?

Is Bitcoin a bubble?

As you can see, the market cap is much larger than invested dollars, so the answer might be: yes, it seems like a bubble. If we take the market cap as 100% then invested dollars comprise roughly 5%.

How big is the bubble?

The difference between invested dollars and the market cap is factor of 20 (at 2017-09-20).

The figure below shows the historical market cap in USD as a green curve and cumulative injected dollars (USD) as a blue curve, respectively.  The horizontal axis represent the time starting at 2010-07-17 as the data is available at cryptocompare. The vertical axis represents the amount of USD on a logarithmic scale.

If we have a look at the development over time, then we see that before 2011 the market cap and the injected dollars were overlapping. However, starting from 2011 till now, the market cap curve is above the injected dollars curve with few exceptions. This means that Bitcoin might be currently overvalued compared to the investment. Of course as we mentioned earlier this is only one part of the intrinsic value, there are number of subjective added values that we can’t quantify.

Cumulative injected dollars versus market cap (in USD) on logarithmic scale


The technology in the crypto currencies is very promising and can be applied to many aspects, not only in finance. Whether Bitcoin is going to make it to the future is still a question. Right now Bitcoin is the market leader for the crypto currencies.

Whether Bitcoin is a bubble or not, the fact is that its market capitalisation is much larger than amount of invested dollars. If Bitcoin owners decide to sell more than 5% of their Bitcoins at the same time, the crypto currency exchanges will not be able to pay out.

What do you think is the real value of Bitcoin? Is Bitcoin a bubble? Let us know in the comments.


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