Valuing Bitcoins or: how I learned to stop worrying and speculate

Lots of posts on Bitcoin recently as the price continues to rise. I don’t want this to be a Bitcoin only blog, but I do have a long position, it’s a hot topic and I have done some thinking on this so I’ve got some value add here (pun intended). This post will be on value. The next one some thoughts on government regulation which I think is really the most important topic surrounding Bitcoin.

So lets put a value on Bitcoins! Should you buy Bitcoins? Well I’m long so you know my opinion. However the main reasons for me starting this blog are:

  • Force myself to articulate my thoughts to help ensure I’m making sense. Sometimes your write things down and it just doesn’t look right.
  • Get feedback! I’m not always right and I can be swayed. I’m searching for intelligent life.

So here is why I’m long. Lets calculate the expected value (EV) of buying a Bitcoin. In “probability theory” expected value is calculated by taking all the possible outcomes multiplied by their probabilities of occurring and adding them together (here is an example with dice). In our case the output of the expected value calculation represents the price below which we should be buying Bitcoins and above which we should be selling.

First lets list the possible outcomes and approximate what the Bitcoin price should be in each of these outcomes:

  1. Disaster! A bug or hack results in utter loss in confidence of Bitcoin system. Or governments uniformly ban Bitcoin. Price goes to $0.
  2. Mediocrity. Merchants don’t universally adopt Bitcoin. Some folks use it as a store of value, but as a medium of exchange the results are well…medium. Price end up around $100.
  3. Success! Bitcoin becomes a commonly accepted medium of exchange competing w/ major currencies although not replacing them. Bitcoin grows to be as used as the US dollar. There are 1.2 trillion dollars in circulation and there will never be more than 21 million BTC so 1.2T/21M = $52,381 per Bitcoin.
  4. Massive Success! Bitcoin becomes the primary currency used world-wide. As of 2008 Wikipedia has global currency circulation at around $4T. USA had 20% of the share so lets assume that share stayed the same making the worlds total circulation is $6T (1.2T/0.2). So $6T/21M = $285,714 per Bitcoin.

Thats right, there is a chance each Bitcoin that is currently trading at a paltry $125, could be trading at $285K each! I’ve seen estimates for 100K-1M per Bitcoin, not sure how So lets chuck these numbers into a spreadsheet and see what they look like when we probability weight them. I’ve provided 2 sets of what probabilities, one optimistic one pessimistic to illustrate my point.

Scenario Bitcoin Price Optimistic Probability Optimistic EV contribution Pessimistic Probability Pessimistic EV contribution
Disaster! $0 69% $0.00 90.00% $0.00
Mediocrity $100 20% $20.00 8.99% $8.99
Success! $52,381 10% $5,238.10 1.00% $523.81
Massive Success! $285,714 1% $2,857.14 0.01% $28.57
Optimistic EV $8,115.24 Pessimistic EV $561.37

So according to these calculations a the price of Bitcoin should be somewhere between $561 and $8,115. I certainly wouldn’t call $125 a bubble. Of course as new information comes in probabilities change and therefore so does the EV. Obviously I’m winging it on the probabilities here, but I think if you are honest with yourself it’s pretty hard to say there isn’t a 1% chance of the “Success!” scenario occurring and munging the numbers to get the EV below $125 is really, really, hard.

So dump all your savings into Bitcoin? Obviously not. This is a speculative bet w/ at least a 69% chance of losing ALL your money, but the upside is tremendous for the other 31% so a small bet could pay big dividends.


6 thoughts on “Valuing Bitcoins or: how I learned to stop worrying and speculate

  1. The global currency in circulation from the wiki article isn’t the biggest theoretical number you can use. There’s almost 50 T of money in the world, it just isn’t printed or coined. This still isn’t the biggest theoretical number you can use because it doesn’t describe real property (and into the real abstract, it doesn’t describe everything in the universe) but with 50 T divided by 21 M, one bitcoin equals over 2.3 million 2013 dollars.

  2. Good write-up. Perception/sentiment wise – I don’t think the crowd is treating bitcoin as a currency at all but rather as a store of value, and therefore it is or theoretically will act more like a precious metal. So while ironically, there is still a lot of mistrust in bitcoin, its rise during this era of bailouts, Cyprus, and government mistrust hints that bitcoin’s true value actually *IS* trust — specifically as a solution for decentralizing trust and moving it away from the system of governments etc. etc.. As such, my personal, rough, middle-ground estimate is much lower than yours — somewhere in the $1,500 range per bitcoin or around the spot price of Gold. But… we’re obviously in uncharted territory here – so who knows.

    • A store of value is only good if it actually has underlying value! The value of Bitcoin is similar to that of a fiat currency; it has value because you can use it as a medium of exchange. “Stores of value” can derive their value from other features (e.g. gold can be made to jewelry), but Bitcoin doesn’t have any other value aside from being a medium of exchange.

      That being said, you are right to point out that Bitcoin will be used as a store of value more than fiat currencies if it is successful, since it won’t suffer from inflation. That will increase the demand for Bitcoin and drive the price up more than what I’ve estimated. But that hinges on Bitcoin being used as a medium of exchange. If that fails to materialize I wouldn’t store my money in BTC. A store of value w/o value? No thanks.

      I don’t get your $1500 price target. Just because that is the price of gold? What would you use there were 42M BTC to be created instead of 21M? Does your price target change?

  3. This is a really cool article and was something I was thinking about the other day when I bought more Bitcoins at 142. I was thinking damn this is expensive for a Bitcoin but after doing the math I thought this could be super cheap in the long run. Only thing is I did the math with market capitalization not money supply so I was wondering why your way is correct? For Example I have the US at around 16T market cap so if Bitcoins was to gain as much traction as USA I get bitcoins to be valued at 16T/21M = 761,000 a coin.

    Also one more thing we need to consider is that there are only around 11M Bitcoins at the moment and are being made slower every single day. If Bitcoin gets mass adoption by 2016 there will only be around 15 million bitcoins so we would be dividing by 15 million not the 21 million in our example. This drastically changes how much money it takes to increase the value of the bitcoin. Using my first example 16T/15M= 1.06M a coin.

    Where I got Market Cap for USA

    • I’ve seen people use market cap as a target value but I don’t know why. Bitcoins aren’t replacing stocks, they are replacing currency (and maybe stores of values like gold, which I didn’t factor in here). I think people assume that because there are 16T worth of stocks there must be 16T worth of currency that was used to buy them, but that is incorrect. Stocks can be bought on margin. Also they are bought with money that has been through the banking system and have been subject to the money multiplier effect. That is the difference between MB and M2, which I reference in my next post. Also see the reference to fractional reserve banking as it applies to Bitcoin. Am I missing something?

      In terms of 11m vs 21m, I assume folks have factored in inflation to the current price. Honestly I wasnt 100% sure whether i should use 21 or 11, so I went conservative. I could be wrong.


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