Quote from: dinofelis on November 14, 2014, 10:13:21 AM

Quote from: smooth on October 25, 2014, 09:43:10 PM

Quote from: oda.krell on October 25, 2014, 09:51:45 AM

Quote from: smooth on October 25, 2014, 07:20:14 AM

Quote from: oda.krell on October 23, 2014, 12:30:53 PM

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

10^ln(x) = x^ln(10)

Thanks. Feel like an idiot for missing that.

Which would make it about quadratic growth. Interesting.

Yes I thought so too. If you buy the Metcalf's Law valuation argument (I don't entirely), that corresponds roughly with linear growth of usage. Which interestingly is what Chris Dixon has said they are seeing in his businesses (mostly Coinbase I think).

Hello everybody,

I'm pretty new to bitcoin, looked first at it this summer. I also did some curve fitting to the historical data in log scale. Of course, one has to be extremely cautious when extrapolating from early price movements, but intuitively the idea that the bitcoin price should "do something" is pretty clear. I'm cautiously also buying modest amounts of bitcoin... for my retirement in a few decades, based upon similar extrapolations.

When looking at the long term (and not doing day trading), one must always look at the fundamentals. Now, bitcoin is supposed to be a monetary asset, in the same way as fiat, or as physical gold: it doesn't serve any other purpose but as "money", that is, intermediate vector of value. A monetary asset is in a certain way a "frozen Ponzi scheme" or a "frozen bubble" to some extend in my opinion: the only reason why you give it value today (why you want to spend real effort and other monetary assets on it) is that you believe that someone else will estimate it has value tomorrow, and that you will get something for it in return.
Shares, houses, and other investments also have a part of "monetary asset", but they usually also have another cash flow associated to them, like dividends, rent or usage (you can *live* in a house), so there is a "floor" to their price, which is their cash flow or usage. Gold has a very limited "usage" in jewels and so on, but is essentially a nearly purely monetary asset.

Now, for a purely monetary asset, its "value" is solely determined by the "quantity theory of money", which states that in steady state:
P x Q = M x V

where P is the price of goods, Q is the quantity of goods bought with the monetary asset, M is the amount of monetary asset, and V is the average velocity of the monetary asset.

The "price of a bitcoin" B is then 1/P, and we have:

B = 1/P = Q / (M x V)

So you can expect the price of a bitcoin to be the amount of stuff (expressed in dollars) divided by the amount of bitcoin in circulation M, and divided by the velocity V.

Now, 1/V is given by the "(harmonic) average holding time" of a bitcoin between two buys, which we can call T.

We hence have:

B = Q x T / M

Or: the market capitalisation is B x M = Q x T

In other words, the market capitalisation is grossly given by the value of all stuff bought with bitcoin, times the (harmonic) average hold time of a bitcoin.

Many expectations of "too the moon" are based upon a similar "holding time" T for fiat and for bitcoin: in that case, the market capitalisation is then comparable to the fraction of the fiat market capitalisation that is done in bitcoin.

If bitcoin becomes a success, in the sense that, world wide, people buy and sell stuff in bitcoin, then this market capitalisation can be potentially huge. Only in dollars, there are 2 - 10 trillion dollars in circulation. World wide, the estimate (M2 money) is of the order of 55 trillion.
If bitcoin would take 1% of the world trade, its market cap would be about 550 billion dollars. If bitcoin doesn't even buy 1% of stuff in the world, then the question can be asked whether it made sense in the first place to consider it as a monetary asset.

That is, under the assumptions of similar average hold times.

So that's about a 100-fold increase in market cap compared to now.

Essentially, this is the "amount of value" one needs bitcoins to have in order to be able to buy all that stuff, and to hold all those coins for a time T.

The crucial point is T: if people would just buy bitcoins (with fiat) to spend them immediately, then T becomes much shorter than the average hold times. This can pretty much lower the market cap needed to buy all that stuff. Essentially, if bitcoins are only held "a few seconds" the time to buy them with fiat, and to spend them buying some goods, you see that the market cap of bitcoin would be extremely limited. If 1% of goods are traded in bitcoin, but bitcoins are held 100 times less long than fiat, then market cap is not going to change !

But bitcoin has promises as a store of value too, so chances are that people will actually hold on bitcoin also as "store of value". Even more so than to fiat which has a bad reputation as store of value. That might actually make T *longer* than the T of fiat.

However, for the moment, I have no idea, but Q is pretty low (except maybe on black markets, which do play a role in the early phases of bitcoin).

So why is bitcoin then worth something ? I think we are still in a hugely speculative phase, where the current price of bitcoin is more the future *expectation* of what its price will be, rather than the actual value in monetary use. Most people (like me) speculate somehow that bitcoin is going to become a success, and that people will not only use it to buy stuff (Q), but also as a store of value (T).

This has the potential to put the bitcoin price B pretty high.

But it won't happen overnight. You are not going to wake up, with people buying suddenly 1% of the world economy in bitcoin. This is going to be a slow process, and to me, *this* is the fundamental value of bitcoin. The current prices are short-term effects of traders, and the longer term consists in the long term belief of high bitcoin value, that is, a long term speculation on the value of B, as a function of Q and of T.

It can also be that bitcoin flops. But for the moment, I'm taking a prudent bet on "to the moon", but over a decade or more. It would be a nice complement to my retirement.

However, in my opinion, there's no fundamental which can support a "to the moon and staying there" in the near term: Q is too low for the moment. For bitcoin to become money, you have to buy a significant part of the world economy with it (1% is a very "significant part").

What is dangerous with curve fitting, is that there will be a transition at some point, from the "speculative" domain where we are in now, to the "monetary domain" when it is really on its monetary fundamentals. There's no reason why fitting laws on the speculative part should have anything to do with the monetary circumstances.

This is an excellent analysis dinofelis and I think your thought process is spot on. I see so many people making estimates that fail to take into account velocity and are therefore fundamentally flawed. If you were to write this as an op-ed or article and get it published somewhere (coindesk perhaps), I think you would be doing the community a good service.