Topic: Logarithmic (non-linear) regression - Bitcoin estimated value - page 13. (Read 117753 times)

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.

Agreed, a market cap version would be awesome as we are still experiencing high inflation.

Thanks for your acknowledgments!
I truly appreciate all your comments (and tips  )



No, Risto also suggested that, but I don't have any "market capitalization" version yet.

Actually working on calculating the "real" R^2 value for the logarithmic regression, and in other curve shapes...

Awesome work Trolololo! I actually came across this thread last week & with this recent movement in price, I figured it deserved a bump.

So, the trend line is currently just above $600. In terms of accuracy, it's at least closer than Stephen Reed's Million Dollar Logistic Model: https://bitcointalksearch.org/topic/stephen-reeds-million-dollar-logistic-model-366214

Great work Trolololo.

Can't see it mentioned yet, maybe it is elsewhere, but do you have a version which utilizes the "market capitalization" (monetary base), instead of the price? For the first decade this may produce a somewhat different curve.

This is in my weekly repertoire of threads I look at to give me that warm blanket feeling   

Following. Great job indeed. Congrats.

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).

I would say for Xmas 2026 

Thanks. Feel like an idiot for missing that.

Which would make it about quadratic growth. Interesting.

Let's now see some new analytics using splines and regressive curvilinear functions. I'm so tired of seeing mspaint lines over boring plots. The speculation threads will love these.

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

Impressive.
Yes, Excel (or equivalent) can do so much things.

EDIT :
I can only agree with the estimate, 1.000 USD by 24-04-2015
But that's only an estimation.

Thank you!

Very nice work man!!

I'll be watching your future updates on this! 

that was fun
We would be > 600k by now

edit: just posting it for the lulz:

That's what I said... the 'S' shape (of slipperyslope, e.g.) is bounded growth, i.e. is convergent. Your function doesn't have a finite limit. It just goes to infinity rather slowly