The proper way to calculate the future value of a bitcoin

[Erdogan]

A while back I found this site: http://www.btcglobe.com/tool/calculate-future

If you play with it, you'll see that it is using this formula:

[(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)]

The formula is bogous. The value of the money supply is not dependent of the output of the economy, whether GDP is in fact a good measure of the output or not. Nor is the value of the money supply dependant of the transactions performed. Not suggested above, but anyway, it is not dependent of the value of all goods existing either.

Shouldn't there be a (velocity of bitcoins) term in the denominator? Like this:

[(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)*(bitcoin velocity)]

The velocity of money is a nonsensical concept made up to make the likewise nonsensical quantity theory of money complete in its nonsensicalness.

That seems to work for some toy examples I invented with an economy of 3 people.

This shows the velocity of the US M1 money supply: http://en.wikipedia.org/wiki/File:Velocity_of_M1_Money_Stock_in_the_US.png

It seems we should be dividing the numbers from the value calculation link by something between 5 and 10, unless we have a good reason to think bitcoin velocity will be much different than M1 velocity. Am I missing something?

The value of the money supply is determined by supply and demand, where demand is the individual's wish to hold money corresponding to some real value, as defined by each individual, summed up. Supply is, in case of bitcoins, predetermined and inelastic.

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[go1111111]

For all the doubters, I challenge you to show me an example of a simple economy (you should need just a few people and a few transactions to prove the point) where the following is not true:

(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)*(bitcoin velocity)]

...I will be very impressed if anyone is able to do it.

[Erdogan]

For all the doubters, I challenge you to show me an example of a simple economy (you should need just a few people and a few transactions to prove the point) where the following is not true:

(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)*(bitcoin velocity)]

...I will be very impressed if anyone is able to do it.

You can not show such a thing, that formula is an example of something that is not refutable. The only thing that is measurable in that formula is the supply of bitcoins, maybe not even that, because we can never know how many is saved, and we can not know the volume of credit. The velocity of money is just stupid, it can not be measured, and if it could, why should it affect the bitcoin value?

This article by Frank Shostak (with citations from Mises and Rothbard) is very readable and explains it far better than I can:

http://mises.org/daily/918

Consider the following: baker John sold ten loaves of bread to tomato farmer George for $10. Now, John exchanges the $10 to buy 5kg of potatoes from Bob the potato farmer. How did John pay for potatoes? He paid with the bread he produced.

Observe that John the baker had financed the purchase of potatoes, not with money, but with bread. He paid for potatoes with his bread, using money to facilitate the exchange. In other words, money fulfills here the role of the medium of exchange and not the means of payment.

The number of times money changed hands has no relevance whatsoever on the baker's capability to fund the purchase of potatoes. What matters here is that he possesses bread that can be exchanged by means of money for potatoes.



From the conclusion:

The apparent simplicity of the equation of exchange and its consequent widespread acceptance by mainstream economists has been instrumental in the erroneous assessments of the true state of the economy. Hence, it is an urgent requirement that this fallacy be removed from the economic literature and from economic textbooks, in order to prevent future theoretical confusions and their practical consequences.

[go1111111]

For all the doubters, I challenge you to show me an example of a simple economy (you should need just a few people and a few transactions to prove the point) where the following is not true:

(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)*(bitcoin velocity)]

...I will be very impressed if anyone is able to do it.

You can not show such a thing, that formula is an example of something that is not refutable.

It's an identity, stemming from the definition of velocity. So the equality does hold. The question seems to be whether it's useful or not.

The only thing that is measurable in that formula is the supply of bitcoins, maybe not even that, because we can never know how many is saved, and we can not know the volume of credit.

The non-measurability claim seems weird to me. Maybe some of these things are hard to measure, and we need to estimate them, but clearly in principle we can measure them.

Here's a simple economy for one year: Frank starts with 3 fish and 1 BTC, Paul starts with 2 peppers and 2 BTC, Carl starts with 4 cows and 3 BTC.

Frank sells two fish to Paul for one BTC. Carl sells one cow to Paul for one BTC. Paul sells one pepper to Carl for one BTC.

We can calculate every term in MV = PT in the above scenario. Is your objection just that these things are hard to measure in real life?

The velocity of money is just stupid, it can not be measured, and if it could, why should it affect the bitcoin value?

Let's pretend we look into a crystal ball to see the year 2020, and we know M (19 million BTC), we know V, because you're assuming we know V, and we know GDP because some economists will have calculated it the same way they do today. Then we can use the MV=PT identity to infer the price of a bitcoin! That's pretty amazing. Without that identity, we couldn't do it. We both agree the identity is true/axiomatic. We've just used it to learn something, assuming we can estimate V. 

This article by Frank Shostak (with citations from Mises and Rothbard) is very readable and explains it far better than I can:

http://mises.org/daily/918

I unfortunately did not find the article very convincing. The author and Mises/Rothbard kept asserting things that didn't follow from their premises. The best example is "since velocity is not an independent entity, it as such causes nothing and hence cannot offset effects from money supply growth."

Some other quotes:

"The number of times money changed hands has no relevance whatsoever on the baker's capability to fund the purchase of potatoes."

Agree, but not relevant.

"Observe that, since bread, potatoes, and sugar are not commensurable, no average price of money can be established. "

They were shown to be comparable since they all have a certain price in terms of money, and thus by extension with each other.

"The peculiarity of these prices lies merely in the fact that they cannot be expressed in terms of money."

The price of anything can be expressed in relation to anything else.

I find the writing of Mises and Rothbard unclear (in comparison to someone like Milton Friedman), so it's possible I'm not understanding them.

[DeathAndTaxes]

For some reason I just noticed your post now. It sounds like via various lending arrangements and contracts, M1 gets converted onto M2, and M1 and M2 get converted into M3. In the bitcoin economy I understand that if I set up a Bitcoin credit card company and you take out one of my credit cards and I give you a 20 BTC line of credit, that 20 BTC has moved into M3. Bit it's also 20 BTC that I can't spend simultaneously, so it is removed from M1, no? M3 still contains only 21 million bitcoins right?

No nothing gets converted.  The higher "M"s are simply broader defintions of money. They all are inclusive of the lower "M"s.

M0 = currency.  Money in physical form.  There is ~$5T globally.  Bitcoin's 21M closest equivelent would be M0.
M1 = M0 + all demand accounts (checking accounts).  Accounts that can be withdrawn instantly w/ no restriction or penalties.
M2 = M1 + all restricted accounts (savings, money market, small value short term CDs)
M3 = M2 + longer term larger value CDs
M4 = M3 + Commercial Paper (short duration high quality corporate debt) and T-bills (short term govt debt).

Another way to look at it is our entire global economy functions on ~$5T worth of currency.   If Bitcoin replaced that completely (the elimination of all other forms of currency on the planet) it would mean that the Bitcoin money supply would be worth ~$5T (purchasing power in 2013 dollars) and each Bitcoin valued at ~$240,000 USD (1 BTC = $5 trillion / 21M = ~$240,000 USD).

You can't use GDP without considering velocity.  Global GDP is roughly $75T but the global economy accomplishes that with ~$5T in currency.  The velocity of M0 is thus ~15x.  In other words a dollar exchange hands roughly 15 times a year.  The above calculation assumes the velocity of Bitcoin (in a global scenario system) would be similar to the velocity of the global money supply.  That may not necessarily true but it is a starting point.   For example if the velocity of money for Bitcoin was twice as high then Bitcoin could support a $75T global economy with an purchasing power (because there would be no exchange rate at that time) of half as much (~$120K not $240K ea).   Likewise some have made the argument that Bitcoin is more than just currency that it would replace some broader definitions of money that potentially could mean a higher valuation of Bitcoin because the velocity of the broader money supplies is much lower.  Velocity of M2 is ~3x (M2 = $25T, GDP = $75T).

So you can either look at the big picture in terms of the relatively money supplies (BTC money supply vs global money supply) directly or you can consider GDP vs 21M BTC using velocity.Money supply is timeless.  GDP is a measure of commerce over a specified period of time (usually annually).  Velocity is the correction between the two.

[justusranvier]

There's no good reason to assume that a Bitcoin economy would have deposit accounts at all (especially since everybody who tries to operate one just steals the coins or gets hacked), or as much debt as the current system.

[Erdogan]

There's no good reason to assume that a Bitcoin economy would have deposit accounts at all (especially since everybody who tries to operate one just steals the coins or gets hacked), or as much debt as the current system.

...and, there is good reason to believe that people would want to hold more value in bitcoin (compared to fiat), since it is possible to save in bitcoin.

[DeathAndTaxes]

There's no good reason to assume that a Bitcoin economy would have deposit accounts at all (especially since everybody who tries to operate one just steals the coins or gets hacked), or as much debt as the current system.

Which is why I said the most relevant "M" would be M0.

[justusranvier]

Which is why I said the most relevant "M" would be M0.

I don't agree with that conclusion.

People actively spend M1 and higher aggregates, whereas in a Bitcoin world they'd be spending base money instead.

So if you are calculating what the purchasing power of a Bitcoin would be if it replaced the dollar, M0 is not going to give accurate results.

[Rival]

In the examples above, just use an IOU instead of money.

John the baker creates an IOU for 10 loaves of bread and gives it to Bill the farmer for a sack of wheat.

When John makes the bread, he gives it to Bill in return for the IOU.

Now, the question to be asked is: What is the value of the IOU that John now holds? The answer is ZERO.

"Money" was created in the transaction and destroyed when the transaction was complete. If Bill had traded off that IOU instead of cashing it in, it would retain it's value only until it returned to John. The only way it can keep it's value is if never gets to John.

The banks are John. They create money that only has value if you don't pay it back. When you pay them back it goes poof into the nothingness from which it sprang. But they don't care, because they collect interest on the money they create.

[go1111111]

You can't use GDP without considering velocity.

I agree. I think that's exactly what I was trying to say with my original post, when I suggested that the following was true:

(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)*(bitcoin velocity)]

In the above, 'velocity' refers to only the currency that is used in transactions at all. That's probably non-standard. If you compute velocity over all money, it would just be:

(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(bitcoin velocity)]

Do you agree with that?

[DeathAndTaxes]

You can't use GDP without considering velocity.

I agree. I think that's exactly what I was trying to say with my original post, when I suggested that the following was true:

(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)*(bitcoin velocity)]

In the above, 'velocity' refers to only the currency that is used in transactions at all. That's probably non-standard. If you compute velocity over all money, it would just be:

(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(bitcoin velocity)]

Do you agree with that?

Yes. One issue is we don't know how Bitcoin velocity will compare to global velocity so it makes any comparison difficult.  Globally M0 has roughly 15 velocity.  M3 is roughly 1 velocity.  In other words the global economy sustains ~$75T in transactions on $5T in currency (M0) and $75T in broad money (M3).

My thinking is that if Bitcoin was widely adopted it probably would have a higher velocity due to the low friction in transactions but honestly that is just a guess.

[Erdogan]

[...]
We can calculate every term in MV = PT in the above scenario. Is your objection just that these things are hard to measure in real life?

No, the principle of the formula is wrong. It is based at best on finding some statistics that seems to be correlated, and guessing on a formula that connects them. The velocity is the universally flexible constant that makes the equation always true.

[aminorex]

Actually it is trivial to calculate bitcoin velocity from the blockchain.  The data is all there.  It as 5.93 last I checked, which is a about normal for the US according to fed numbers.  (Isn't that a leading term "fed numbers" -- the numbers we are fed, to make us think what they want us to think.)

[DeathAndTaxes]

Actually it is trivial to calculate bitcoin velocity from the blockchain.  The data is all there.  It as 5.93 last I checked, which is a about normal for the US according to fed numbers.  (Isn't that a leading term "fed numbers" -- the numbers we are fed, to make us think what they want us to think.)

Well no it isn't.  Every Bitcoin tx isn't not an act of commerce.  If I move funds from one wallet I own to another wallet I own there is no contribution to the Bitcoin GDP.   This would be no different than moving a $100 bill from on pocket to another pocket and thinking you are boosting the economy.  I mean we could have a national move your dollars day and boost the GDP 15% this year.

You may guestimate velocity by analyzing the blockchain but it will be at best an educated guess.

[go1111111]

The velocity is the universally flexible constant that makes the equation always true.

I agree that velocity is the number that makes the equation true, given the other values, but the velocity has a real and intuitive interpretation. I don't see why you think that makes the "principle of the formula wrong." If we have any reason to think the velocity will be within a certain range, then the equation gives us useful knowledge about price ranges.

[theonewhowaskazu]

What they're saying is if you take:

A * f(x,y, ...) = price

and let A vary to 'whatever you want', then you're statement is true no matter what f(x,y, ...) is.

[go1111111]

What they're saying is if you take:

A * f(x,y, ...) = price

and let A vary to 'whatever you want', then you're statement is true no matter what f(x,y, ...) is.

But because the value of the 'free variable' is expected to be within a certain range, and has a real world interpretation of how many times each bitcoin is spent (which is a real thing), we can still infer useful info from the equality.



 

[theonewhowaskazu]

What they're saying is if you take:

A * f(x,y, ...) = price

and let A vary to 'whatever you want', then you're statement is true no matter what f(x,y, ...) is.

But because the value of the 'free variable' is expected to be within a certain range, and has a real world interpretation of how many times each bitcoin is spent (which is a real thing), we can still infer useful info from the equality.



 

It has a real world interpretation, but no way of telling that.

bool god is true if god exists

[greenlion]

You're saying that during Step 4a/4b, the money supply has grown?

That's correct, that's exactly how fractional reserve banking increases the money supply.