However 20$ seems a little far fetched. Also the logic that market cap should equal transaction volume seems a lil flawed.
Nope, it is monetary theory. If a monetary asset serves the purpose, and only serves the purpose, of buying stuff with, then its value (in fact, the inverse: the price of the goods expressed in that monetary asset) can easily be found using P x Q = M x V.
It's simple bookkeeping:
"the amount of money over the counter" = "the total price of all the goods and services bought with it" (in a given period).
The amount of money over the counter = the amount of money existing, times the average number of times a same unit has been spend. That is M x V. M = the amount of money existing, V is the average number of times the same unit is spent (in the given period). It is also called the VELOCITY of the money. V = 1/T, where T is the average holding time (in number of periods).
If the considered period is 1 year, and a coin gets spend on average 12 times per year (once a month), then the velocity is 12. The holding time is 1/12 (of a year which is a month).
If there are 1000 coins, and they are on average spend 12 times a year, then 12 000 coins went over the counter to buy stuff with that year.
That must then be equal to the total price of goods that was bought, which is P x Q, where Q is a "reference good" and P is the price of the reference good. Say that the reference good is "a loaf of bread", then the total amount of goods (expressed in equivalent loafs of bread) exchanged in a year is Q, and P is then the price of a loaf of bread.
P x Q is nothing else but the total price of all the goods that was bought, so it must be 12 000 coins too.
Hence, M x V = P x Q
Example: if the total amount of goods bought with bitcoin is $20 billion a year, and a bitcoin is held on average 14 days, then V is about 25. M being 15 million (coins) we have that M x V = 375 million (coins traded a year).
If we take as "reference good" something that's worth $1.0 we have:
375 million = P x $20 billion.
P is the price (in bitcoin) of the reference good (worth $1). So 1/P is the price of a bitcoin.
We find: 1/P = 20 000 / 375 = $53.3
So if bitcoin is used to buy 20 billion worth per year, and coins are on average held 14 days between a trade, the price of a coin should be $53.
What we have is that a lot of coins were held a lot longer, but a lot less stuff was bought with it.
It was not really used as a currency.
