That's the trillion-dollar question. Or is it the __cantillion __dollar question?

Determining the value of cryptocurrencies is a developing science.

A pitch book type trick is to say - If any Group (Asset Management firms/ Insurance firms/ High Net Worth Individuals) were to put a certain percentage (1%/5%/10%) of their assets into bitcoin then what would be its value. I did that in an earlier article where I arrive at a price of $55k/$280k/$560k in 3 different scenarios. You can check it out __here__.

In today’s article, I get more technical. I arrive at the value of bitcoin using 2 math models:

1. Stock-to-Flow model (S2F)- This has been developed by Dutch institutional investor __PlanB__

2. Quantity theory of money (QTM) - The original QTM was developed by Irving Fisher. I adapt it for bitcoin in this article.

**Stock-to-Flow Model**

Stock-to-Flow model centers around the ratio: Stock/Flow.

“Stock” refers to the stockpile of a product

“Flow” refers to the annual production of the product

The conclusion it arrives at is that compared to consumables, the production of non-consumables cannot be adjusted in a meaningful way to arrest a rise in price.

I know that sounded dense. Let me explain by comparing magic beans (fictitious consumable item) to gold (real non-consumable item).

__Applying Stock-to-Flow to Magic Beans____ __

S -> Total stockpile of magic beans in the world = 100

F -> Annual production of magic beans = 50

=> S/F=100/50 = 2

(S/F of 2 can be interpreted as meaning that the current stockpile is equal to 2 years of production)

If the annual consumption of magic beans is 50 (i.e annual production replaces the amount consumed), the price remains constant. If on the other hand, consumption increases to 80, then there will be a spike in price as consumption will eat into the stock.

In this situation, the S/F will fall to 1.4 [(100+50-80)/50]. In the case of a consumable like magic beans, it is possible to quickly increase production to meet the increase in demand and bring the price back to the pre-demand surge level __because Stock is not a large multiple of Flow.__

__Applying Stock-to-Flow to Gold__

The situation is different in the case of a non-consumable like gold. Think about it. All the gold produced from the time of the pharaohs is still in existence today. This means that the stockpile keeps increasing and production as a proportion of stockpile keeps falling.

S -> Total stockpile of gold = 185,000 metric tonnes

F -> Annual production of gold = 3,000 metric tonnes

S/F = 62

(The current stockpile of gold is equal to 62 years of gold production)

If the demand for gold increases, then supply (as a percentage of stockpile) cannot suddenly be increased meaningfully and hence any increase in price is sticky.

__Applying Stock-to-Flow to bitcoin__

So how does this apply to bitcoin? Roughly every 4 years, the rate of production of bitcoin halves. (As an incentive for maintaining the bitcoin network, miners are awarded block rewards for every block processed. The block reward started at 50 bitcoin per block, then fell to 25, then 12.5, and then 6.25). The last halving happened in May’2020. With every halving, the denominator F, of S/F halves. With the last halving, the S/F of bitcoin has come very close to gold.

S-> Total stockpile of bitcoin = 18,600,000

F-> Annual production of bitcoin = 900 BTC per day * 365 = 328,500

S/F = 56

The actual S/F of bitcoin is a little lower than 56. How much exactly depends on your estimate of how many bitcoins are lost (either owned by Satoshi Nakamoto or lost when holders lost their keys).

__What is the price of bitcoin as per Stock-to-Flow model?__

I’m not going to get into the details of the mathematical model developed by PlanB where he fits a linear regression to the data, but I share the conclusions here. As per his model:

The price of bitcoin before the current halving should have been around$10,000.

After the May’2020 halving, the price of bitcoin should be$100,000.

And after the next halving in 2024, the price of bitcoin should rise further to$1,000,000.

Image Source- __PlanB__

**=> Intuitively**, the way to think about it is - Given that the S/F of bitcoin is close to gold, shouldn’t the bitcoin market cap be closer to gold than it is? And since its S/F will be higher than gold at the time of the next halving in 2024, shouldn’t the bitcoin market cap climb beyond gold then?

__S2F more applicable to bitcoin than gold__

The Stock-to-Flow model has been quite accurate in explaining the price of gold and hence has credibility that it should be able to predict the price of bitcoin. In fact, bitcoin is a more ideal subject for the Stock-to-Flow model because the supply of bitcoin is exactly fixed. Gold supply can vary by a few percentage points using current technology in response to changes in demand. There’s also the outlier situation where gold is discovered in say an asteroid and development in asteroid mining technology suddenly increases gold supply substantially. There is no such risk with bitcoin. The total supply and rate of supply increase are cast in code.

**Quantity Theory of Money**

Fisher’s equation for exchange looks like this:

**M*V=P*T**

M = Total supply of money

V = Velocity of money (the number of times a unit of money changes hands in a given period of time)

P = Price of a unit of output

T = Total quantity of output of the economy

While constructing this equation, one needs to be careful to enter data related to the economy to which it pertains. For example, if evaluating the fiat economy then prices must be entered in fiat like USD. If evaluating say the __Chainlink__ ( a protocol that supplies oracle data to smart contracts) economy, then prices must be entered in LINK and not USD equivalent of LINK.

Allow me to explain with (made up) numbers. Let us assume that:

M-> Total supply fo LINK = 100 tokens

V-> Velocity of LINK tokens = 10

P -> Price of 1 unit of output = 5 LINK

T-> Total quantity of output in the Chainlink ecosystem (completed data requests) = 200 units

M*V=P*Q

=> 100 * 10 = 5 * 200

Further, if 1 unit of output in Chainlink costs 5LINK and in $ terms costs $75, then:

5LINK = $75

=> 1LINK = $15 => Exhange rate (E)

P=M*V/Q

=> P=100*10/200

=> 5= 100*10/200

=> 75/15= 100*10/200

Therefore, if you have the price in US$ and not LINK, then it must be divided by the exchange rate to maintain equality.

### Pf = 75 = Price in fiat

E = 15 = Exchange rate of token and fiat

=> Pf/E = M*V/Q

=> E= (Pf*Q)/ (M*V)

__Applying Quantity Theory of Money to bitcoin__

Let us use this to find the exchange rate of bitcoin and USD (value of bitcoin)

M -> Total supply of bitcoin = 21,000,000

(To be conservative, I'm taking total supply instead of current circulating supply)

V -> Velocity of bitcoin =10

(Velocity of M1 was at a high of 10.5 around the time of the 2008 Financial Crises and has fallen to 3.94 post-Covid as per __FRED Economic data__. A higher V leads to a lower price of bitcoin so I'm assuming a high V to be conservative)

Pf*Q = $87,265,226,000,000 (__Global GDP of 2019__)

(Since GDP is the value of all the goods and services produced, I use global GDP. This assumes that all goods and services globally are the market for bitcoin. I know some people believe that bitcoin can only be used to purchase drugs but I disagree)

=> E = 87,265,226,000,000/(21,000,000 * 10)

Price of bitcoin=$415,549

**Final words**

I know that the price of bitcoin that we arrive at is way off current prices. I'm aware of a lot of criticism of the Stock-to-Flow model. The criticism in __this__ piece by Strix Leviathan is quite insightful. The adaptation of the Quantity Theory of Money I present above is more original work and I'm open to critique on the same.

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