(Continued from the first part, "Is Bitcoin a fraud?")

In this writing, I use Bitcoin almost interchangeably with cryptocurrency. For example, when I say Bitcoin economy, I could have said cryptocurrency economy.

This writing is not an investment advice. You should follow your own judgment and be responsible for buying or selling cryptocurrencies.

How can you calculate the fair price of Bitcoin?

If the value of the cryptocurrency is not zero and if it survives thanks to its advantages over the fiat currency, we can now think about what a reasonable price of it. How do we do it?

Previously I said the value of (fiat) currency must be at least 20% of the economy. But that value is the total utility people enjoy, not the price of currency.

I am using two well-known formula from economics to derive the price of Bitcoin.

Purchasing power parity

Bitcoin’s price means how many Dollars per Bitcoin, which means an exchange rate of Bitcoin and the US dollar. The Purchasing Power Parity(PPP) is a well known method to assess an exchange rate, which is expressed as follows.

S = P1 / P2

• S: Exchange Rate
• P1: Price of a product purchased with currency 1
• P2: Price of a product purchased with currency 2

According to this, Bitcoin price (i.e. exchange rate) can be expressed as the following.

Bitcoin exchange rate = Price of a product purchased with USD / Price of a product purchased with Bitcoin

Now we need to get USD-based and Bitcoin-based prices. To do this, I use the Equation of Exchange from Quantity Theory of Money.

Equation of Exchange

The quantity theory of money is an old economic theory about the relationship between quantity of money and price level. Here is a simple explanation. If the quantity of products is the same and only the quantity of money increases, products will be more scarce relative to money. So the price of products will go up. When the quantity of money increases, this will happen with many products and services and the price level of overall economy will go up.

The equation of exchange, which expresses the theory, is this.

MV = PY

• M: Supply of money
• V: Velocity of money
• P: Price
• Y: Quantity of production

Alternatively, it can be written as the following.

MV = PT

• T: Quantity of transactions

For our purpose it is not important whether to base on production or transaction. As long as we apply the same variable for both Bitcoin and USD.

We now have methodology ready. We just need to get prices with the equation of exchange, and apply them to the PPP to get the exchange rate.

Preliminary valuation of Bitcoin

To explain the process, let’s do a valuation using simplistic assumptions. After that let’s improve it to be more reasonable.

Let’s forecast the economy after 10 years, assuming the cryptocurrency economy will reveal itself clearly. (The assumption of 10 years is not critical. What is important is for us to be able to see cryptocurrency economy: where it is applied, and how big it is. If you think 10 years are not enough, you may take 20 years or even longer.)

Here are recent data about the US economy.

• USD supply (monetary base) = 3.8 trillion USD (average of 2017)
  • Source: https://fred.stlouisfed.org/series/BASE
• Nominal GDP = 18.9 trillion USD (2016)
  • Source: https://fred.stlouisfed.org/series/GDP

Nominal GDP is a product of P and Q, and we can get V from the equation of exchange. V is 4.97. Based on that, here is a forecast of the US economy in 2026.

• USD supply (monetary base) = 6.19 trillion USD
  • Assume 5% annual growth
    • Actual annual growth from January 1984 to January 2017 averaged at about 10%. But took into account a sharp increase of money supply after 2008 financial crisis and assumed a conservative monetary policy going forward.
  • Source:
    • https://fred.stlouisfed.org/series/BASE
    • https://fred.stlouisfed.org/series/BASE
    • https://ycharts.com/indicators/monetary_base_growth
    • https://ycharts.com/indicators/monetary_base_growth
• Velocity of USD = 4.97
  • Assume equal to 10 years ago
• Real GDP of USD economy (in 2017 price) = 23.039 trillion USD
  • Assume 2% annual growth

If we get price level of the US economy in 2026 based on these assumptions, we get 1.34. That is, the price level became 1.34 times, when we take the price level in 2016 as 1.

Now let’s get to the price of the Bitcoin economy in 2026.

• Bitcoin supply = 20 million Bitcoins
  • The maximum supply of Bitcoin is predetermined as 21 million Bitcoins, and the expected schedule of supply is known.
  • Source: https://bashco.github.io/
• Velocity of Bitcoin = 4.97
  • Assume same as USD
• Real GDP of Bitcoin economy = 2.304 trillion USD
  • Assume that Bitcoin economy is 10% of USD economy.
  • You may feel it is strange to express the size of the Bitcoin economy in USD. Think of USD as a common product of both economies. Actually, you could apply ‘bushels of wheat’ instead of USD.

In this case, the price of the Bitcoin economy is 0.0000432.

Finally, let’s derive the exchange rate of Bitcoin and USD, that is the price of a Bitcoin.

USD economy price / Bitcoin economy price = 1.34 / 0.0000432 = 30,949

So, 1 Bitcoin is 30,949 USD.

What will be the price of Bitcoin?

The preliminary analysis was done to show the process, not the final number. Even if the model was rational, the assumptions and input numbers should be reasonable for the forecast to be predictive. Especially important are the variables which have wide range of input numbers and can have large impact to the result. Here are those.

• Growth rate of USD supply
• Velocity of Bitcoin
• Size of Bitcoin economy (production or transaction)

Of these, the variable that has the largest impact to the result as well as is most difficult to predict must be the size of Bitcoin economy. But, let’s review them in the order of appearance in the preliminary valuation.

Growth rate of USD supply

Supplies of USD and Bitcoin are important variables in determining prices. Maximum Supply of Bitcoin is predetermined, towards which the addition every year is also well projected. But the supply of USD is not known, as it is up to the Fed’s discretion.

Before we dive into the numbers, we have to address what the measure should be of currency supply. As there is little financial market or regulation around Bitcoin, I don’t think there is much argument against using Bitcoin’s base supply itself.

But there are more options with a fiat currency. There are different measures of money supply, such as monetary base (MB), M1, and M2. Monetary base is all of the paper currencies and coins that exist in the market.

I think monetary base is a good choice to compare with the Bitcoin supply. Measure like M1 and M2 include monetary supply through banking systems, of which meaning makes it more difficult to compare directly with the Bitcoin supply. (I don’t have the capacity to explain them clearly, either.)

The supply of USD based on MB is as follows. (Source: https://fred.stlouisfed.org/series/BASE, author analysis)

• 1984 to 2016: Arithmetic average growth rate 10.7%, Compound annual grow rate (CAGR) 9.62%
• 1984 to 2006: Arithmetic average growth rate 6.71%, CAGR 6.5%
• 2000 to 2006: Arithmetic average growth rate 4.72%, CAGR 3.44%

To take a long term average, 10% would be reasonable. But it would be much higher than 5% used in the preliminary forecast. (We could use even longer term data using another source.)

But if we believed that the sudden growth of money supply after the financial crisis of 2007-2008 had been an exception, we could take 6.6% or so.

If we believed we could go back to and stay at the policy of early 2000s, we could apply 4%.

Overall, 5% growth of USD supply is within a reasonable range. Maybe it feels a bit underestimating as a long-term forecast, but I am inclined to take a less optimistic stance for Bitcoin valuation.

Velocity of Bitcoin

Velocity of money means how many times a currency changes hands. The preliminary analysis assumed that the velocity of Bitcoin was equal to that of USD. But if the nature and market of Bitcoin are not the same as those of USD, the velocity is likely different too.

Many people seem to think that Bitcoin, a digital-native currency that does not need an intermediary, must have a higher velocity. Silicon Valley venture capitalists seem to imagine people conducting transactions on a mobile phone incessantly.

A fortune article says this, quoting professor Susan Athley.

Because bitcoin, unlike paper money, is very low-friction, there’s the possibility of a very high-velocity bitcoin, if, for example, vendors or traders only held bitcoin very briefly, cashing it in and out to government currencies on either end of transfers."
(Source: http://fortune.com/2014/02/18/could-there-be-a-50000-bitcoin/)

An Investopia article suggests the cryptocurrency will have the same or higher velocity than that of a fiat currency.

Models often consider the velocity of money, frequently arguing that since bitcoin can support transfers that take less than an hour, the velocity of money in the future bitcoin ecosystem will be higher than the current average velocity of money. Another view on this though would be that velocity of money is not restricted by today's payment rails in any significant way and that its main determinant is the need or willingness of people to transact. Therefore, the projected velocity of money could be treated as roughly equal to its current value.
(Source: http://www.investopedia.com/articles/investing/091814/what-bitcoins-intrinsic-value.asp)

But I have a different view on this.

The velocity of Bitcoin is more likely to be lower than USD or other fiat currencies. Velocity of money means how many times the entire currency supply changed hands to make all the transactions. But we do not do an unnecessary transaction just because it is easy. Transaction itself is quite easy to do even now with Internet banking, credit cards, and mobile payment. I doubt that people are holding transactions back now because transaction is difficult.

We should rather understand the velocity of money in relation to the demand of money. The Cambridge Equation (or Cash Balance Equation) explains money demand simply and intuitively.

Md = kPY

• Md: Demand of money (demand to hold cash)
• P: Price
• Y: Income
• Same as production
• k: cash balance ratio

To put in words, people want to hold some portion of income as cash, the total demand of cash is shown as a ratio of nominal income.

So the money calculated from this is the cash that people have as paper dollars or coins, in a wallet, under a bed, or in a safe. People will hold cash when it is preferable. On the other hand, buying goods, making investments, or depositing in a bank are actions that reduce the cash balance.

If M in the exchange equation and M in the cash balance equation are equal, meaning supply and demand are equal, the following relationship is derived.

V = 1/k

Therefore, velocity of money is inversely proportional to cash balance ration. The implication is this. People holding their money under their beds has the effect of quantity of money being decreased. For example, if more people hold cash, price of goods will go up.

Real commercial transactions using cryptocurrencies are increasing, but more seem to be for investment in cryptocurrencies themselves. We could say people are holding Bitcoins. It means high cash balance ratio and low velocity of money for Bitcoin.

What about in 10 years? When the price of Bitcoin is high enough, the speculative demand for Bitcoin will decrease. But I think the cash balance ratio will still be higher than that of USD.

The government, or the Fed, controls the supply of fiat money, and historically they have kept increasing the supply. As a result, we live in an economy that has inflation as a constant feature. But most of cryptocurrencies including Bitcoin explicitly limits their supply. An economy without constant inflation is possible, and maybe one where decreasing price is normal assuming rising productivity.

Of course, financial markets will develop in the crypto economy, and people might deposit at banks rather than hold cash (of cryptocurrency). Cash balance ratio is still likely higher as the benefit of holding cryptocurrency is higher compared to the current fiat money. So, I believe the velocity of Bitcoin will be lower. I don’t know if it will be much lower or a little lower, but with caution let’s assume the velocity of Bitcoin is 20% lower than that of USD.

Size of Bitcoin economy

The most important variable is the size of Bitcoin economy. Velocity and supply of money are uncertainties within a rather foreseeable range, but the size of crypto economy is literally from 0 to 100%. I used an assumption of 10% of the US economy in the preliminary analysis, it could be smaller or even bigger than the US economy itself.

Here are some benchmark markets for predicting scenarios for the cryptocurrency economy.

• Global remittance
• Global cross-border ecommerce
• Global retail ecommerce
• Global underground market
• Global trade

Let’s have a look at one by one.

[Scenario 1: Global remittance]

This is people who work abroad sending money back to home countries.

• Global remittance size: 575 billion USD (2016)
  • Source:
    • http://www.worldbank.org/en/news/press-release/2017/04/21/remittances-to-developing-countries-decline-for-second-consecutive-year
    • http://blogs.worldbank.org/peoplemove/trends-remittances-2016-new-normal-slow-growth

If we apply 3.7% growth rate that the World Bank used in a source above, the scale of global remittance in 2026 will be 827 billion USD.

[Scenario 2: Global underground market]

The underground or black market consists of transactions made outside official economy. If we define it as transactions that do not pay taxes, it is much larger and estimated at 15-25% of global GDP. But the number below only includes transactions of illicit products and services like drugs, prostitution, and counterfeit products.

• Global underground market size: 1812 billion USD
  • Source: http://www.havocscope.com/market-value/

IMF forecasts that the global economy will grow at 3.7-3.8% per year. Applying 3%, which is lower, we get the global underground market of 2,435 billion USD in 2026.

[Scenario 3: Global cross-border ecommerce]

This means ecommerce between different countries.

• Global cross-border ecommerce size: 230 billion USD (2014)
  • Source: http://www.alizila.com/cross-border-e-commerce-to-reach-1-trillion-in-2020/

The above source predicted 27.4% growth up to the year 2020. Assuming it will be slower after that, we apply an overall growth rate of 25%. And we get 3,347 billion USD in 2026.

[Scenario 4: Global retail ecommerce]

This is global ecommerce purchase of consumers, in other words online shopping.

• Global retail ecommerce size: 1.9 trillion USD (2016)
  • Source: https://www.emarketer.com/Report/Worldwide-Retail-Ecommerce-Sales-eMarketers-Estimates-20162021/2002090

We apply 15% annual growth rate, considering the growth trend in the above source, and get 7,687 billion USD in 2026.

[Scenario 5: Global trade]

This is the amount of trade between all countries in the world.

• Global trade: 20.8 trillion USD (2016 product export 16 trillion USD, commercial services export 4.8 trillion USD)
  • Source: https://www.wto.org/english/res_e/statis_e/wts2016_e/wts2016_e.pdf

Recently global product exports grew 3% annually and services 4%. Taking 3% overall, global trade in 2026 will be 27,953 billion USD.

Bitcoin’s price and total market value according to each scenario is as follows.

Scenario	Bitcoin economy size (BN USD)	Bitcoin price (USD)	Bitcoin market cap (BN USD)
1. Global remittance	827	13,885	278
2. Global underground market	2,435	40,891	818
3. Global cross-border ecommerce	3,347	56,201	1,124
4. Global retail ecommerce	7,687	129,070	2,581
5. Global trade	27,953	469,384	9,388

If Bitcoin represents the overall cryptocurrency, market value may be better than price to compare with the present. As of this writing, total cryptocurrency market value is about 1.3 trillion USD. If the more conservative scenarios of 1 or 2 are right, the market cap will become 2.1 to 6.3 times that of the current.

Somewhat optimistic scenario 3 turns out to be correct, and it becomes 8.6x.

Scenario 4 or 5 implies that cryptocurrency reaches a status of an internationally accepted currency, and if that happens the market cap will be 20x to 72x of the current.

No one knows which scenario will become reality. The usefulness of this analysis to apply a prediction to estimate the price and market value of cryptocurrency. I believe the model is pretty sound, but the real difficulty lies in foreseeing how the Bitcoin makes progress in the real markets.

This is not comprehensive and there are many other possible scenarios.

I did not present any scenario in which cryptocurrency replace a fiat currency of a national economy, but no one can say it is not possible. Perhaps countries with very high inflation or poorly managed economy may adopt cryptocurrencies.

Or you could have a scenario based on micropayment. It differs by country, but currently people tend to pay small amount with cash rather than a credit card. And online micropayment is still a problem to solve. If cryptocurrency can address these cases, it could make micropayment its market.

One thing to keep in mind is, none of the scenarios presented is the worst case. It is possible for cryptocurrencies to fail to take roots in the world and simply disappear.

In the next article, let’s think about the risks that cryptocurrency faces and the strategy for it to survive.

(Try your own cryptocurrency valuation with an Excel spreadsheet that I developed. It has a valuation template for anyone to use, and contains valuation examples in this article.)