# Is It Possible to Evaluate Crypto Assets Mathematically?

On July 22, following the meeting of the finance ministers and heads of central banks of the G20 countries in Buenos Aires, it was concluded that crypto assets do not pose a threat to the stability of world finance at present, but "it is necessary to remain on guard,” because the situation may change. Indeed, the perception of cryptocurrencies has recently changed. Back in 2015, economists assured the laymen of the immateriality of Bitcoins and other coins, and a few years later, the same researchers began wondering about the evaluation of electronic money, because the total market capitalization amounted to more than \$280 billion. Despite large investments, crypto assets are "incomprehensible" for economists, because they cannot be estimated as common objects. Therefore, many researchers put forward their theories on the evaluation of cryptocurrencies as assets.

Crypto assets are a completely new class of assets, which, at first glance, cannot be estimated, and are completely different from traditional assets (money, bank deposits, investments in securities, and real estate). Indeed, tokens and coins cannot simply be called currencies, since their use goes beyond the usual medium of exchange, they are not related to interchangeable resources or goods, and they do not provide a constant flow of investments, which means that tokens and coins are not property. But some researchers have found ways to evaluate crypto assets using known economic formulas.

## By the Exchange Equation

There is a well-known equation of the American economist Irving Fisher used to calculate the value of traditional macroeconomics, which describes the ratio of the money supply, money circulation rate, price level, and output, and it looks like this:

MV = PQ,

Where:

M is the money supply or a combination of cash and non-cash funds, but when working with cryptocurrencies, especially with altcoins, it is better to use the average annual volume of the asset due to high volatility;

V is the velocity of money for which the average frequency is taken. It characterizes the number of transfers of assets from "hand to hand" for the observed period (for example, this figure for Bitcoin in 2016 was 6.5);

P is the level of prices or their rise (inflation) or a decrease (deflation) in the crypto industry. This is the price of the resource provided by the network. For example, the price for gigabytes will be expressed in \$ / GB;

Q is the volume of production or an indicator of the real costs of new goods and services.

The co-creator of Ethereum Vitalik Buterin suggested using a more modernized model of the formula for the evaluation of crypto assets, which is used in calculating national incomes, where instead of the volume of production of Q, T is the number of transactions or their economic value per day.

"A trivial example can be proof of this equality: if there are N coins, and each of these quantities passes from hand to hand M times a day, then the economic value of the coin in 24 hours is M * N. If there is an economic value of \$T, then the price of each coin is T / (M * N), and the "price level" itself is inverse, so it is found using M * N / T," says Buterin.

In addition, to evaluate and simplify the analysis of crypto assets, two variables from the classical Fisher equation can be replaced.

"We refer to 1 / V with H (H = hour) the time when the user holds a coin before making a transaction, and at 1 / P from C the price of the currency (C = cost).

Now we have:

M / H = T / C

MC = TH

The left side is market capitalization, the right side is the economic value per day, multiplied by the amount of time that the user holds coins before making a deal,” Buterin states in his article.

Chris Burniske, co-author of the book "Cryptoassets: The Innovative Investor's Guide to Bitcoin and Beyond" and partner of the venture fund Placeholder, which is engaged in investments in decentralized technologies, agrees with Buterin’s statements and adds that the evaluation of cryptocurrency assets cannot be done through the forecasting and the discounting of the cash flow method (DCF), as in the world of digital coins these flows are absent.

"It is necessary to develop a model similar in structure to the DCF method with projections for each year, but instead of traditional indicators (revenue, margins, and profits), the model will use the current utility (CUV or current utility value) to obtain a fair price for each period. In the protocol, crypto assets serve as a medium for exchanging and preserving the value and unit of the account. Therefore, each crypto asset serves as a currency in the economy of the protocol which it supports. And the exchange equation (MV = PQ or MS = TN) is used to understand the flow of money supply necessary to support the economy," says Burniske.

The product of two indicators P and Q in classical monetarism is considered as a country's GDP. In the case of the crypto industry, instead of the gross product and large accounting calculations, a blockchain is the case in which all transactions are already registered. Therefore, the GDP of a crypto ecosystem is the total volume of valid transactions of crypto assets.

## Metcalfe’s Law

The second, but no-less-popular way to evaluate crypto assets, in particular, BTC and ETH, is the law of the engineer Robert Metcalfe, who was originally involved in the development of the technology of wired Ethernet LANs. He argued that the larger the network of users, the greater the value of this network. For example, two phones will have one network: five phones can create a network of 10 connections, and 12 phones will form more than 66. This theory has moved to economics and is now called network effects.

Metcalfe’s law (denoted as M) fully justifies the blockchain with its numerous users and the cryptocurrency, which was repeatedly called a bubble. After all, the more active the user base, the more a technology develops. This statement, as Dr. Ken Alabi from the University of Strathclyde proved in his article, can be applied to crypto assets. A user at Reddit /cryptocurrency, using Metcalfe's estimation coefficient (P / n2), compared the figures with the main cryptocurrencies (Bitcoin, Ether, and Litecoin) and concluded that the data was similar to the P / B ratio in the capital analysis.

"Higher ratios prove the hopes and expectations of investors that in the future, the network will get more value thanks to each new user. So far, it is difficult to determine the exact number of people in a crypto ecosystem. The vast majority of addresses have no activity, and many of them have a balance that is either zero or too small to cover the average transfer fee," the material says.

Researchers from Clearblocks analyzed Bitcoin and Ether, showed the compliance of Metcalfe's law (denoted as M with formula N2) with prices (\$), examined the modifications of M (M1, M2, and M3), and compared with similar Sardoff laws (denoted as S with formula N) and Zipf (the formula N * ln (N)). The linear correlation coefficient of r Pearson was used to study two variables in the same sample. The data of the first table showed that all formulas showed an almost perfect correlation with the BTC price in dollars, especially in natural logarithmic scale, which is unacceptable for the classical economy. Table 1. Pearson correlation coefficients (r) of the dollar price to BTC with uncorrected formulas (line 1), for 30-day data (line 2), and with 90-day return average values ​​(line 3) are shown. Lines 4 and 6 measure the correlation of the natural logarithm of the price in dollars. Source. Table 2. Data is shown when using active addresses. Using unique active addresses increases the correlation of formulas with the dollar's price to BTC. V still works best on a non-local scale, whereas S, M, and M2 work best on a natural logarithmic scale. As above, however, the differences in the correlations are so small that they can be considered equal. Source.

But with Ethereum things are different, because compared to Bitcoin, researchers' formulas from Clearblocks showed a very strong correlation with ETH to the dollar when using transactions, even on a non-local scale. Probably, as analysts suggest, the formulas lost some correlation force over time (Bitcoin has existed for about eight years, and Ether has existed less than three years). Table 3. For ETH, V, S, and Z show the best overall performance. As in the case of BTC, however, the difference in the correlation between the formulas is so small that they can be effectively considered equal. Source.

Thus, at the moment, there is no single indicator that could accurately predict the price of a speculative asset such as ETH or BTC because too many variables are needed. If we accept the premise that the blockchains which prevail in the speculative stages of adoption behave like online telecommunications networks, however, then Metcalfe's law will help better understand the place of intersection of use and price, and when one indicator is significantly ahead of the other.

## The Discount Model of Dividends

The DDM (Dividend Discount Model) is used to evaluate the altcoins that offer token dividends (for example, Binance Coin (BNB), Kucoin Shares (KCS), COSS (COSS), and Cryptopia Fee Shares (CEFS)), in the form of a fee-designated activity. The calculation using this model uses the expected rate of growth in the volume of exchange trade (g). For the crypto enthusiast and founder of Bear Studios, Venture Focus, and The Ledger Group Avi Felman, it is clear that due to this, there will be a broad projection of exchange rate growth, and DDM can give some idea of which assets have significantly depreciated. The required rate of return (r) is equal to the yield in the general cryptocurrency index.