# Complicated Fisher formula with a new variable: we continue to mathematically calculate the value of the asset

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At the beginning of November the exchange rate of bitcoin is about \$6500, which corresponds to 2017 for the same period. Many analysts believe that the cryptocurrency market is losing its investment attractiveness, however, even this annual volatility of the first digital coin below or equal to the nominal value of the shares of Apple (AAPL) or Netflix (NFLX). The cost of Fiat assets has been calculated according to the equation of exchange, which with some modifications from the theoretical point of view suitable to evaluate the cryptocurrency. However, this unique economic phenomenon, as a digital currency, requires the introduction of new variables for a more accurate analysis.

Bitcoin is considered to be one of the new forms of funds. The most popular formulation of crypto-assets as the payment system using the equation of exchange (Fisher), which looks like MV = PQ. About using this equality in the cryptocurrency sector, we wrote in the article about mathematical assessment of digital assets.

Their improved equation of exchange economy from Fiat to cryptocurrency previously represented the Creator of Ethereum, Vitalik Buterin, co-author of the book «Crypto-assets» and partner of the venture capital Fund Placeholder Chris Burniske, resident BlockChanel Alex Evans. However, there was much debate about whether the steady-state equilibrium growth cryptanalysis (V) to outpace GDP growth (PQ), which can reduce money supply (M) and a reduction in prices (P).

The researcher Blockchain Advisory Group Joni Entos argues that it is wrong to discuss «the speed problem» at the values. Also Entos sure that the correlation is effective when the indication of the relative magnitude of changes in PQ and V.

### The differences in the formulas Bernice and Evans in the evaluation of crypto-asset

Methods for the evaluation of crypto-asset unlike traditional monetarism first was based on M as the dependent variable, and PQ as the independent variable. Work Burniske, according to Entos, sets V as a parameter a fixed value. And Evans uses the average M, measured in U.S. dollars, although the value of M should be suitable for any measured period.

In the model Burniske using PQ – independent variable, get the mean value M on the basis of this PQ and then derive V endogenous.

where

Then it follows that

In turn, the researcher Evans unlike Bernanke recognizes that this is a common link between PQ and V with respect to each other is informative in the case, when considering the prediction of price movements of the token over time.

Entos says that most investors implicitly think about a simple assessment methodology MV = PQ, which is true at any point in time by definition. «If you take M V – dependent variable, PQ – the independent variable, and define V on the basis of PQ, then output M:M is the dependent variable, (PQ / V) – independent variable. At the highest level, the real question is: does this approach make sense? Therefore, we are not concerned about the specific value of the variable. We are interested in the interaction between changes in these variables. Have you changed the indicators PQ to V or transformed variable V in PQ? How did this happen?» – does the researcher these questions.

### The main problem of Fisher’s formula for the evaluation of crypto-assets

According to the Entos value of the velocity is very sensitive to the specific PQ selected. For example, to use means to protect the value of V is likely to be low. Because of this, users believe that the price of bitcoin is increasing.

«Changes in PQ indices, e.g. growth of the network with new users, are the driving factor influencing the rate of change with time. If many people were holding bitcoin as a means of savings, now virtually all new users use the coin only for payments. Obviously, this specific increase in PQ leads to a corresponding increase in V. Therefore, for this indicator it is necessary to determine the degree of increase in the indicator, which will be determined (V). A measure M will be determined by the interaction between the relative growth rates of PQ and V,» says Entos.

### To complicate the classical formula

The loss of ecosystems cryptanalysis to a simple monetary formula eliminates economies of the new possibilities that have a crypto-assets. It turns out that Joni Entos and his team of researchers propose to study digital coin without frames simple phrase «cryptoassets-as-money» – «crypto-assets like money» and to complicate the formula MV=»QP» variable, the beta for the measure V. This is required for averaging the rate of change.

«If the PQ increases faster than V, then M increases as the value of the token in dollars, and everything else is the same. But if V is growing faster than that of PQ, then M decreases as the value of the token in dollars. Therefore, this correlation is insufficient to describe the relationship between V and PQ,» – says Entos and leads a hypothetical table of growth of the two economies and their GDP.

To the left are the economy, where V is increasing at the same rate as GDP. In the result, the monetary base remains constant over time. The correlation between PQ and V perfect and is 1. The right table shows the economies with the same GDP growth at a rate twice the GDP growth rate. Because the rate ahead of GDP growth, the monetary base decreases over time, as well as symbolic value. Thus, two economies with the same profile of GDP can have very different monetary framework, depending on the speed of the growth rate V relative to the growth rate of GDP. Source.

Based on the concepts of classical Economics, the correlation between PQ and V is equal to 1 and will always be extremely high for a number of values that have the same directed vector. Because correlation measures the probability for increasing values in one variable and their correspondence to the increase in the values in another variable.

Entos, however, focuses on the fact that the changes are neither a correlation between the variables GDP and the speed, nor the correlation of their rate, which is important when assessing the impact on the value of utility of the token. After all, the only statistical relationship between PQ and V is not quite correct, because it does not provide useful information about the size of a relatively-synchronous volatility between PQ and V. the Covariance or the correlation moment alone also does not give an adequate understanding because it does not take into account the variance of the independent variable, which is characteristic of crypto-assets.

To adapt the classical equations of Fisher, to formalize the simple concept of the classic building of the portfolio and the underlying linear regression and add a new variable . Thus the derived formula is similar to the traditional calculations of the beta of the stock, but still will not refers to the traditional definition , which compares the volatility of the stock return to the return of the market portfolio.

The crypto-assets by analogy with the formula in the Fiat economy, changes in M in accordance with the calculation formulas of linear regression are determined by the following formula:

where V – beta speed

Cov – the covariance of the estimated and reference value,

Var – variance of the reference value,

rV – % change V,

rPQ – % change crypto-asset.

«For our «instant» concept M – the total monetary base needed to support PQ and V at any point in time, we are worried how the relative transformation in PQ and V change in M from one time to another , so we are interested in how the MV = PQ is shifted from one time to another,» adds Entos.

The result is that beta is used for clarity in the discourse about the «problem of speed». Instead introduce vague concepts about the future potential «high or low speed» or «speed-ahead GDP», it is necessary to find out whether the speed of the beta of the asset that can be < 1, = 1 or > 1, and this beta may change over time. For clarity, the table is presented:

Arrows show the change in the value of the asset depending on the beta and its significance in relation to 1. Source.

Remember that V in this already existing set of data is calculated metric and the mapping result of the historical changes of PQ change V is just an alternative view of the changes bitcoin market over time. The result is that the beta provides relevant information to predict future changes in the value of M.

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