#### What is a fair value?

The concept of fair value might sound familiar to an investor. There are two kinds of assets; those whose fair value is intrinsic, and those whose fair value can be expressed as a function of intrinsic fair values.

The intrinsic fair value is the function that converts the ordinal preferences of an individual’s mind into a price. Therefore, the price at which a person buys something ordinary (ie., a banana) is always smaller or equal to the fair value that the individual assigns to the thing he is buying. When many people trade an ordinary good or service, we can refer to the current fair value of that good or service as the price of it. If we were to invest in that ordinary good or service, then we would need to predict the future changes in the scale of preferences that exist in society with regard to the specific ordinary good or service. We can refer to this unit as; the fair value, predicted fair value, future fair value, or speculated fair value.

We can further conclude that the compounded fair value represents any fair value that is expressed as a function of intrinsic fair values, the existence of which can be justified under the rules of compounded assets. One would first assess the intrinsic fair values of the underlying ordinary assets, and then use the rational function to obtain a compounded fair value. Some examples of compounded assets with compounded fair values are stocks, bonds, derivatives, mortgages or currencies. All these derive their fair values from intrinsic fair values like cash flows, interest rates, ordinary goods and services, or even other compounded fair values (such as in the case of financial derivatives).

Any compounded fair value has a degree of uncertainty. The source of biggest uncertainty is usually the inclusion of future intrinsic fair values in the rational model. One of the best-known variables based upon the future, included in almost any fair value model is the interest rate.

One last thing to mention is that the cardinal value of something can only be expressed in terms of another. There is no such thing as an absolute price. Every price comprises of a pair of assets which consists of the priced asset, and the reference asset. For instance, one can say that a car is worth ’N’ units of a currency (eg. USD), however it is impossible to imply that the car is worth an absolute number. Everything has a relative value in economics because the value of everything is derived from the ordinal scale of preferences that apply to each and every individual. Therefore, when determining the fair value of a currency, one will find themselves always comparing the value of one currency to another.

#### What is an interest rate?

People prefer to receive goods and services today rather than having to wait for a time in the future. This is called the originary interest, which is also considered to be the intrinsic fair value of time. When individuals with different time preferences interact in markets where future assets are traded, they will attempt to negotiate, or accept the available counter-party. Those markets are known as the markets of time as a result of time being indirectly priced. Currently those markets are highly intervened by central banks, and as a consequence the official price of time is monopolistic. Conversely, when we take into consideration that black markets operate on an unhindered interest rate, and not the monopolistic interest rate of time, it becomes clear that the function of originary interest in markets certainly has not been lost.

To further conclude, if one where to use an expected market interest rate for his rational model (eg. Discounted Free Cash Flows), they would be completely wrong if they extracted the results from the official interest rate.

I am sure the investor would be shocked if they were made aware that the time preference of aggregated real humans is closer to 8% than to 2%.

#### What fair value model is this website based upon?

This website is based upon the Currencies Fair Value model published by @pablompa in 2017. You can read the whole article here. Or, if you prefer PDFs, you can download it here.

#### What is a money transaction?

In regards to how the fair value of a currency is determined, a money transaction is a particular subset of all the money movements. In particular, it refers only to the transactions which are actual trades for goods and services, as it is possible to gather that a proportion of the transactions will be actual trades.

Nevertheless, if we allow the average basket value to absorb goods and services trades, along with the rest of the transactions, then the requirement to determine which of those transactions are actual trades vanishes entirely. Thus, allowing the investor to consider all transactions as legitimate trades in his calculations.

Transactions per unit of time is an extensive variable. Meaning it depends directly on the number of individuals using the currency. This extensive variable is the key indicator of adoption, which can change very fast in the cryptocurrencies markets. Thus, we have decided to use a 2 weeks exponential moving average of transactions in our calculations.

#### Velocity of money and transactions per day are totally different concepts

The velocity of money is the number of times a unit of a currency is transacted per unit of time. It represents the willingness of individuals to trade their savings or account balances. Those that are willing to trade their savings provoke a higher velocity of money. One shall not confuse the concepts of number of transactions per unit of time with the velocity of money. Transactions per unit of time is an aggregated concept. The more individuals that are using the money, the more transactions per unit of time there will be, whilst the velocity of money will not be affected. Nonetheless, if individuals reduce their willingness to trade their savings or account balances, this will reflect a decreased velocity of money.

#### How do you know the velocity of money of the coins?

As we have discussed, the velocity of money represents the overall willingness of the market to trade a particular currency, which is often influenced by a number of factors, for instance, there could be special incentives for a holder to retain their currency rather then want to spend it. It possible to determine the market’s inclination to trade a particular currency, and as a matter of fact, it’s rather straightforward.

We use two important and different definitions of the Velocity of Money: the Velocity of Money and the Total Discounted Velocity of Money. The first one is defined as the number of times an issued unit of a currency is transacted per unit of time (regardless if there are units are in the hands of big holders). The latter is defined as the number of times a unit of a currency is transacted per unit of time, including units not yet issued. Another way of defining the two concepts is considering the first one as the willingness of individuals to trade their current savings, and the later as the willingness of individuals to trade their current savings plus their expected future savings.

The overall Velocity of Money can be found by calculating the aggregate total of units traded each day divided by the total supply in circulation, or by the total discounted supply in the case of the Total Discounted Velocity of Money.

Velocity of money is an intensive behavioral variable. Meaning it does not depend on the number of individuals using the currency, but rather on the way they use it. The way individuals use a currency does not change very fast and, thus, we have decided to apply to it a simple moving average with a 1 year span. This is a neutral assumption which relies on past data of observed behaviour.

Be careful in the cases where a slow velocity of money is a consequence of a token issuer or company holding the majority of the currency supply. In these cases, one single person can change the overall velocity of the currency in an unpredictable instant.

To be consistent with the fair value model, we are using the Total Discounted Velocity in the calculation of the Fair Value.

Keep in mind that a lower velocity leads to a higher fair value.

#### What is a basket and how can it be calculated and used?

The basket of a currency is the average list of goods and services bought with the currency in a period of time. It is impossible to obtain this information from the provided data, but on the other hand its value is indeed apparent. The value of the average basket, in simple terms, is the average value of transactions, which can be referenced in any currency base.

Like the velocity, the average basket value is an intensive behavioral variable. Meaning it does not depend on the number of individuals using the currency, but rather on the way they use it. We decided to use the same moving average factor that has been applied to the velocity of money, also giving it a span of one year. This accounts for changes in the overall market’s average basket value, which as we have mentioned can occur from time to time in such a turbulent and competitive market.

Calculating a basket shift factor between currency A and currency B is as simple as dividing the value of their average baskets. A higher value of the average basket leads to a higher fair value.

#### Difference between a certain and an uncertain money supply function

Until the appearance of cryptocurrencies, there were no forms of money with a known future supply. Even metals had a degree of uncertainty on their future supply, for new mines could always be found. Now we have world full of flavours. We have currencies with full uncertainty on their supply (i.e. US Dollar or Euro), as well as currencies with zero uncertainty and others with some uncertainty. When including future information about the supply, one must be careful to distinguish the exact future from the expected future. Uncertainty requires expectation techniques whereas certainty just requires the knowledge of the future supply function. Expectation requires an expectation function and a rule. The easiest and most respected rule is the long term inertia.

#### Understanding Total Discounted Supply

When people use money to buy goods and services, they don't make decisions solely according to the number of currency units available today in their pockets. For example, if by decree the entire population’s salary was to be doubled tomorrow, then a large number of people would start spending today. In a similar scenario, if someone were to be made aware that everyone around them was about to double the number of currency units in their pockets tomorrow and they would not, then they would rush to buy groceries today before the prices increase. That is exactly what takes place with inflation, it is the issuance of new currency units. People advance their purchases as much as they discount future inflation. The discount rate is exactly their originary interest.

With the former in mind, it is very straightforward to formulate a model where the supply of a currency is not just the current supply, but also a discounted future supply. That model is the Total Discounted Supply (TDS). For a deeper understanding of the TDS model, click here.

#### How can I calculate the fair value of a currency?

Calculating an exact fair value for a currency with respect to another currency can be laborious if done rigorously. The trickiest part would be integrating the future expected supply to obtain the Total Discounted Supply. Nonetheless, one can take some approximations for a quick calculation. The general formula for the Currencies Fair Value is the following:

$$\text{Fair Value}_{\text{ of currency A in terms of currency B}}$$ $$= b_{AB}·\frac{T_{\text{A}}}{T_{\text{B}}}·\frac{M_{\text{B}}}{M_{\text{A}}}·\frac{V_{\text{B}}}{V_{\text{A}}}$$

Making the following assumptions leads to a fast calculation:

• Common basket structures: $$b_{AB} = 1$$

• Velocities:
• Similar velocities: $$V_{\text{A}} = V_{\text{B}}$$

• Capped velocities: $$\frac{V_{\text{B}}}{V_{\text{A}}} = \frac{RatioCirculating_{B}}{RatioCirculating_{A}}$$

• Total Discounted Supply ($$\text{M}$$):
• Both fiat currencies: TDS equal to current supply.
• Both crypto: TDS equal to maximum future supply.
• One fiat, one crypto: unfortunately there is not a good approximation for this case.

• The proportion of trades $$\text{T}$$ in the total number of transactions per period is similar in both currencies.

Please, keep in mind that these assumptions are approximations. This website does not make approximations in the Total Discounted Supply, but calculates it exactly, extrapolating the unknown future linearly in most cases and exponentially when applicable.

The following is an example of how the fair value of Bitcoin Cash with respect to Bitcoin is calculated using current data. The following has been assumed:

• Equal velocities.
• Equal proportion of trades in the total number of transactions per period.

$$\text{Fair Value}_{\text{ BCHBTC}}$$ $$= 1·\frac{ 5,119 }{ 309,993 }·\frac{ 20,376,462 }{ 20,385,487 }·1$$ $$= 0.028$$

#### Is it possible to check if the model works?

One of the most interesting parts of Currencies Fair Value model is that it arrives at the rational conclusion that currencies must be trading at their fair value when the number of speculative trades in the particular currency itself is negligible with respect the the total number of overall trades conducted using the same currency as a tool, such as in the case of when someone trades BTC for BCH because he thinks BCH will perform better. It also arrives at the conclusion that even when the number of speculative trades is not negligible, and the aggregated number speculative trades is also unbiased and cancels out, then this indicates that the currency must be trading at its Fair Value. With that in mind, while analyzing the charts, it is in fact possible to determine how much speculation occurred. Furthermore, it can be observed that if the fair value model was wrong, then the values yielded by it would not have anything to do with the price itself, they would actually be totally different numbers, which may differ by any factor between 0 and somewhere in the millions. The reality however is that the findings are as a matter of fact quite close together, which is something reassuring. Proofs are empirical, the more data that’s made available, the more one can be sure that the model is much closer to reality.

#### Does the model have uncertainty?

Indeed it does, nonetheless, it is difficult to assess. Evaluating the uncertainty of a model requires an uncertainty model. Our uncertainty model targets the fact that we cannot be sure that our moving averages are an indication of the non-speculative behaviour —utility trades—. We take the difference between the logarithm of each model variable and its actual value as the 99th-percentile of the uncertainty. This way, changes in the behavioral variables and fast changes in transactions lead to a higher uncertainty.

The uncertainty model also accounts for the fact that the future supply function of some coins is unknown or inaccurate. The portion of the Total Discounted Supply that is calculated by extrapolation is added to uncertainty as being 100% uncertain.

Using the concept of uncertainty, one can think of the fair value of a currency as an approximate region instead of an exact value. The probability distribution within this region is unknown, and as a consequence it is not possible to assert that the correct fair value is more likely to be close to the center of the region, although it may be sometimes.

If you navigate to the Fair Value chart of any of the coins, you will find the uncertainty regions depicted. Remember that sometimes the logarithmic scale works best to visualize the data. Navigating the main page you can find another way of displaying uncertainty. The uncertainty column shows a relative magnitude of the model's uncertainty highlighted in three colors (green —low—, orange —medium— and red —high—). The colors aid locating the uncertainty within its range by dividing it in three regions: 0% to 33.3%, 33.3% to 66.6% and 66.6% to 100%. A value of 100% would indicate no certainty at all, whereas a values of 0% would indicate absolute certainty. It is easy to calculate the fair value lower and upper bounds using this uncertainty level $$U$$:

$${\text{FVU}}_{\text{LOW}} = FV·(1 - U/100)$$

$${\text{FVU}}_{\text{HIGH}} = FV·(\frac{1}{1 - U/100})$$

As an example, using the former equations, a value of 50% uncertainty would indicate an uncertainty region covering from half to two times the indicated fair value.

#### What do the four types of capitalization metrics mean?

As it can be seen here, for instance, four types of capitalization metrics are defined:

• Market Cap
• Fair Cap
• Total Discounted Market Cap
• Total Discounted Fair Cap

Let us explain each one of them.

##### Market Cap:

The well-known Market Cap of a currency is calculated as the current circulating supply of the currency times its price. It is an approximate metric of the total wealth in circulation living in the form of the currency. It does not take into account how the future supply of the coin will be. For instance, if the supply were to be duplicated tomorrow, that would not be reflected in the Market Cap metric. It is also a market metric, meaning wealth is weighted according to current market prices.

##### Fair Cap:

The Fair Cap of a currency is very similar to the Market Cap. It is calculated as the current circulating supply of the currency times its fair value. The difference is that it is not a market metric, but a fundamental metric. It measures the total wealth in circulation in fundamental terms. In other words: it measures what the Capitalization should be according to the current usage of the currency.

##### Total Discounted Market Cap:

The Total Discounted Market cap is also very similar to the Market Cap. It is calculated as the Total Discounted Supply of the currency times its price. The difference is that it does not measure the explicit current wealth in circulation. What is measures is the a wealth in circulation taking into account that individuals discount the future supply when they trade (see Understanding Total Discounted Supply). It is the Market Cap that takes into account the supply increments of the future. As well as the Market Cap, it is a market metric.

##### Total Discounted Fair Cap:

The Total Discounted Fair Cap is the combination of the two new concepts. It is calculated as the Total Discounted Supply of the currency times its fair value. It is similar to the Total Discounted Market Cap, with the difference that it is not a market metric, but a fundamental metric, like the Fair Cap.

Neither of them is the correct metric for the Capitalization. They measure different things. Understanding their differences is key to be able to leverage on their analysis.

#### Why does your Market Cap differ from Market Caps in other sites?

Our Market Cap differs from Market Caps in other sites because we do not make the artificial distinction between Circulating Supply and Supply. Let's put it simply: the fact that the founders hold a part of the supply does not make their part of the supply less circulating than a part of the supply supply held for years by an investor. "Static" supply is reflected in the Velocity of Money. The more "static" supply within the total supply, the smaller the velocity -hence, the higher the tendency to hold savings-.

#### Is everything below its fair value a bargain?

Definitely not. The fact that the market speculates something based off the fair value does not mean that the market is wrong. Speculation is the human assessment of the future outcomes. If the price is below the fair value is because the market thinks its usage is going to decrease with respect to the reference currency. Whether it will do or not is what the investor has to analyze. The opposite applies if the price is higher than perceived fair value. In this later case, it is the investor's responsibility to decide whether the currency is too expensive and they should sell, or they can determine wether the usage of the currency with respect to the reference currency is going to increase, and thus the fair value is also likely to correct upwards. This very same principle applies to fundamental investing in stocks.

Do not forget you are the investor. We do not speculate. We just help calculating the fair value according to current usage of one currency with respect to another.

#### How accurate is the fair value of EURUSD?

Contrary to what it might seem, there is not much data available on the number of trades for a given period for fiat currencies. The data is very sparse and the consequence is that there is poor clarity on their fair value. Nonetheless, this is not the only source of uncertainty when dealing with fiat currencies. Fiat currencies have an uncertain future supply function. This means the Total Discounted Supply is based purely on the expectation of the supply itself. Inertial expectation is easy to deal with for smooth asymptotic or linear supply functions, but this also does not apply to fiat currencies. Their supply functions are exponential on average and the problem with exponentials is they are very sensitive to their rates.

Due to this lack of fundamental data resolution, the calculation of the fair value of fiat currencies with respect to a fiat currency has been discontinued. Current fair value being equal to price implies the Efficient Market Hypothesis.

#### How the Price to Fair Value Ratio is to be interpreted and how does it relate to the Price to Earnings Ratio of stocks?

The Price to Fair Value Ratio is the simplest yet powerful fundamental investor metric. It does not have units, and what it measures is the number of times the market thinks the usage of the currency is going to increase / decrease in the discounted future. A P/FV equal to 1 means the market thinks the currency is neither going to increase nor decrease its usage in the discounted future. A value below 1 might represent an opportunity to buy cheap, whereas a value above 1 might represent an overpriced investment. All this depend on the speculation factor the investor wants to apply. Remember that at coinfairvalue.com we do not speculate.

The P/FV Ratio resembles the famous P/E Ratio that was popularized by Benjamin Graham and applies to stocks. Price to Earnings differ from Price to Fair Value in that the fair value of currencies is calculated differently from the fair value of stocks. Stocks are a future promise on cash flows whereas currencies are a tool for trading value. A neutral (zero-growth) discount of cash flows to perpetuity, for a company with an average Debt to Equity Ratio, yields a P/E Ratio of approximately 15. 15 is to stocks what 1 is to currencies. Thus, multiplying P/FV by 15, we get a P/E Equivalent Ratio for currencies.

The P/E Equivalent Ratio is very convenient for the typical stock market fundamental investor.

#### How do lightning networks and off-chain transactions affect the fair value?

Lightning networks and off-chain transactions such as those produced within the servers of an exchange are not individually registered in a blockchain. At some point, a transaction whose value is the net value of several off-chain transactions gets registered.

In CoinFairValue we work with the settled basket; that is, the value settled at the end-point (the blockchain). We make the hypothesis of a slow change of the basket shift ratio with respect to the settled basket and, thus, the fair value model is still equally valid. Let's explain it with a simple real time example.

Say Alice buys bread from Bob with an off-chain transaction carrying 1 mBTC. After a while, Bob buys apples from Alice with an off-chain transaction carrying 3 mBTC. Then the transactions are settled up in the blockchain with a sigle net transaction of 2 mBTC from Bob to Alice. Let's check the impact in the fair value formula, counting the off-chain transactions and excluding them -counting only the settled transaction-.

Counting all transactions (off-chain and settled), the real time factor in the fair value formula would be:

3 (transactions) x 6/3 (basket average value) / 6 mBTC (velocity) = 1

Counting just the settled transactions, the real time factor in the fair value formula would be:

1 (transaction) x 2/1 (basket average value) / 2 mBTC (velocity) = 1

Yet one might be wondering what happens if the transactions for bread and apples are separated in time. This, indeed, is the only side effect of excluding off-chain transactions in the CFV model: time resolution.