Using observed data for both Facebook and Bitcoin, we derive the relationships between price, number of users, and time, and show that the resulting market capitalizations likely follow a Gompertz sigmoid growth function. This function, historically used to describe the growth of biological organisms like bacteria, tumors, and viruses, likely has some application to network economics.Read More
It becomes very difficult to find downward pressure on bitcoin price, even with perfect regulatory enforcement and large, pessimistic ranges for price estimates.Read More
As an investment manager I am forced to strive to be objective about the assets in client portfolios. An investor must be able to answer three questions about each portfolio holding: (a) what is it that you own? (b) why do you own it? and (c) what is its value?
That is why when it came to bitcoin, I set out to determine a value based on fundamentals, so that an appropriate price-to-value comparison could be made. The paper I wrote has become one of the most cited works on the topic of cryptocurrency valuation. I later applied that methodology to other cryptocurrencies, as well as other network-based assets (like internet companies and payment systems firms). Since that time I've concluded three things about Litecoin, none of them very good:
Litecoin’s price was manipulated in early 2017
Between march and July of 2017, bitcoin's price went from $4 to $50. The price-to-Metcalfe ratio went from 0 (equilibrium) to 800%. The approximate odds of this happening naturally: 1 in 25 million. In late 2017 it fell victim to the same manipulation that hit bitcoin, and LTC traded at 25 times Metcalfe value by December that year. This means that, whereas most of bitcoin's price has corrected to fundamental value, Litecoin probably has further to drop.
Litecoin’s user base is declining
This next graph shows network (Metcalfe) value per coin. It is based on number of users and number of transactions. Except for a brief period in late 2017, bitcoin continued to add users and transact on the network. After the initial price correction in 2018, Litecoin users continued to leave the network.
Litecoin promised to correct the perceived deficiencies in bitcoin. If the market liked this alternative, it would adopt Litecoin. The verdict is in: it hasn't. Litecoin’s market cap relative to bitcoin has never made it beyond 10%. As of today, it's lower than where it started in 2013. While Litecoin may well be a better designed and implemented cryptocurrency, the graph below shows the power bitcoin has as "first mover." You can also see that it has only broken 5% during periods where the price was suspected of being manipulated, followed by gradual declines in dominance. If Litecoin’s compelling use case is that it is a better, business-friendly bitcoin, its value has yet to materialize in the market. The eventual advent of sovereign cryptos will not help, either.
Bitcoin’s price was artificially inflated in 2011, 2013, and 2017. Though the evidence for this claim received some minor press, it was not carried by the mainstream media and within the crypto community it was derided as Fear, Uncertainty, and Distrust. Having reviewed the math myself I was able to confirm the 2013 and 2017 events using a different mathematical model. The 2013 high price was a 1-in-13,000 year event. The 2017 high price was a 1-in-600 year event. These are not “bubbles” in the traditional sense, though there was some of that as well.
2018 was a year when bitcoin’s price was retreating from its artificially inflated value, and returning to its fundamental value (found by applying Metcalfe’s law, below). People were not retreating from bitcoin, however. For nearly the entire year, Bitcoin added users and transaction activity.
Metcalfe’s law really does explain network pricing, including cryptocurrency networks. Excluding the periods where bitcoin’s price was manipulated, Metcalfe’s law is perhaps the single greatest factor that explains bitcoin’s price. I wrote the first peer-reviewed rigorous paper to validate this relationship with bitcoin. Since then I have done it for many other cryptocurrencies, and track their price to value weekly.
Bitcoin’s price behaved exactly as predicted, and I publicly tweeted about its price trajectory on a regular basis since April 2018:
o From my presentation to CAIA in Houston March7th
o July 6th CAIA Australia:
o From my presentation at DASS October 17th and TMA Houston November 7th:
3. Confirmation bias plays a role. Confirmation bias, also called myside bias, is the tendency to search for, interpret, favor, and recall information in a way that confirms one's preexisting beliefs or hypotheses. People also tend to interpret ambiguous evidence as supporting their existing position. Crypto bulls view positive information as a reason to buy or HODL. They ignore evidence to the contrary, or disparage it as FUD. Crypto haters view any negative information as proof that bitcoin is worth nothing. Evidence to the contrary must have been developed by idiots and therefore cannot be correct. Neither belief system is true, let alone objective.
Summary: Steadily declining premium-to-NAV for Grayscale’s GBTC and ETCG instruments show the premium dissipating fully by the end of this month. The shrinking premium cannot be explained by recent price declines or decrease in adoption rates of cryptocurrency in general. Nor is it well explained by an increase in existing securitized cryptocurrency vehicles. We think the most viable explanation is that a widely available cryptocurrency ETF will be approved in the foreseeable future.
For the past several months, the premium to net asset value of two cryptocurrency trusts – GBTC and ETCG – has been declining. This past week, the premium reached the lowest levels ever in their history.
The Grayscale Bitcoin Investment Trust and Grayscale Ethereum Classic Trust are two (the only two) pure-play publicly available securitized cryptocurrency investments. The trusts hold actual bitcoin or ethereum classic, and each has a discrete number of shares issued. Each GBTC share holds 0.00099395 bitcoin. Each ETCG share holds 0.95776552 ethereum classic.
Investors purchase shares of the trust through Grayscale Investments. There is a two-year lock-up period, after which shares of the trust may be traded over the counter. Grayscale operates several such trusts, but only bitcoin and ethereum classic have publicly available shares.
Investors have been willing to pay premium for these shares, in part because they originally offered the convenience of cryptocurrency access through a traditional securities brokerage account.
That premium has been declining through 2018. ETCG now trades at a discount to net asset value. As of October 12, 2018, that discount was 24%, meaning you could but $1 worth of ETC for just 76 cents!
What is behind this drop in premium?
The first suspected cause is the overall decline in price in cryptocurrency in 2017. As the price falls, fewer investors are interested in cryptocurrency, and so the demand for these trust investments should also decline.
We see that there is a relationship between the premium of GBTC and the 9-month trailing return of bitcoin. This is consistent with a momentum strategy and individual investor behavior, both of which use historical return as a predominant criterion for investment. As performance wanes, the “performance chasers” leave. This effect is also found in ETCG, but with a 4-month trailing return.
While there is definitely a relationship, the R2 statistic tell us that even if this hypothesis were true, past performance only accounts for 10% of the change in GBTC premium and 17% of the change in ETCG premium. What about the remaining 80-90%?
Also, demand for bitcoin and ethereum classic has not been declining over this time, it has been increasing. Network value is an estimate of a cryptocurrency’s equilibrium value. It is calculated using number of active users and transaction counts.
In the case of ETC and BTC, both have increased user counts and transaction counts. So what else could responsible for the decline in premium for GBTC and ETCG?
Increasing Investment Alternatives
2018 has seen an increase in the number of securitized alternatives to Grayscale’s products. An aggressive marketing campaign by BitcoinIRA, Inc. has likely drawn some prospective investors away from these trusts. Bitcoin IRA has charged an up-front fee of 15%, 3% of which is kicked back to investment advisors that implement the BitcoinIRA platform for their clients. When Grayscale’s premiums were high, this might have seemed a cheaper investment option. But with Grayscale trust premiums declining or negative, it does not seem so compelling.
In August, U.S. investors could purchase a Swedish exchange-traded note (ETN) OTC, Bitcoin Tracker One (BITCOIN-XBT.ST). While this investment has the potential to better track the underlying bitcoin price, ETN’s are notoriously illiquid.
This does not explain the decline in ETCG premium, except that the market may be anticipating similar investment vehicles for ETC and other coins.
Finally, a True Cryptocurrency ETF
This brings us to the final possibility, that widely available, pure-play securitized cryptocurrency instruments will be approved soon. We looked at the average premium for GBTC and ETCG since May 2018. This decline has been steady through this period. Interestingly, the average premium for both securities is expected to reach zero in the last week of October.
Why is this important? The SEC has opened the floor to comments either in support or opposition of cryptocurrency ETF products through Oct. 26. Many that the SEC could make an announcement regarding ETF approval shortly thereafter.
Regardless of the specific comments the SEC will make or has made, it is clear that the market is demanding, and fully expecting, cryptocurrency ETFs to be made publicly available in the foreseeable future.
We use Metcalfe’s law to calculate an estimate of a cryptocurrency’s value. The methodology we used is based on a paper by Timothy Peterson.
The formula uses three components:
M: Metcalfe’s number based on number of active accounts. Increases in n increase value.
A: a decay factor based on the number of transactions (t). Higher t means smaller A. Smaller A increases value.
b: inflation caused by the issuance of new coins. Increases in b decrease value.
The general formula is:
We also must take into account periods of extreme pricing, such as those resulting from price manipulation or investor bubbles. Adjusting for these factors, we have developed a valuation model for each of the following cryptocurrencies:
*Bitcoin's model uses 60-day periods.
Explanatory power is the extent to which Cane Island’s network economic model explains a cryptocurrency’s 30-day price change. For example, Cane Island’s model explains 98% of Ethereum’s monthly price changes. Based on these results, as well as the theory behind the model, we believe we have one of the most robust and valuable tools for valuing cryptocurrency ever developed.
Standard error is a degree of accuracy associated with the model. About 68% of observed prices fell within the range predicted by the model. For example, if ZCash’s forecast price is 120, then there is a 68% chance its true price will fall between $80 and $160.
 Peterson, Timothy, Metcalfe's Law as a Model for Bitcoin's Value (January 22, 2018). Alternative Investment Analyst Review, Q2 2018, Vol. 7, No. 2, 9-18.. Available at SSRN: https://ssrn.com/abstract=3078248 or http://dx.doi.org/10.2139/ssrn.3078248
 Two documented examples are Gandal, Neil and Hamrick, JT and Moore, Tyler and Oberman, Tali, Price Manipulation in the Bitcoin Ecosystem (May 2017). CEPR Discussion Paper No. DP12061. Available at SSRN: https://ssrn.com/abstract=2977479 and Griffin, John M. and Shams, Amin, Is Bitcoin Really Un-Tethered? (June 13, 2018). Available at SSRN: https://ssrn.com/abstract=3195066 or http://dx.doi.org/10.2139/ssrn.3195066
The problem with digital currency is that it can be easily copied and counterfeited. The inventor of bitcoin, Satoshi Nakamoto, came up with an ingenious solution to what is known as the “double spend” problem: give everyone who so desires a copy of the transaction ledger. While it is relatively simple to “cook the books” on a single ledger, it is nearly impossible to alter hundreds or thousands of ledgers, especially if those ledgers are dispersed in a variety of locations. So long as there is a means of comparing multiple, distributed ledgers, the system itself provides the trust in ledger integrity.
Also, it is not necessary to compare all ledgers to each other. One need only compare a few ledgers to get a high degree of confidence that the subject ledger is legitimate. With two ledgers one can make one comparison. With four ledgers, it is possible to make six comparison. With six ledgers, it is possible to make 15 comparisons. It takes fewer than 50 ledgers to make a possible 1,000 comparisons! This relationship is known as Metcalfe’s law and is discussed later.
Providing everyone a copy of the transaction ledger poses a major problem. Would you want your bank history in the hands of anyone and everyone? The information would need to be encrypted, and done so in a way that would be virtually impossible to break or hack. To accomplish this, Nakamoto invented the blockchain.
How is this different from a traditional encrypted ledger?
Here is a sample ledger that has been encrypted using traditional means: Although it looks complicated, experts would be able to crack this code in a reasonable time.
With blockchain encryption, there are several layers of encryption, including encryption within encryption. Specifically, the previous encrypted record is included as part of the next record. This “nesting doll” effect makes it impossible to change only one record.
In the example below, we take the encoded transaction and add an encoded portion (called a hash) of the previous transaction. Think of a hash as a sausage grinder. You put two kinds of meat and some spices through the grinder. Once ground, you cannot undo the sausage into its original ingredients. But if you have the recipe, you can make the same sausage and do a taste test to ascertain the recipe is the same. This taste test is called a “proof of work.” A blockchain is like a string of linked sausages, but each new sausage has a bit of the previous sausage in it too.
With a database, this is a set of linked encrypted records:
The actual encryption and blockchain implementation for cryptocurrencies is more robust than this relatively simple example. Most use public key encryption technology. Public keys may be disseminated widely, and private keys which are known only to the owner. This accomplishes two functions: authentication, where the public key verifies that a holder of the paired private key sent the message, and encryption, where only the paired private key holder can decrypt the message encrypted with the public key.
To validate that a transaction is legitimate, one just needs a public key and the previous stored record, which is also public. This approach also permits viewing the transaction ledger amounts, while preserving a degree of privacy (some would say anonymity) about the parties to the transaction.
As blockchains are shared and everyone can see what is on the blockchain, this allows the system to be transparent and as a result trust is established.
Blockchain is simple and cheap to implement. Nakamoto provided his blockchain code in full when Bitcoin was developed. Any first year university computer science student can build a blockchain application.
Blockchain allows the quicker settlement of transactions as it does not require a lengthy process of verification, reconciliation, and clearance because a single version of agreed upon data is already available on a shared ledger between financial organizations. No third party or clearing houses are required in the blockchain model, this can massively eliminate overhead costs in the form of fees that are paid to clearing houses or trusted third parties.
 Satoshi Nakamoto is believed to be a pseudonym. In our research, we have concluded that Nakamoto represents at least two individuals who collaborated on the project, both of whom are now deceased.
 For cryptologists, this was encoded using a Vigenere cypher with a random key. .
I our “Is Cryptocurrency Real?” blog we described the interesting example of how an Italian telephone token (the gettone) behaved like currency, even though it had limited use and no intrinsic value. The gettone analogy is important because Metcalfe’s law, upon which our work is based, originated from a description of telephone networks. The holders of gettoni and the payphones themselves are a network. The value of a gettone to someone in that network, when spending the coin, is one of convenience and the value of the information relayed over the network. If we assume a growing number of pay telephones and callers, and then apply the constraint of a limited number of gettoni, we have mirrored the key elements of cryptocurrency’s supply and demand characteristics.
Network economics is a new field, and so much of the economics around cryptocurrency is foreign to most. The network economy is the emerging economic order within the information society. The name stems from a key attribute−products and services are created and value is added through social networks operating on large or global scales. This is in sharp contrast to industrial-era economies, in which ownership of physical or intellectual property stems from its development by a single enterprise. Examples of network effects can be found in internet websites, mobile phone proliferation, and social media applications like Facebook, Twitter, LinkedIn, SnapChat, and Instagram.
Metcalfe’s Law is regarded as the first and most reliable explanation of the network effect. It is a calculation of the maximum number of connections a network can make, based on the number of nodes (or users). The value of any network, be it currency, internet, telephone, or social, is dependent upon the number of users. Here is an example of the calculation:
"If only one person has a telephone, then the device is obviously quite useless. If two people have telephones, it is possible to make one connection between two people. As the number of people (n) rises in a linear fashion, the number of possible connections increases exponentially. Thus, if 5 people have telephones, letting n in the equation equal 5 will produce 10 possible connections. If n were equal to 10, there would be 45 possible connections. In other words, a doubling of n, or a doubling of the nodes so to speak, increases the number of possible connections by a factor of 4.5. If one then further increases the number n to 12, the number of possible connections increases to 66. Hence, a 20% increase in n produces a 46.67% increase in possible connections."
 Reed E. Hundt, then the chairman of the U.S. Federal Communications Commission, declared that Metcalfe’s Law and Moore’s Law “give us the best foundation for understanding the Internet.” Marc Andreessen, who created the first popular Web browser and went on to co-found Netscape, attributed the rapid development of the Web—for example, the growth in AOL’s subscriber base—to Metcalfe’s Law.
 From the FRMO Corporation Annual Meeting of Shareholders, September 15, 2017.
In 2017, we performed a comparison of Facebook’s growth to that of Bitcoin. Facebook is uniquely suited for comparative study because it shares with Bitcoin many similar circumstances:
Both have characteristics of networks.
Both have observable market values.
Both have observable values for nodes (wallets and accounts).
Both had nearly identical early growth rates, averaging 100% per year (doubling).
Both were banned in China.
Facebook was the subject for proof of Metcalfe’s law in two papers.
At the time, Bitcoin was 8 years into existence; Facebook IPO’d in its 8th year.
Facebook, for its first 8 years, did not have an observable market value. But using data on the number of accounts, we can derive the value from Metcalfe’s law. Likewise, we can derive a value for Bitcoin from a projected growth rate and apply Metcalfe’s law. We can also compare Facebook’s actual market capitalization to the value predicted by Metcalfe’s law.
Both Facebook and Bitcoin doubled the number of network nodes (user accounts and wallets) early on. Since its initial public offering, Facebook has grown its users at a rate of about 16% per year. Using Metcalfe’s law, we can impute a value for Facebook pre-IPO using actual users . Using Facebook’s post-IPO growth rate of 16%, and Metcalfe’s law, we projected a value for Bitcoin going forward.
 These Metcalfe values have been scaled by a coefficient so as to better visually align with the subject price/market capitalization under scrutiny. The underlying Metcalfe value itself is not modified, it is only adjusted by an order of magnitude.
Despite its rapid growth, people could not declare Facebook to be a bubble in its early years because, unlike Bitcoin, its market value was not visible. Had Facebook users been co-owners of the company, they would have experienced Bitcoin-like returns. However, its early growth rate in user accounts of 100% was not sustainable in the long run. Likewise, Bitcoin’s adoption-stage growth rate of 100% is also not sustainable.
We don’t know what Bitcoin’s future annual growth rate will be, but 16% is not unreasonable. If Bitcoin ceased is supernormal growth today, and grew at 16% for the next five years, a reasonable expectation of return based on Metcalfe value would be just over 50% per year. By comparison, Facebook’s post-IPO growth in market cap was 31% per year.
There is one glaring problem with an analysis that only considers number of users: the value of networks cannot go up forever. An incomplete application Metcalfe's law measures only the potential number of contacts, i.e., the technological side of a network. However the utility of a network depends upon the number of nodes actually in contact (transactions) and the quality of information transacted. Metcalfe said that, over time, this utility declines. In other words, the effect of growth in users on value is subject to the Law of Diminishing Marginal Returns.
Practical examples of this degradation in network value include things like spam, excessive advertising, and other bits of false, irrelevant, or uninteresting pieces of information.
Imagine you throw a party. Only a few people show up, and it’s pretty boring. There is some opportunity to interact with the people who are there, but there just isn’t much potential for interaction in general. As more people show up, the party gets better. But then consider a party where too many people show up. It’s too noisy, and people can’t hear each other clearly. Most people are strangers to you, and some behave badly. Drinks are spilling everywhere. It’s so crowded, people can’t move around or dance. This is an example of diminishing marginal returns. We call this the Goldilocks effect: the network cannot be too big or too small, it must be just right to maximize value.
Metcalfe expressed this concept in his formula with a term he called “Affinity,” dimensioned as value-per-user, and labeled as A in his equation. As n goes up, A goes down. This puts a limit on the network effect.
In our experience, most cryptocurrency models do not account for diminishing marginal returns. As a result, they generate values that are too high for cryptocurrency.
To date we have been able to use Metcalfe’s law to explain prices in dozens of cryptocurrencies We believe Metcalfe’s Law explains a large number of economic and financial phenomenon.These include social media applications like Facebook and LinkedIn; payment systems like PayPal and Square; and mobile phone companies like Apple, Samsung, and Google. We also believe that Metcalfe’s law has been a predominant factor in the most successful economies throughout history:
The Roman Empire with its network of roads;
The British Empire with its network of shipping routes; and
The United States with its network of navigable rivers; transcontinental rail, telegraph and telephone; electrical grids; interstate highway; air transport; internet; and communications satellites.
There are two types of money: commodity money and representative money.
Commodity money is traditionally found in gold and silver coins. Gold and silver are suitable for coinage because they do not decay, rot, or rust; were malleable and divisible into smaller parts (such as gold “pieces of eight”); and were rare and not able to be counterfeited. Gold and silver have been used as money for 2,500 years.
The risk with commodity money is debasement. This involves reducing the quantity of gold or silver in a coin without changing its face value. The Roman Empire substantially devalued its currency by debasement. By 300 A.D., the once invincible Roman Denarius was no longer accepted as currency by the public.
The origin of the word “Eurerka!” (Greek: “I found it!”) is attributed to Archimedes, who, while bathing, discovered a method for determining the purity of gold objects by water displacement. This method would be used for centuries to ascertain the validity of commodity money.
Representative money is money that does not have intrinsic value itself, but can be exchanged for things that do have intrinsic value. There are two types of representative money: fiat money and fiduciary money.
Fiat money is money that has a stated value by decree of a government. It is legal currency and only has value because the issuing authority says so. Nearly all money in the world, including coins and banknotes, is fiat money. The U.S. dollar has been pure fiat money for less than 50 years.
The primary problem with fiat money is the risk of inflation, which is caused by issuing more money. Since it costs almost nothing to make fiat money, the temptation to use it to pay the public debt is overwhelming. Modern examples include German Marks post-WWI, and Venezuela’s Bolivar today.
In 1918, a German Reichsmark was worth one gold mark. Five years later, it would take 1 trillion Reichsmarks to exchange for one gold mark.
In 2005, the Venezuelan Bolivar was worth about 40 U.S. cents. In early 2018, one Venezeulan Bolivar was worth about 10 cents. By August 2018, it took almost 2.5 million Bolivars to buy one U.S. dollar.
Fiduciary money has value only because parties engaging in exchange agree on its value. You have been using fiduciary money for most of your life. It includes things like frequent flyer points, transit cards and tokens, even grocery coupons. Cryptocurrency is fiduciary money because the users agree on its value.
A great example of fiduciary money involves a once-popular Italian telephone token−the gettone.
The word gettone (pronounced “jet-TONE-ay”, plural: gettoni) literally means "token." The first Italian telephone token was created in 1927. It was a little disc made of an alloy of copper, nickel and zinc, or bronze. Production stopped in 1983 when it was replaced with magnetic phone cards. It is estimated that 600 million such tokens were produced.
Gettoni were commonly used as and interchangeable with a 50 Lira coin until 1980, when its value (and the cost of a phone call) suddenly doubled to 100 Lira. The doubling occurred again in 1984, to 200 Lira, again a result of a price increase associated with pay-phone calls. It remained at that value until 2001, when the Euro was introduced and the gettone suddenly lost its money-like nature in the Italian economy.
The parallels between the gettone and cryptocurrency are many. Both serve only limited roles as a literal form of currency, and as fiduciary money both are intrinsically worthless. It was not necessary to have a gettone to make a phone call; one could use a phone at the home or office to do that. Likewise, one is not required to use cryptocurrency to make purchases, but can choose to do so for convenience or other reasons. People carried both gettoni and Lira, in the same way people hold cryptocurrency and sovereign fiat money. Like cryptocurrency, the cost to counterfeit a gettone, relative to its value as a medium of exchange, was so high it was ridiculous to even consider it. And, like cryptocurrency, a user could do one of three things: spend it, exchange it for government currency, or hold it.
“Come see! Look at us!” replied the first man. “We’re all getting rich!”
These are some of the most pervasive lies and misrepresentations I have encountered.
Alternative Investment Analyst Review (Jul 10, 2018: Q2 2018 Vol. 7 No. 2) has published our paper. The paper is available for download to CAIA members. https://caia.org/aiar/archive
I'll be speaking at CAIA's Coin Texas on March 7, 2018. "Four Things that Will Change Your Mind about Cryptocurrency."
As early as November 2017, a writer named bitfinex’d posted a serious allegation that the Bitfinex exchange was using the tether digital currency to prop up bitcoin prices, ostensibly to support its own bitcoin exchange business which was faltering.
"Metcalfe's Law as a Model for Bitcoin's Value" will be published in an upcoming issue of AIAR
"METCALFE'S LAW AS A MODEL FOR BITCOIN'S VALUE" was recently listed on SSRN's Top Ten download list for: Banking & Insurance eJournal, Capital Markets: Asset Pricing & Valuation eJournal and Capital Markets: Asset Pricing & Valuation eJournals.