The Crypto Impossibility Theorem

by David Irish | July 27, 2021

an edited extract from a Strategy Report published by Peter Berezin, Chief Global Strategist at BCA Research1 on 21 May 2021

The Crypto Impossibility Theorem states that a cryptocurrency will be viable only if it offers a higher return than equities. As we discuss below, the assumption that cryptos can generate a return in excess of equities is almost certain to be false since it would require that cryptocurrency holdings rise more quickly than income in perpetuity. This implies that the value that investors currently attach to cryptos will turn out to be illusory.

To see the theorem in action, recall that money serves three functions: As a unit of account, as a medium of exchange, and as a store of value. It is doubtful that anyone seriously thinks that the price tag on a box of cereal will ever be displayed in units of Bitcoin, ether, or any of the various dog coins currently in vogue. Thus, we can scratch “unit of account” off the list of possible crypto uses.

What about medium of exchange? One can imagine a scenario where the prices of goods and services are still listed in dollars, but one may transfer the equivalent in cryptocurrencies to purchase them. However, this raises an obvious question: Why would anyone choose to hold a cryptocurrency if wages and prices are denominated in fiat currencies such as US dollars or euros? The only possible answer is that people must see cryptocurrencies as fulfilling the third function of money, namely being a store of value.

Would people be willing to hold cryptocurrencies if their prices generally moved sideways? It is doubtful. Cryptocurrencies are risky. Cryptocurrency accounts are not subject to deposit insurance. Crypto prices are also extremely volatile. During the pandemic, the S&P 500 fell by 34%, but the price of Bitcoin sank by an even greater 53%. Other cryptocurrencies fared even worse. In contrast, the trade-weighted US dollar strengthened by about 4% while gold prices only fell marginally (see Chart 1). Thus, to incentivize people to hold cryptos, the prospective capital gain has to be large enough to offset the inherent volatility in owning these currencies.

Chart 1
Cryptocurrencies Fared Badly During Last Year’s Equity Sell-Off

This is where the Crypto Impossibility Theorem comes in. Unlike dividend-paying stocks, cryptocurrencies do not provide any income to their holders. Thus, even if cryptos were just as risky as stocks, the price of cryptos would still need to rise more than the price of stocks in order to ensure that investors remain indifferent between the two asset classes. In practice, as the experience of the pandemic demonstrates, cryptos are even riskier than stocks. Thus, the expected return on cryptos has to exceed the expected increase in stock prices by more than the dividend yield.

The problem for crypto holders is that this is not mathematically possible. Even if one controls for the rise in price-earnings multiples over time, equity returns have generally exceeded nominal GDP growth (see Table 1). Hence, if cryptos need to offer superior returns to equities, and if the return on equities is at least equal to nominal GDP growth, then the market capitalization of cryptocurrencies will not only end up rising faster than for stocks, it will rise faster than aggregate national income. In a digital world where people need ever-less money to facilitate transactions, there is no good reason to expect this to happen.

Table 1
Equity Returns And GDP Growth

A Fashion Choice

Crypto-optimists might argue that the required rate of return to holding cryptos will decline as the market matures. This is wishful thinking. Equities derive their value from the fundamentals of a company’s business. In contrast, cryptocurrencies have no intrinsic value. Their value is whatever others are willing to pay for them.

Not only does this make cryptocurrencies inherently more risky than equities, it also makes them highly susceptible to fashion trends. It is not surprising that many upstart cryptocurrencies have crafted ties with celebrities and other “influencers.” The whole point is to get enough people interested in a cryptocurrency to generate a feedback loop of wider adoption, thus allowing the currency’s early backers to cash out.

In this sense, cryptocurrencies are even more vulnerable to affinity scams than other assets such as precious metals. While apocalyptic warnings of “currency debasement” have long been used to sell bullion, at least with gold and silver, you truly do get something that is in short supply. In the case of cryptocurrencies, while the supply of any individual cryptocurrency may be limited, the overall supply is unbounded. This means that the average price of each currency is likely to rise much less than the aggregate value of all cryptocurrencies, making the entire asset class even less viable over time.


The drubbing that cryptocurrencies have received over the past two weeks is just a taste of things to come.

The Crypto Impossibility Theorem will prevent cryptocurrencies from ever being stable stores of value.

In the meantime, an ebbing of input price inflation will take some of the wind out of the sails from the argument that cryptos are an indispensable hedge against the “inevitable” debasement of fiat monies.

Cryptos are like sharks; they need to move forward or they will sink. Back when they were unknown to most investors, a speculative case could have been made for buying cryptos. However, that case vanished earlier this year when the aggregate value of cryptocurrencies briefly surpassed the entire stock of US dollars in circulation (Chart 2). Even with the recent correction, there are 17 cryptocurrencies with market capitalizations above $10 billion (Table 3).

Chart 2
Aggregate Value Of Cryptos Briefly Surpassed The Entire Stock Of US Dollars In Circulation

Table 2
Close To 20 Cryptos Have A Market Cap In Excess Of US$10bn

What will the ongoing crypto collapse mean for the broader investment landscape? In the near term, the pain in crypto markets could drag down other speculative assets such as tech stocks. In the long term, diminished investor interest in cryptos will benefit the stock market, as investor attention focuses back on equities.

For the broader economy, the impact of a crypto bear market will be limited. The banking system has very little exposure to cryptos. There will be a modest adverse wealth effect from falling crypto prices. However, the inability of a few laser-eyed crypto traders to buy their Lambos is hardly going to matter much against the backdrop of strong stimulus-fueled consumption growth in the US and a number of other economies.


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