Since the heady days of late 2017 and January of this year, cryptocurrencies have gone into retreat. Bitcoin, the best-known example, is now worth just a third of its value at its peak.

But there remain plenty of true believers in digital currencies. They point out that prices are still well above where they were in 2016. And interest from institutional investors is still strong enough for analysts to want to make sense of the crypto-phenomenon.

The latest bank to take a shot is Barclays, which devotes a lot more of its “Equity Gilt Study 2018” to the impact of technological change on finance and the economy than it does to either equities or gilts. Its report describes crypto-technology as “a solution still seeking a problem”.

It identifies four challenges in particular. The first is trust. In most countries, consumers and businesses have faith in the currencies issued by the government.

The second is sovereignty: the potential for tax avoidance and loss of financial control means that neither governments nor central banks will be keen to see private cryptocurrencies take off.

A third challenge is privacy. Although they can be used pseudonymously, cryptocurrencies are less reliably anonymous than cash since the blockchain that lies behind them records all transactions. If a pseudonym is cracked, the user’s purchase history is revealed. A fourth relates to the ability to undo a transaction in cases of error or fraud — blockchain transactions are hard to reverse.

On top of all these problems is the fact that existing alternatives seem to work perfectly well. It is easy to make payments and transfer money in an instant.

So what is the appeal of digital newcomers? Private cryptocurrencies can be attractive in societies where trust is low, or where governments are unwilling or unable to provide reliable means of exchange — in wartime or during periods of sovereign default, for example. Barclays also suggests that in countries where opportunities to invest are limited, “cryptocurrencies may be one of the few ways to diversify savings out of domestic assets.”

None of these conditions applies in rich countries. But they hold in some emerging markets. There could also be demand in the developed world from criminals (although they now strongly favor cash). By making generous assumptions about the size of these low-trust and criminal markets, Barclays comes up with a maximum total value for all cryptocurrencies of $660 billion to $780 billion. That is roughly where they were priced at the beginning of 2018.

Maximum value is not the same as fair value. Surveys indicate that most people who buy bitcoin are doing so as an investment. Just 8 percent of Americans who hold bitcoin do so for purchases or payments. That suggests the main motive for buying cryptocurrencies is speculation, which also explains their spectacular recent rise and fall, as with so many bubbles before them, from tulips to dot-com stocks.

Speculative bubbles are hard to model — how to find a rational way to assess irrationality? But Barclays uses the ingenious parallel of an infectious disease. A bubble starts with a small number of asset owners (the “infected”). New buyers are drawn in (or catch the bug) because they witness price increases and fear they will miss out. A large share of the population is immune and will never succumb.

Buyers use a combination of the current price and an extrapolation of the recent increase in price to estimate their expected target value. The faster the price rises, the wilder investors’ hopes and the more the infection spreads. Eventually the market runs out of potential participants and the price rise slows. Once it starts to fall, holders lose hope of big gains and start to sell. The epidemic dies out.

The Barclays model fits the history of the bitcoin price pretty well. And it suggests that the long-term outlook for the value of cryptocurrencies is bleak. After all, plenty of people will have bought in the past few months, when enthusiasm was at its height. Some will have taken extra risk to buy the currency, via spread betting or other types of gambling. Instead of the riches they expected, they will be nursing losses. Some will be keen to sell their holdings. But new buyers will be harder to tempt now that cryptocurrencies no longer look like a one-way bet.

All of this is good news. Perhaps the blockchain will turn out to be useful for other purposes — for example, recording property transactions. But it has been hard to think about such potential innovations when all the attention was focused on an ever-rising price.

The crypto-fever has finally broken.