DEUTSCHE BANK is one of the financial industry’s hardest problems. It is not a viable business when judged by any sensible yardstick, because it is unable to make enough profits to generate a remotely adequate return. Its existence does not seem to be in the public interest, since it is dominated by an investment bank that has paid its lucky staff a colossal €40bn ($49bn) over the past decade. The bank’s governance has misfired for ages. On April 8th Deutsche fired John Cryan, its chief executive, in the third regime change in seven years. If the rules of capitalism apply to banks, Deutsche should be wound down. Is that possible?

Deutsche was founded in 1870 to help German companies go abroad. In 1999 it bought Bankers Trust, a Wall Street firm, and went on a long expansion in the investment-banking business. Today it has four elements. A decent asset-management operation called DWS; a profitable payments business that ships money around the world for companies; a mediocre German retail bank that uses the Postbank and Deutsche brands; and a faltering global investment bank that soaks up half of the bank’s capital.

The bank’s profitability has been dismal. Over the past decade its average return on equity (ROE) has been 5%; it was 2% last year. These figures exclude the cost of fines and goodwill write-downs and assume that today’s capital levels were always in place. Shareholders have almost lost hope, valuing the bank at 0.4 times its book value, roughly where American banks were during the 2007-08 crisis. Creditors have not panicked, but have got gloomier this year. They think that Deutsche is riskier than other banks, judged by the cost of insuring its debt against default.

The bank’s troubles reflect weak businesses but also weak governance. Paul Achleitner, the chairman since 2012, has presided over chaos. As a German company, half of the supervisory board are staff representatives, who may have opposed deeper cost cuts. As Deutsche has drifted, its shareholder register has become bizarre. Its largest investors include HNA, a Chinese tourism conglomerate loaded with debt, and funds linked to Qatar’s royal family that lack an established record of stewardship.

Deutsche offers two defences. First, that it has a plan to restore profitability. Not really. To make a passable ROE it needs to generate pre-tax profits of €7bn a year, compared with the €1.5bn it managed last year. Planned cost cuts are not nearly deep enough to close the gap. Deutsche’s weakness is structural. The German retail operation is badly run and has to compete with state- and mutually owned banks that do not care much about profits. The investment bank, meanwhile, has decent market shares in some activities such as currency dealing, but is unable to cover its massive overheads. One way to demonstrate this is to compare it with its big four rivals, Goldman Sachs, and the investment-banking units of JPMorgan Chase, Citigroup and Bank of America. Deutsche’s division is less than half their size in terms of its revenue. Yet it spends a similar sum—$9bn—on non-compensation expenses such as fees and IT.

Deutsche’s second defence is that it is indispensable to Germany. That is debatable. The investment bank books only 5% of its revenue in Germany. Deutsche’s corporate-loan book in the country is only about €40bn, equivalent to 5% of the total debt of all the country’s listed firms, and only twice as big as JPMorgan Chase’s German book. The payments business has a better case, with a quarter of its business from German customers.

Any benefit that Deutsche brings to Germany should be weighed against the potential cost to the government of hosting a barely profitable bank that relies on wholesale funding. During the subprime and euro-zone crises, the benefit to Deutsche of having an implicit government guarantee was worth billions of euros a year. Germany has a new “bail-in regime” that is meant to protect taxpayers and eliminate subsidies by imposing losses on bank bondholders. But it has never been tested in an emergency.

No one would recreate Deutsche. Breaking it up would take several steps. DWS could be spun off or sold. The retail bank could be merged with Commerzbank, another German lender, in a government-blessed deal. The payments business could be sold to the likes of BNP Paribas, a solid euro-zone bank that took on the global payments arm of Royal Bank of Scotland in 2015.

Its investment bank would need to be wound down responsibly over ten years, reflecting the long life of some of its positions. For example, 16% of its €42trn of notional derivatives have a maturity of over five years. Revenues might fall faster than costs, resulting in losses. There would be redundancy costs for 30,000 staff. And regulators would allow the capital trapped in the business to be released only gradually. It would be messy. But the net present value that shareholders would recover from the investment-banking division could be roughly €15bn. While that is only half of its book value, it is more than investors attribute to it today.

The hardest job in finance

The new boss is Christian Sewing, a lifetime employee who has worked across the bank. It is unlikely that he will dissolve the institution he owes his career to. But he should, at a minimum, halve the size of the investment bank, push the authorities for a new supervisory board and attempt to merge the retail operation with Commerzbank. He should find new shareholders—one option would be to persuade a good bank, such as BNP, to buy a stake, in order to provide a credible force on Deutsche’s board.

The danger is that Deutsche just staggers on, cloaked in patriotism and paying only lip service to making an adequate ROE. Germany’s politicians protest that they will never bail out Deutsche but they probably want one big German bank that is active abroad, just as they did back in 1870. That is a slippery slope. The world’s best-run lenders, such as JPMorgan Chase, are safe because they are disciplined enough to crank out high and stable profits. A bank that cannot pay its way is no champion at all.