BANKS the world over are wrestling with low interest rates. Nowhere have they grappled for longer than in Japan. Although the Bank of Japan (BoJ) introduced negative rates only in January, almost 20 months after the European Central Bank, its rates have been ultra-low for years: they first hit zero in 1999. In its long battle against deflation, it pioneered "quantitative easing"—buying vast amounts of government bonds—which depresses longer-term rates and thus banks' lending margins. Since September the BoJ has also aimed to keep the ten-year bond yield at around nought, while holding its deposit rate at -0.1%.

Banks have had some relief lately: since Donald Trump's election in November, the yield curve has steepened slightly—and share prices have leapt—as American interest rates have risen and the yen has tumbled. But on December 20th the BoJ kept policy on hold.

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For Japan's biggest lenders, negative rates are "an irritant, not a catastrophe", says Brian Waterhouse of CLSA, a broker. Every tenth of a percentage point below zero, he estimates, shaves 5% from the earnings of the three "megabanks": Mitsubishi UFJ Financial Group (MUFG), Mizuho Financial Group and Sumitomo Mitsui Financial Group. For smaller fry, sub-zero rates are more painful.

With rates ultra-low and the economy becalmed, pickings from lending to Japanese companies have been thin. The three megabanks reported spreads from domestic lending to corporate customers of only around 0.5 percentage points in the six months to September. Cheap money has not stirred up demand for credit: Ryoji Yoshizawa of S&P Global Ratings notes that Japanese companies have been net savers since the late 1990s.

However, domestic lending accounts for only one-sixth of the megabanks' profits, against more than three-fifths at the 100-odd regional banks, calculates Katsunori Tanaka of Goldman Sachs. Some regionals have moved into consumer lending, a field that was dominated by (at times shady) specialists until caps on interest rates and the size of loans got in the way.

Home and away

Big lenders are chasing non-interest income, too. Mizuho, for one, styles itself as a "financial-services consulting group", cross-selling investment products to bank customers. "The quantity of the Japanese market is shrinking. However, the quality is changing positively," says Koji Fujiwara, the chief strategy officer. He expects, for example, that to pay for care in old age people will shift money from deposits—over half of households' financial assets—into higher-yielding investment funds. Through tax breaks, the government is trying to give share-buying a shove. If a falling yen helps keep inflation above nil, real interest rates will be negative, sharpening the incentive.

The megabanks have also made a determined push abroad. Since 2012 the share of foreign loans has risen from 19% to 33%, according to Moody's. This brings higher returns but has also meant more risk, for instance from lending to American oil producers. And although they have foreign-currency deposits—notably, in America MUFG owns Union Bank, which has around $80bn in the vaults—their stable funding does not match their lending.

True, the gap has narrowed as the pace of foreign lending has slowed and the banks have built up deposits. But it remains; and the cost of bridging it with short-term borrowing has climbed. This reflects both tighter American money markets and a breakdown of "covered interest parity", the principle that the difference between spot and forward exchange rates should mirror the interest-rate differential between the currencies. "If shocks happen in the financial markets," says Shinobu Nakagawa, a BoJ official, "they may face difficulty in funding."

Regionals' prospects are bleaker. Under the BoJ's policy banks are sure to be less profitable, says Isao Kubota, chairman of Nishi-Nippon Financial Holdings, in Fukuoka on the south-western island of Kyushu. But he avers that close ties to corporate clients remain a big advantage. He adds that life is harder for the smaller co-operative banks, and insurers and pension funds, with lots of long-term liabilities.

Mr Kubota spies danger in the government's encouragement of savers to switch to shares: if it succeeds, banks' funding will become "much more unpredictable". Hence Nishi-Nippon's enthusiasm for its own securities arm, set up in 2010; it is now involved in an asset-management venture with six of its peers. Through another subsidiary, Kyushu Card, it has branched into credit cards and consumer loans