Online banking customers are a third more profitable than traditional bank-based clients, Piyush Gupta, chief executive of Singapore’s biggest bank, DBS, told investors a year ago during a presentation of the bank’s digital strategy. The remark sent DBS shares sharply upwards.

Since launching its mobile phone-based “disrupter” banks in India and Indonesia in the past two years, DBS has signed up more than 2.6m people by using fingerprint recognition to match them against biometric national identity cards.

Such new digital customers generate on average a 27 per cent return on equity for the bank, compared with the 18 per cent return it earns on its traditional branch-based customers.

DBS says it makes S$1,300 (£722) of revenue a year from each of its digital customers, more than double what it makes from traditional customers. Digital customers cost it S$478 each a year for acquisition and back office administrative expenses, compared with costs of S$306 for each traditional customer.

These figures explain why DBS’s shares rose more than 40 per cent last year and are still outperforming almost all major rivals despite losing some steam this year. Its S$61bn market capitalisation is above many European rivals, including Barclays, BBVA and Deutsche Bank.

Few big banks can tell such a compelling story of how they have responded to the rising challenge of digital disruption that is sweeping across their industry.

In Europe alone, there are 1,400 new neo-banks, payment providers and fintechs that have sprung up since 2005, according to research by Accenture. As of 2016 they had managed to make €58bn of annual revenue, equal to between 6 and 7 per cent of the industry’s total.

Adding to the pressure, big technology groups are deepening their financial services sector.

Amazon is providing payment services and loans to merchants on its platform, while Facebook has an electronic money licence in Ireland and its WhatsApp messaging service is building a payments offering in India. Alibaba and Tencent have become dominant operators in China’s $5.5tn payments industry.

“The message is out there that new digital players are in town and the banks are under attack,” says Richard Lumb, head of financial services at Accenture. “What they are scared of is a leakage of customers and that leakage becoming a flood over time.”

Banks are responding in different ways to this digital threat. The Financial Times has spoken to more than a dozen bankers, consultants and fintech executives to analyse how they are doing so. Broadly, they can be grouped into five categories.

1. Digital attackers

Those in this group consider that the best form of defence is attack. Banks with the most advanced digital strategies, like DBS, have launched their own digital banks to enter new markets or defend their patch.

Goldman Sachs launched a consumer digital savings and lending operation two years ago. Named Marcus — after Goldman’s 19th century founder — the new digital operation has accumulated more than $26bn in deposits and lent $3bn to customers, generating over $1bn of new revenue for the Wall Street bank. Marcus recently launched in the UK, its first international expansion, offering the highest interest rate in the country to entice savers.

Dutch bank ING adopted a similar approach when it launched Yolt last year, offering customers a way to collate all their financial information in one place, track their spending and saving and get prompts to save money on utility bills. Yolt has signed up more than 400,000 users in the UK and recently announced plans to expand into France and Italy.

Royal Bank of Scotland chief executive Ross McEwan told the FT that it had six standalone digital units in development. They include one called Bó — from the verb to stay in Danish — which aims to compete with fintechs like Monzo by helping customers manage their money better.

2. Acquisitions

Hampered by the vast cost and complexity of maintaining their old systems, sometimes banks find it easier to buy or invest in a start-up that has built a digital platform from scratch.

One that has pursued this strategy is Spain’s BBVA, acquiring a string of digital upstarts including Simple in the US, Atom Bank in the UK and Holvi in Finland. BBVA has invested $250m in Propel Venture Partners, a standalone venture capital fund to invest in fintechs around the world.

BPCE, the large French mutual bank formed by the merger of Banques Populaires and Caisses d’Epargne, recently followed suit by acquiring Fidor Bank, the online bank with more than 120,000 customers in Germany and the UK.

3. Partnerships

Bank bosses complain loudly of an uneven playing field that allows big technology groups to offer financial services without the burdensome regulation that traditional lenders face. That has not stopped some banks teaming up with Big Tech groups.

One example possibly in the making is the potential partnership between JPMorgan Chase and Amazon, which would bring together the US’s biggest bank and the largest US ecommerce company. The deal would give JPMorgan access to 100m Amazon customers using the Prime service. The partnership might be extended into other areas such as an Amazon-branded checking account.

In Asia, Standard Chartered has teamed up with China’s Alipay to launch a digital remittance service, using blockchain technology to send money across borders quickly and cheaply. The duo has also teamed up with GCash, the mobile payments arm of Globe Telecoms in the Philippines, to allow people to send money between Hong Kong and the Philippines using their mobile phones. The plan is to expand the service to other markets.

4. Diversification

While their core payments and lending businesses may be under pressure from digital competitors, some banks are using new technologies to move into new markets.

Dave McKay, Royal Bank of Canada’s chief executive, recently unveiled a strategy to turn Canada’s biggest bank into a broader “platform” offering diverse services, from registering a start-up company to helping people rent their house on Airbnb.

When its customers are looking to buy or sell a home, RBC offers to research neighbourhoods, move furniture, paint a house and even decide which bins to take out each week.

Other banks, too, are branching out. Barclays offers to store important documents, such as passports and birth certificates, on the cloud for customers. Commonwealth Bank of Australia gives businesses insights into the spending habits of its customers through its Daily IQ tool.

5. ‘If you can’t beat them, join them’

Sometimes banks decide that the threat from digital competition is so great that they just have to amend their business models.

Ana Botín, executive chairman of Spain’s Banco Santander, said it was seeing her son using a rival service in order more quickly and cheaply to transfer money overseas, that persuaded her to make Santander the first international bank to launch a cross-border payments system based on blockchain.

Five years ago, France’s BNP Paribas launched Hello Bank as a standalone pan-European digital bank. Hello Bank now has more than 3m customers, including some gained through the acquisitions of Consorsbank in Germany and Compte-Nickel in France.

That said, launching new services is not easy.

Switzerland’s UBS said in August it was closing its automated online investment service, SmartWealth, to new clients. It had launched the robo advisory service in 2016, as part of a $1bn investment aimed at attracting younger clients and expanding its wealth management service beyond just the seriously rich.

The high price of using the service and a high minimum investment were deemed to have put off potential users, however, and UBS concluded that the “near-term potential” of the service was limited.