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To thrive in the digital age, big banks need a two-pronged approach that spans the traditional and the new: a broad physical branch network that caters to Baby Boomers and a robust online (and mobile) presence for Generation X and Millennials. Sure, financial technology—or “fintech”—disrupters will pick their spots and target specific channels such as fat credit card processing fees. But the zealot’s view that “banks are screwed and just don’t know it” is wrong: Challengers will face a stiff hurdles to become bona fide banks. And if you want to mold the financial colossus of the future, don’t even think about using today’s banks as your model––emulate the best customer service of the superstar companies in industries as diverse as retailing and ride-hailing.

Those are a few of the strategic insights that Citigroup CEO Michael Corbat shared last week at Brainstorm Finance, Fortune‘s inaugural finance conference, held in the oceanside hamlet of Montauk, N.Y. Fortune executive editor Adam Lashinsky interviewed the banking executive in the closing session of the conference; here are what I’ll call Corbat’s Big Five: the trends and best practices that he views as guiding the future of financial services.

A big consumer franchise is essential, and Citi is belatedly building one.

Citi has long been handicapped versus Bank of America, J.P. Morgan and Wells Fargo because of its small consumer footprint. Citi missed out on most of the merger mania that started in the 1980s while its Big Three rivals feasted; its key failure in creating a national presence was losing Wachovia to Wells Fargo during the financial crisis. Giant branch networks are extremely valuable because they’re a magnet for super-low cost checking deposits that banks can lend at, even in today’s low rate environment, for lucrative loans, especially on credit card balances.

Corbat wants Citi to start catching up. The plan: Recruit customers who already do business with the bank. “We have a bank today with 700 branches that are predominantly located in six cities,” he said in Montauk. “Compare that to Chase, Wells, or B of A that have branch counts in the thousands.” But Citi does operate a national consumer franchise, he added: credit cards. “Today, 28 million people carry the Citicard, so we know what you spend on and what your bank is, and you probably get American Airline miles or other affinity awards from Citi.” But fewer than 10% of those plastic customers bank with Citi.

That’s a fat target for Corbat, who’s using digital marketing to show credit card customers how they could could, for example, reap richer rewards by shifting their banking to Citi. Corbat says the initiative started just six months ago and remains a pilot, but adoption rates are so high that in the first quarter, Citi attracted $1 billion in deposits from new customers while barely tapping the reservoir of credit card holders who now bank elsewhere.

Bank branches aren’t dead; they’re the cornerstone for success.

Lashinsky asked Corbat to weigh the assertion that there are two kinds of banks, “the ones that know they’re screwed, and the ones that don’t know they’re screwed.”

“You’re screwed if you’re in denial,” Corbat responded. “We’re absolutely not in denial. The next chapter is being written as we speak, and it’s digitally led.”

Still, the executive defended the traditional banking feature most frequently attacked by the fintech crowd: branches. “My kids are 26 and 30 and they’re saying all the time, ‘Dad, branches, get rid of them!'” Corbat said. But that kind of disruption would fatally undermine the big banks’ profitability, he argued. Branches serve baby boomers, the cohort that currently controls most of America’s wealth. “The Millennials are coming and they will dictate the future,” he said, “but the vast majority of the profitability of banking today is driven by the worldwide baby boom era.”

Banking has a delicate balance to strike: Running ‘old’ and ‘new’ banks under one big tent.

According to Corbat, “You have to provide two [customer] experiences at the same time: the truly digital experience where they open their phone to look at their balance or use Zelle [to transfer money], but they also like having their branch and a person to speak to.”

That dynamic forces financial institutions to run effectively two banks—”one that meets the needs of those who want a truly digital experience,” he said, “and an analog bank.” Shuttering the physical part of the business and playing fully into a fintech future means “we’d lose a significant amount of our bank customers,” he added.

Corbat pointed out that the ATM, first commercialized by Citi in 1977, didn’t eliminate (or even reduce) the legions of bank branches, as many financial futurists predicted at the time. “We have 60,000 ATMs today, but the first year the branch count in America actually declined [over that entire period] was last year,” he said.

Yes, branches will play a declining role moving forward, Corbat acknowledged. But the decline will be slower than fintech zealots believe. Yet sticking to the status quo will prove fatal, Corbat said. The financial institutions that best foresee and navigate the shift to digital without losing high net worth boomers will be the winners. “I’m not prepared to lock all the branch doors,” he said, “but there will be a point where the nature of physical presence and branches will probably change materially.”

Unbundling services will be a feature of the war between banking challengers and incumbents.

Corbat believes fintech challengers will target select products that have long been exclusively supplied by banks. But that’s not the same thing as becoming full-fledged banks, he said. “What you’ve got going on in banking is dis-aggregation of certain channels like payments,” he said. For a retail giant like Amazon, hammering down the cost of processing credit card payments—fees that come out of the retailer’s pocket—is a natural goal. “Take [credit card fees] on $150 billion in sales—2% when everyone swipes or uses the card,” he said. “You run the math on that. I’m sure [Amazon] would like to get in there and figure out a way to dis-intermediate that and save that.”

Fintech challengers to mainstream banks will succeed in bringing greater speed and efficiency, not to mention lower costs, to areas such as retail payments and cross-border money transfers. But what happens when a fintech company wants to combine a wide range of services to directly challenge incumbents? “The trick is, you dis-aggregate to create value, and then re-aggregate—and as you re-aggregate, the world changes,” he said. “Because in order to take deposits [and lend], you need to be a licensed institution. That’s the rubicon that people need to decide if they want to cross.” Corbat noted that the industry is currently in the midst of the dis-aggregation or unbundling phase as the challengers attack incumbents piece by piece. It’s impossible to predict what the look and feel of a direct fintech challenge to an incumbent bank, he said.

The big news story during the conference? An announcement that a consortium led by marquee players from Facebook to Visa are backing a new global cryptocurrency called Libra. Asked if Citi had been asked to join the group, Corbat said that “Facebook did not approach us or to my knowledge any of the other banks.” Though Corbat said he’s a “true believer” in cryptocurrencies and their underlying blockchain technology, Citi can’t enter the cryptocurrency realm because of regulation.

“The challenge with cryptocurrencies is the opaqueness as to the sources of the money,” he said, noting that regulated institutions must rise to anti-money laundering standards and the Bank Secrecy Act of 1970. “It would be outside our ability to take or send those monies on behalf [of people who hold them.]”

Being the best bank is necessary, but not sufficient, to survive the disruption that awaits the finance industry.

“With all due respect to the great banks or great fintechs,” Corbat said, there’s no use in showing up to work and striving to be best in class—that is, being as good as the best banks. The class has changed. “We need to match the best-in-life experience, because that’s the expectation of people today,” he said. “People don’t look at things and say, ‘From a bank experience, that’s great!’ They look at their Amazon experience, their Uber experience, that are best in life, that reduce friction time money and hassle.”

Like his big-bank CEO peers, Corbat faces one of the toughest challenges in American capitalism: maintaining a highly profitable legacy model (that would undermine profits if abandoned) while simultaneously anticipating the needs of a new generation of customers. For Citi’s part, investors aren’t optimistic: It now carries a puny price-to-earnings multiple of just 10, meaning markets think that its currently strong earnings per share will actually drop in the future.

If Corbat can reverse those dour expectations, Citi will go on a roll. Onstage at Fortune Brainstorm Finance, it was clear that he plans to hold onto tradition and the profits it generates without remaining in the status quo. It’s a flexible, forward-looking strategy. The question is whether those skills will be enough versus fierce competition.