One company saddled with that baggage was American Express. Amex’s then-chief executive acknowledged that its 2015 financial performance was “disappointing.” The stock’s forward price-to-earnings ratio fell to under 10 times in early 2016, an unusually low level for the company.

Fast forward to 2024. Amex shares are now zooming, up over 25% this year. The stock has returned an annualized 17% since the start of 2020, beating the S&P 500’s annualized return by almost 4 percentage points. It is now trading at over 17 times forward earnings. And at its investor day presentation in April, Amex’s current chief executive Stephen Squeri reiterated the company’s belief that it can deliver 10%-plus annual revenue growth over the long term.

Younger card members have been one driving force. Over three-quarters of new accounts acquired in 2023 for U.S. consumer premium Gold and Platinum cards were Gen Z or millennial-aged, according to company figures. It appears that many of Amex’s young consumers are going straight to cards such as the $695-annual-fee U.S. consumer Platinum, rather than starting with no-fee cards and working their way up.

It may be the case that a cohort of millennials, some of whom started their financial lives around the time of the 2008-09 financial crisis, did feel some reluctance about credit cards. But Gen Z members who have entered early adulthood may not suffer the same hangup: TransUnion found in a recent study that 84% of Gen Z consumers in the study had at least one credit card as of the fourth quarter of 2023 at ages 22 to 24. This was “significantly higher” than the 61% of millennials at the same ages a decade ago, TransUnion found.

Roughly half of U.S. families headed by someone under age 35 held credit-card balances back in 2001, according to the Federal Reserve’s Survey of Consumer Finances. It was about the same percentage in the latest survey in 2022. In TransUnion’s study, more early-adult members of Gen Z were 60 days or more late with debt payments than Millenials at a similar age 10 years prior. That is partly reflective of current conditions across credit. For all borrowers, 2023 consumer delinquency rates are higher across many credit products than in 2013, according to TransUnion data.

Of course, the younger people coming to Amex for premium cards aren’t necessarily representative of their entire generation. The company’s data suggest its U.S. Gen Z and millennial consumers have higher incomes and credit scores than the same groups across the industry.

Many are likely coming for the rewards of spending. Over the last several years, including during the pandemic when travel briefly lost its allure, Amex has been “refreshing” its card rewards and perks. This has included credits for a range of nontravel activities such as streaming video services and food delivery.

The annual fees don’t appear to be as much of a barrier, either. “They’ve been raised on subscription fees,” Howard Grosfield, Amex’s president of U.S. Consumer Services, says of younger card members. “They do the mental math of…am I getting value in excess of the subscription fee?”

Amex has called out benefits aimed at experiences, and in particular dining, as a notable driver. Millennial and Gen Z U.S. consumers on average use their cards at restaurants over 70% more often than older spenders, Amex says. From 2019, when Amex acquired online reservation platform Resy, to 2023, its U.S. consumer dining spending grew about 80% faster than U.S. dining spending overall, as measured by retail sales data.

Via Resy, Amex offers features like what it calls “exclusive reservations” or “priority notify” for available tables. Perhaps the appeal of this is no surprise: Gen Z is a generation that is coming of age at a time when waiting lists for a choice restaurant might be a thousand names long.

Among investors several years ago, “the big concern was, ‘Will [Amex] be able to pivot their brand to focus on the young?’ ” says Craig Maurer, co-director of equity research at Financial Technology Partners. “Well, they have been able to continually refresh the value proposition to appeal to younger consumers.”

Naturally, satisfying demand for perks doesn’t come free. Amex has reported rising costs of cardmember rewards and services, or what it terms variable customer engagement expenses, as a percentage of revenue. These costs were about 37% of revenue prepandemic, then 41% in 2023. This also reflects a shift in Amex’s spending mix toward more premium consumer cards. The company says it currently expects this expense line to grow faster than revenue.

Gen Z and millennial cardholders may be the most engaged with rewards, but they can also be the pickiest, according to a recent survey study of over 3,000 U.S. consumers from market research provider PYMNTS Intelligence. In that study, 41% of Gen Z respondents reported discontent with their credit-card rewards programs—well above what it was for other generations.

Plus, the more important rewards become to a customer, the more may be at stake if they don’t work out as anticipated. The Consumer Financial Protection Bureau has reported that in 2023 it received over 70% more consumer complaints about credit-card rewards than prepandemic, with issues such as problems redeeming benefits or having benefits devalued.

Competition for these young, engaged and affluent spenders—who will be lucrative customers for years to come—will surely be fierce. Notably, Robinhood Markets recently launched its own Gold Card, a 3% cash-back card available to subscribers to its Gold program. It has even offered cards actually made of gold for users who make a certain number of referrals.

To justify ongoing investment in enticing young power spenders, spending growth needs to keep up. Amex can find other cost efficiencies. It can continue to keep credit losses low, and expand other ways to monetize card members, like by offering more lending. Amex believes it can deliver midteens earnings-per-share growth to accompany that 10%-plus revenue growth.

With the stock already trading around record highs, expanding profitability while still keeping young customers spending may be key to also rewarding shareholders.

Write to Telis Demos at Telis.Demos@wsj.com