Millennials with money in the bank are big on saving—but they’re not so eager to invest.

A new report from Merrill Edge, a retail banking division of Bank of America, which surveyed over 1,000 affluent Americans, paints a portrait of a young generation that prides itself on thrift. More than a third (38%) of respondents between the ages of 18 and 34 said they save upwards of half their paychecks. Fifty-four percent said they were cutting back on going out to build their nest egg, and 42% said they were postponing vacations to save.

They’re counting on those savings accounts as the cornerstone of their financial futures. When asked what they can rely on most in 20 years, millennials’ top choice is their savings accounts (66%). The majority of Gen Xers (71%), by contrast, said they count most on their 401(k)s. And boomers rely most on pensions (54%) and Social Security (50%).

The survey focused on affluent millennials, those with either investable assets of $50,000 to $250,000, or those with lesser assets (between $20,000 and $50,000) and earnings of at least $50,000 each year. While that’s definitely not representative of all millennials, the survey does show this subset of millennials place less emphasis on investing not because they don’t have funds—but because they don’t want to.

Those millennials who do invest tend to channel their money to big-tech stocks. According to TD Ameritrade, the most popular millennial investments are Apple, Facebook, Amazon, Tesla, and Netflix. (Millennials also favor companies they know, like Snapchat and Twitter.) The problem is that these companies are volatile investments—not companies with a steady stream of dividends.

Millennials’ do-it-yourself, self-sufficient attitude might come at cost. While socking away a substantial chunk of your paycheck is more financially prudent than spending it all, interest rates on savings accounts have been near zero since the global financial crisis. The S&P 500, meanwhile, has risen 188% since 2009.

The irony is that many Boomers and Gen Xers think of millennials as irresponsible. But millennials’ financial habits suggest they may be the most financially conservative group of all.