One in six millennials say they have $100,000 saved up, according to a survey from Bank of America (you can read the whole thing here).

That impressive statistic has set the Internet ablaze with overly generalized headlines like this one from American Banker:

As in, “You thought millennials were lazy people who mooched off their parents, weren’t loyal to their jobs, and saddled with debt. But it’s not like what you thought!”

More realistically, the BofA survey results contain reasons to be both excited and concerned about the situation facing our generation.

Reasons to be optimistic

It’s getting better — for some

The 16 percent of millennials who say they’ve saved $100,000 actually looks better with context. It’s doubled from 2015, when only 8 percent of millennials said they had $100,000.

If you’re reading this and saying, That doesn’t sound like me!, keep this in mind: the survey includes responses from people ages 23-37. It’s a lot more likely that a 37-year-old would have $100,000 than a person in his or her mid-20s.

Millennials faced a tough job market and an equally tough investing climate early in our careers. Plus, skyrocketing student loan debt hit our generation hard. But given time — and some impressive stock market returns in the past 15 months — and our savings seem to be increasing.

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Many have something to fall back on

I’ve written before that an emergency fund is a key milestone to achieving financial peace of mind.

According to the BofA survey, 47 percent of millennials say they have $15,000 saved. (This number is also up; it was 33 percent in 2015.)

This is roughly the amount of what many millennials would need for a six-month emergency fund (more or less, depending on where you live and what your expenses are). It could also be a combination of a starter emergency fund — say, $1,000 in the bank — and some savings in a 401(k).

Most who have savings/budget goals attain them

If you’re a regular reader, you know that budgeting and savings are a big part of this blog.

Sixty-seven percent of people who have a savings goal say they stick to it every month or most months, according to the survey. And 73 percent of those who keep a budget stick to it.

If you have goals — and if you spend a little time each week holding yourself accountable — your chances of success go up dramatically.

You never know if you don’t ask

The stereotype is that millennials are demanding employees. But that seems to be working out OK for us.

People ages 23-37 are more likely than other generations to ask for a raise, according to the survey. And of those who do ask, 80 percent said they received the raise!

So, if you think you’re worth more than what you’re making, be professional, lay out your case, and be firm. You stand a good chance of getting what you want.

Reasons to be concerned

Half of millennials have little to fall back on

It’s looking good for the 47 percent of millennials who have at least $15,000 saved. But what about the other 53 percent?

A single life emergency — being laid off, having a medical emergency, car breakdown, etc. — could leave some of us turning back to our parents for help and others with nowhere to turn. And for those who have nothing saved in a 401(k), they’re losing out on prime years to gain the advantage of compound interest.

To help fix this, The Miser thinks employers should automatically enroll workers in the company 401(k) plan at a rate that gets the full match (workers could still go in and reduce their contributions, of course). And millennials need to focus on socking away enough to build at least a small emergency fund.

We worry a lot

According to the study, 35 percent of millennials say they’re worried that they’re not saving enough money.

Another 24 percent are stressed about their career path. A third of us want to make a career change but worry it’s too late.

And 21 percent are already worried that they won’t have enough saved for retirement, even though our generation has years and the magic of compound interest on our side. With no hope of pensions, little hope of Social Security, and perhaps $2 million or $3 million required to last through a 30-year-long retirement, it’s an understandable fear.

It’s also one you can do something about, by deciding to put a chunk of your paycheck into a retirement account.

Lack of a steady job

Twenty-six percent of millennials say they do contract work or freelancing. While some likely do this by choice, this can’t be the case for everyone (maybe not even a majority of the 26 percent).

No full-time job means no full-time benefits. And that means no health insurance. With health care costs skyrocketing, not having insurance could cost tens of thousands of dollars in a medical emergency.

The verdict

There’s no doubt millennials face challenges that previous generations didn’t face. We don’t have the luxury of putting in our 40 hours a week, having a cottage on a lake, health insurance with $0 copays, and retiring after 25-30 years with a full pension.

So, it’s good to see at least some reasons to be optimistic about our personal finance outlook — even among many reasons for pessimism.