Millennials are wary of entering the stock market. New data from the latest Merrill Edge Report shows that, when asked what they'd be able to rely on in 20 years, millennials' top response was their savings account, according to 66 percent of respondents. When Merrill Edge asked older generations the same question, the majority of Gen-Xers (71 percent) said they'd be able to rely on their 401(k). The top response among boomers (54 percent) was their pension. "In stark contrast to older generations who are relying on outside sources for their future financial security, millennials are looking to their self-created savings years down the line," Aron Levine, head or Merrill Edge at Bank of America, writes in the report. "Millennials place even greater trust in their own stewardship than they do in their personal relationships with their significant other and friends."

The report shows that young people today are taking a "do-it-yourself" approach to finance and investing, choosing to rely primarily on their own savings in place of vehicles like a 401(k) or IRA. Though many millennials do utilize these tools as well, there's still an underlying feeling that their own efforts are more dependable. The biggest reason for this shift in trust is the climate many millennials grew up in. "This is really reflective of coming of age in the 10 years since the financial crisis and what they saw of the recession," Levine tells CNBC Make It. Throughout the crisis, millennials "saw their parents and grandparents suffer and struggle with either Social Security not being there or being there and not being enough," Levine says. Because of this, millennials have developed the mindset that they "need to be relying on themselves and their own ability to save and invest." Even when young people do invest, they're not taking big risks. According to the report, 85 percent of millennials say they "play it safe" with their day-to-day investments. Forty-six percent of millennials say they're more financially conservative than their parents, and 35 percent say they're more conservative than their grandparents as well.