"Today's affluent women are financially savvy working women, but investing confidence doesn't follow hand-in-hand with increased wealth," said Karen Wimbish, director of Retail Retirement at Wells Fargo. "Through our research, we see that investing confidence seems to be the linchpin to so many other positive behaviors that would provide an opportunity for women to grow their savings and to build a solid foundation in retirement."

More than 40 percent of those surveyed said they do not believe the stock market is the best way to grow savings, but 52 percent do. Thirty-four percent of affluent women say that the stock market is "too risky" for them. In fact, as affluent women have built wealth, 64 percent say they have become more risk-averse.

A whopping 58 percent say they are not interested in learning more about how to invest in the stock market, but 91 percent of respondents said it is important that women be confident in their ability to invest. Only 8 percent of those surveyed labeled themselves extremely confident and 49 percent say they are somewhat confident.

"I find it so interesting nearly all of these women say confidence in investing is very important – they recognize the power of confidence but at the same time, they are ambivalent about their own confidence and a majority is not interested in learning more. These women are in households with very strong resource levels, so the next step is to be totally aware of how the market can help them and to feel in control of their efforts to invest and grow savings for retirement," added Wimbish.

Women who label themselves as confident when it comes to investing are more likely to say the stock market is the best place to grow savings over time. Seventy-three percent of confident married women say either they alone or in conjunction with their spouse make the household investment decisions versus 49 percent of those who describe themselves as not confident in investing.

More than half of affluent women say men were given more of an opportunity to learn about investing than women, while 41 percent say both sexes were given equal opportunity.

Women say that a successful retirement is comprised of having enough money to live the lifestyle they want, being health and spending time with family and friends. Forty percent say that running out of money in retirement scares them and 45 percent of working affluent women say the prospect of living in retirement without a paycheck is something they will "resist as long as possible by working." Women in their 40s say they will resist as long as possible.

The survey was conducted between June 27 and Aug. 4, 2013.