And interestingly, the largest improvement in awareness among consumers comes from those with the least money, frequently much of it in cash.

Says the report, “Consumers with under $100,000 in investable assets increased product ownership awareness by 15 percentage points from 63 percent to 78 percent in the last two years as compared to a nearly flat awareness level for consumers with over $100,000 during the same time.”

Many of those owning mutual funds or ETFs aren't sure who their asset managers are, and 20 percent can't name any asset managers of funds they're sure they own.

Many can cite an average of three fund families in which they're sure they have holdings, and five fund families they think they might own shares in—but they're not sure about that last.

Hearts & Wallets created a shareholder awareness score to measure the ratio of shareholders who are definitely sure of ownership. And tracking consumer certainty by fund family, Fidelity and Vanguard come out the winners. Over the past three years, five companies have seen the most improvement in the shareholder awareness score: Wells Fargo Funds, iShares (BlackRock), Vanguard, Fidelity and American Century.

Numerous “well-respected” asset managers only manage a shareholder awareness score of less than a third, and according to the report, “Some asset managers may have made a strategic decision to not spend money on direct communications with shareholders, and some firms may feel they can't be responsible for general consumer confusion.”

But that could be a mistake. “Helping consumers become more aware of product ownership can give them more control of their financial future, and really, increase their overall financial literacy,” Laura Varas, CEO and founder of Hearts & Wallets, is quoted saying. Varas adds, “Firms have a wonderful opportunity to stand out among commoditized offerings that are only differentiated on price. Consumers tell us that are really confused not only about products, but also about the firms that create them.”

Failure to develop closer bonds with their shareholders could cost firms clients, since not all shareholders are alike. Says Varas, “Out of the thousands of investment products offered, consumers remember ones that solve their problems. Asset managers can build awareness for products and their firms, especially with insights on unique shareholder attributes in comparison to competitors. Firms can also raise visibility through consumer products approaches, including offering online comparisons of products by feature and price, and providing engaging communications. Being a shareholder establishes a special relationship.”