The third quarter's stock market volatility took its toll in terms of market share on mutual fund companies that didn't offer equity portfolios already well-established in the brokerage community, a new study shows.

For several companies, even as they raked in new money, market share remained flat or declined during the three months ended Sept. 30, according to a study by Financial Research Corp., Chicago. Many of these companies, including big names like Federated Investors and Dreyfus Corp., are considered to be bond fund shops, niche players with aggressive portfolios, or sector funds.

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