SSgA also has launched 109 new ETFs since 2011, including one recently with DoubleLine's star bond manager Jeff Gundlach, and boosted efforts to produce more research to help advisors educate their clients about tax management, wealth transfer and raising financially independent children.

To get on track with advisors, the bank poached a number of senior executives from rivals such as Morgan Stanley, UBS Wealth Management and BlackRock Inc. Its recent hire of Ronald O'Hanley, the former asset management chief at Fidelity Investments, underscores the importance of penetrating the retail market where advisors hold growing sway.

State Street also slashed fees on 41 of its SPDR ETFs earlier this year, joining a years-long price war that has entrenched Vanguard and BlackRock.

Despite being a pioneer in the ETFs, State Street is still best known as the world's No. 2 custody bank. It safeguards $28 trillion in assets, and that's where it gets most of its revenue and profit. In 2014, State Street's investment management unit, which includes ETFs, generated $1.3 billion in revenue, or about 13 percent of the company's total revenue. Custody and asset servicing generated nearly all of the rest.

Ben Johnson, an analyst with Morningstar in Chicago, said State Street's challenge is cultural.

For State Street, "asset management is a secondary business," he said. "They've been geared, they've been tooled, and they've been built to deal with institutional investors and not necessarily toward a more advisor audience."

Meredith Rice, senior director at Cogent, said advisors give State Street high marks for having a broad range of ETF products that are easily traded. "The only thing with State Street has been their institutional focus," Rice said. "Their rivals are more focused on retail."

Reliance on institutional investors––hedge funds, pension funds, asset managers and Wall Street banks that are the bread and butter of State Street's custody business but who sometimes use ETFs for hedging and shorting markets––also has added a volatile dimension to State Street's ETF business.

In January, for example, investors withdrew $28 billion from State Street's big SPDR S&P 500 ETF, or 13 percent of assets, according to Lipper Inc data. By contrast, BlackRock's comparable iShares fund held about steady and Vanguard's S&P 500 ETF had net deposits of $1.5 billion.

"Honestly, I don't lose sleep anymore about the big swings in outflows in SPY," Ross said. "There is not a competitor of mine in the ETF space who wouldn't want SPY in their business."

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