Franklin Templeton, the No. 5 mutual fund company in the United States by assets, did not respond to a request for comment.

In its most recent quarter, Franklin Templeton's assets fell 6 percent from the year prior, while operating revenue fell by 11 percent.

For the wider industry, Morgan Stanley analysts' base case is fee compression of 10 percent to 15 percent and more than 25 percent in its bear case.

"We foresee a multi-year adjustment process that will affect the earnings and shares of publicly traded traditional asset managers," Morgan Stanley analyst Michael Cyprys said in a separate, recent research note. He added that fee cuts and product re-engineering could drive some companies to go private "and usher in an era of large-scale consolidation – not without risks."

Consolidation is already happening. Janus Capital Group Inc agreed in October to sell itself to UK-based Henderson Group Plc for $2.6 billion. Anglo-South African financial services firm Old Mutual this month sold a 25 percent stake in its U.S. fund management arm to China's HNA for $446 million.

Years Of Fee Pressure

Actively managed U.S. stock funds have not reported a year of net inflows since 2005, according to Morningstar.

Over the past 12 months alone, fund companies including household names such as American Funds, Fidelity Investments, Franklin Templeton and T. Rowe Price Group Inc have endured withdrawals totaling $131.8 billion, the research service said.

By comparison, index-fund pioneer Vanguard Group attracted $342 billion in the United States, much of it into its passively managed index funds and exchange-traded funds.

A look at industry fees helps explain why. Despite a 15 percent drop in U.S. equity fund fees in the decade ending in 2015, mutual fund managers on average still charge $131 for every $10,000 they manage, according to the Investment Company Institute, a trade group.