Asset management firms exist, among other reasons, to watch over other people’s money. But these days they increasingly have reason to watch their own. Redemptions, withdrawals and market depreciation have caused a sharp drop in assets under management — and profits from fees based on those assets.

"Expenses are at 2008 levels, but revenues are more like 2001 to 2003," the last great bear market, observes Chandresh Iyer, New York–based head of global custody and investment administration services at Citigroup.

Confronted with tighter margins and looking for ways to cut costs, an increasing number of money management firms are outsourcing ...