After years of ratcheting back trading operations in favor of more stable businesses, Morgan Stanley is quietly plotting a comeback.

The Wall Street firm is pushing for more fixed-income trading business, where it lost billions of dollars during the crisis and historically suffered from bad timing. Now, the firm hopes adding market share in the division, which trades bonds, swaps, currencies and other debt securities, could help Chairman and Chief Executive James Gorman hit long-held profitability targets. But the effort could also turn off analysts and investors who have lauded the firm's recent embrace of less-risky activities.

Since Morgan Stanley nearly collapsed in late 2008, the firm has diverged from chief rival Goldman Sachs Group Inc., which largely has stuck to its knitting in trading. Morgan Stanley's shift toward wealth management over sometimes volatile trading businesses has won plaudits from regulators and shareholders—its stock price has outperformed Goldman's in the last two years despite Morgan Stanley's lagging profitability.

With U.S. interest rates expected to rise and Morgan Stanley's own credit rating boosted two notches last month by Moody's Investors Service, Mr. Gorman and his top lieutenants see an opportunity to boost the firm's share of the some $100 billion in annual Wall Street revenue tied to fixed-income trading, people familiar with the matter said.

In recent weeks, Morgan Stanley has been soliciting more fixed-income business and pitching more trading ideas to clients like BlackRock Inc., the giant fund-management firm, the people said. The firm believes it could generate several billion dollars in additional revenue over time in its debt-trading arm, which produced $3.8 billion in 2014.

Morgan Stanley thinks it can rack up more business trading bonds and other debt securities without enlarging its balance sheet. The firm expects to benefit from the ratings upgrade as well as the gradual retreats from some of its peers. Adding business from existing clients—especially large money managers—can help speed up the pace of securities cycling in and out of the firm's trading inventories, the people said, while keeping a lid on the balance sheet. Some analysts are skeptical.

A decision to dive deeper into bond trading is potentially significant as big banks deal with regulators who have judged certain trading businesses harshly since the crisis, often requiring that banks set aside more capital to guard against adverse bets.

Fixed-income trading is one of Wall Street's most volatile—and potentially lucrative—businesses. While it has been out of favor in recent years, volatility in parts of the bond market and exits by other players have prompted some analysts to wonder whether remaining Wall Street firms could see an expanded role in coming years.

Morgan Stanley's past only underlines the fleeting nature of many strategic decisions on Wall Street; banks have repeatedly withdrawn from certain activities only to recommit when the business booms—and rivals that once ceded market share can roar back with the right investments.

The upgrade from Moody's also potentially makes the firm a more attractive trading partner, because clients see a higher-rated firm as less likely to default on an agreement.

"The firm's strategy in fixed income remains unchanged, as does our strategy for the firm. The metric we are focused on continues to be return on equity," a Morgan Stanley spokesman said in a statement.

Shedding assets from Morgan Stanley's fixed-income business has been a central plank in Mr. Gorman's turnaround plan. A smaller balance sheet has freed up capital the firm has begun to return to shareholders through stock buybacks and bigger dividends, which in turn has helped lift returns. Risk-weighted assets within the bond-trading arm slipped below $180 billion this year, meeting Mr. Gorman's goal. Those assets totaled $370 billion in 2011.

The renewed push in fixed income comes as the firm begins what its executives hope is a final ascent toward a long-elusive goal: producing an annual return on equity of more than 10%. Morgan Stanley hit that target in the first quarter when its fixed-income business churned out a $1.9 billion quarter. It was the division's best performance since the first quarter of 2012—the last full period before Moody's moved to downgrade the firm's ratings.

Rivals and former Morgan Stanley executives have questioned privately how any Wall Street firm could produce double-digit returns consistently without a bigger fixed-income trading division.

The firm has identified the rates business, which traditionally generates more revenue than other parts of fixed income, as having the biggest potential, the people said. Rates traders buy and sell government bonds and interest-rate swaps, or derivatives in which one investor trades one stream of interest payments for another, allowing the buyer to place a bet on or hedge against a rate's direction.

Morgan Stanley's debt-trading business has seesawed violently several times over the past decade, both in profits and in the firm's commitment.

The firm had dialed up its riskier trading activities right before the financial crisis, with disastrous results. Then, when the debt markets sprung to life in 2009, leading to massive profits at rivals such as Goldman Sachs and J.P. Morgan Chase & Co., Morgan Stanley's traders sat on the sidelines. The firm reversed course again the following year, but the buildout ended abruptly amid a flurry of new regulations, slumping volumes and a 2012 ratings downgrade.

As recently as last year, the firm was eliminating jobs from its rates and foreign-exchange trading desks. While the fixed-income division's head count has been flat of late, the firm has been hiring selectively.

Debt markets have flashed signs of emerging from a long stretch of meager client activity. In addition, Morgan Stanley sees an opening as traditional European fixed-income heavyweights such as Barclays PLC and Deutsche Bank AG have signaled they would shrink their assets.

"We're also seeing, I would say, significant disruption to some of the European business models," Morgan Stanley finance chief Jonathan Pruzan said during an investor conference this month. "So I think, as people redefine who they want to be and what they are, there's going to be some market share up for grabs, so we do think that that's going to be a longer-term opportunity."

Moody's Investors Service raised its debt rating on Morgan Stanley by two notches in late May, reversing a 2012 downgrade that had revived concerns about the Wall Street firm's prospects in a postfinancial crisis era of smaller bank profits and more regulation.

Wall Street firms' ratings matter to many large investors, especially those that manage money for pension funds. If a fund manager enters a derivatives contract with a bank—or any counterparty—under duress, it risks not being able to collect on its side of the trade.

At the June 9 investor presentation, Mr. Pruzan said the firm "had gotten some good feedback from clients" related to the two-notch Moody's upgrade. Executives at BlackRock, the world's biggest money manager, have recently indicated they want to direct more fixed-income trading business Morgan Stanley's way, people familiar with the matter said.

Write to Justin Baer at justin.baer@wsj.com

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