The Standard & Poor’s 500 Index rally isn’t over and the gauge could jump 50 percent more by 2020 as the U.S. economic recovery heads for a record winning streak, according to Morgan Stanley.

A slower though sustained period of growth could help the equity benchmark gauge peak near 3,000, according to a report dated today. The world’s largest economy, which began recovering in July 2009, may continue growing for five years or more, making it the longest period of expansion, Morgan Stanley said. The S&P 500 closed at a record 2003.37 last week.

Three rounds of stimulus have helped spur growth in the world’s largest economy. The S&P 500 almost tripled from its low in March 2009, sending the value of U.S. shares to a record $23.9 trillion on Aug. 26. A report showed last week that gross domestic product rose in the second quarter more than forecast, pushed by the biggest gain in U.S. business investment in more than two years.

“Equities should benefit from a scenario where the probability of a cycle peak remains low for some time,” Adam Parker, chief U.S. equity strategist at Morgan Stanley, and economist Ellen Zentner wrote in the note. “As the prolonged expansion becomes more visible, we’d expect a materially higher U.S. stock market.”

The S&P 500 rallied 3.8 percent in August, the most since February, as investors bet central banks will continue to underpin global economies. Minutes from the Federal Reserve’s July meeting released last month reinforced the central bank’s commitment to supporting the recovery even as some policy makers indicated a willingness to raise rates sooner than anticipated.

The U.S. economy will grow 2 percent this year and 3 percent next, which would be the most since 2005, according to the median forecast in a Bloomberg News survey.

If profits for S&P 500 companies increase about 6 percent every year from 2015 to 2020, earnings will be close to $170 a share, Morgan Stanley said. Should the equity index trade at 17 times its companies’ reported earnings, its peak level could near 3,000, the bank said. The gauge currently trades at a multiple of 18 times, data compiled by Bloomberg show.

Earnings for S&P 500 companies will climb 8.1 percent in 2014, according to the average analyst estimate compiled by Bloomberg as of Aug. 29. Profits will grow 11 percent in both 2015 and 2016, the projections show.