"There is always a bull market somewhere and right now it's in government bonds," the firm wrote in a note to clients.
In the U.S., Morgan Stanley believes the benchmark 10-year Treasury note yield will tumble all the way to the 1.55 percent to 1.75 percent range, compared with the current level hovering around 2 percent. Bond prices move inversely to yields.
Globally, the firm sees opportunities in euro zone and Japanese bonds, thanks to continuing monetary policy easing from the European Central Bank and Bank of Japan.
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"We believe the idea of additional easing by the ECB and BoJ will underpin the recent bid for duration over the coming months," Morgan Stanley said. "We expect the idea of additional sovereign bond buying by the ECB and BoJ to also buy time for duration longs to hold on."
The firm's strategists point to possible near-term risks by temporary loosening in financial conditions. For that reason, it recommends as a trade selling short duration ahead of Wednesday's Fed meeting, then covering afterward.
"We think the front end of the yield curve is vulnerable to a less dovish January FOMC statement than priced into the markets," Morgan Stanley wrote. "The market is pricing in a 1-in-4 chance of a March rate hike. In addition, the market is only pricing in one full rate hike in the year ahead. We think the consensus message from the FOMC will read closer to a 1-in-2 probability of a rate hike in March."
In addition to liking government bonds in the U.S., Japan and the euro zone, the firm also likes U.K. gilts as well as New Zealand and Canadian bonds.
Investors poured $5.1 billion into government bond funds last week, the biggest inflow in a year, according to Bank of America Merrill Lynch.
That came as exchange-traded funds tracking the sector have offered strong performance. The best so far have been the Vanguard Long-Term Government Bond, iShares 20+ Year Government Bond and SPDR Barclays Long Term Treasury, all of which have gained just north of 3 percent. They have easily outperformed the S&P 500, which is down about 10 percent.