Secondary bond market

"A lot of retail investors are still very distracted by the stock market," said Pat Luby, head of municipal strategy at CreditSights.

With nearly $4.5 billion of tax-exempt bonds, a restructuring or bankruptcy would be among the muni market's largest to date.

The status of the war in Iran is confusing, Hennion & Walsh's James Pruskowski said, but high absolute rates are giving the muni market a strong start to June.

Considering the "huge calendar this week," NewSquare Capital's Kim Olsan said, "if we can hold steady, that's probably a good result."

This week will see continued stability, given the recent bumps on deals in the primary market last week and the lack of negative headlines about the war with Iran, said Elaine Brennan, executive director of the public finance department at Roosevelt & Cross.

The muni market is experiencing "some short-term optimism," said Hilltop Securities' Tom Kozlik, but there are still "pressures that could potentially be with us for not just weeks, but months."

Markets grew stronger upon news of the extended ceasfire in Iran, but the reaction was less pronounced than Tuesday's rally.

June redemptions are $44.4 billion. July and August will see $37.7 billion and $38.4 billion returned, respectively, said Pat Luby, head of municipal strategy at CreditSights.

The muni market's gains are likely a continuation of Tuesday, Charles Schwab's Cooper Howard said, but markets could turn sour after personal consumption expenditures data is released Thursday.

Munis and USTs both received a boost from news of a possible peace deal with Iran.

The market has seen a trend of "happy endings to each week, disappointing Mondays," according to James Pruskowski, managing director at Hennion & Walsh.

"We're going to have some weak days, we're going to have some stronger days, maybe they wash out against each other," said Kim Olsan, senior fixed income portfolio manager at NewSquare Capital.

Ajay Thomas, head of public finance at FHN Financial, said the market has been "totally driven" by headlines out of the Middle East this week.

As the war in Iran drags on, fears of inflation and higher oil prices are driving up yields, according to Schwab's Cooper Howard.

Munis cheapened ahead of what may be another volatile week, according to AllianceBernstein's Daryl Clements.

Rate hikes appear to be more realistic following this week's hotter-than-expected consumer price index and producer price index data, said Kevin McGuigan, director at Municipal Market Analytics.

The complicated environment has created different outcomes for different parts of the muni market, Hennion & Walsh's James Pruskowski said.

Although muni valuations became "less compelling" in April from March's highs, Pat Haskell wrote for BlackRock, technical conditions "are likely to provide a degree of support in the months ahead."

Inflation and heavy supply have finally worn on muni yields after a week of stability.

The muni market continued to shrug off volatility in Treasuries, but NewSquare Capital's Kim Olsan said a reaction is building up.