The largest exchange-traded fund tracking the $3.7 trillion municipal-bond market is having the biggest rebound since 2008 after falling to the lowest price in two years.

The $3.4 billion iShares S&P National AMT-Free Municipal Bond Fund, called MUB, jumped 3.5 percent in the last two trading sessions to $104.87 at 2 p.m. in New York, the biggest two-day increase since October 2008, data compiled by Bloomberg show.

The price change reflects yields on 10-year benchmark state and local bonds stabilizing after surging to the highest levels since April 2011, Bloomberg data show. They were at 2.95 percent at 2 p.m. in New York today, little changed from yesterday.

Investors should buy municipal securities for their relative value and tax-free benefit, David Kotok, chief investment officer at Sarasota, Florida-based Cumberland Advisors, said in a report released today.

“We see no more attractive alternatives,” Kotok said in the report. “We are taking advantage of this very opportunistic time.”

While ETFs are similar to mutual funds that track an index of equities, bonds or commodities, they are bought and sold on stock exchanges and their prices may rise or fall more than the value of the assets they hold.

For investors in the highest tax bracket, 39.6 percent, the 2.96 percent benchmark yield for 10-year munis is equivalent to a taxable return of 4.89 percent, Bloomberg data show. The yield on U.S. Treasurys maturing in 10 years fell to 2.54 percent at 1:30 p.m. in New York, according to Bloomberg data.

Highest Ratio

The ratio of the yield of munis to those on Treasurys is about 116 percent, the highest since July 2012, Bloomberg data show. The higher the ratio, the cheaper local debt is when compared with equivalent U.S. government securities.

MUB’s price plummeted to $101.35 June 24, the lowest since April 2011. It sold at a record 2.86 percent discount to the value of its assets June 21 after Federal Reserve Chairman Ben S. Bernanke said the central bank may moderate purchases of federal and mortgage debt in 2013 and end them around mid-2014 if the economy performs as forecast.

Improving investor sentiment toward munis today was also reflected in a $1.3 billion sale of general-obligation debt by Illinois. The lowest-rated U.S. state was able to reduce yields by 0.10 percentage points, to 4.46 percent, on an uninsured portion of the issue maturing in July 2023, Bloomberg data show.