A historic rout in the bond market this year has resulted in the highest yields on municipal bonds in 15 years—and what looks like an excellent buying opportunity.

At midweek, the muni market, as measured by the Bloomberg Municipal Bond Index, was down 13%, its worst showing in at least 40 years, as the yield has jumped to 4.2% from 1.1%. Long-term bond mutual funds have done even worse, off about 15%.