http://media.pimco.com/Documents/PIMCO_Quantitative_Research...
However, that paper only looked at the correlation between the S&P500 and long-term treasuries. A well diversified portfolio should have a mix of bonds including commercial bonds.
The disclaimer in the paper points this out: Bonds are represented by long treasuries (Ibbston) which should not be interpreted as a full sample representative of the bond market. Different asset class proxies will have different results.
The data that I've seen on stock-bond correlation shows a pretty consistent negative correlation over the 1927-2010 time period. It's not perfect, I admit, but it serves you well when you're trying to minimize risk.
Municipal bonds are not really derivatives, there is no underlying asset that backs it except for the repayment history from the borrowing entity. If I buy a muni bond slated for an affluent county in New Hampshire to build a new high school then my risk is considerably lower than buying a security where you are dependent on a group of individuals with unknown repayment ability actually completing the terms of their loan (MBS). They are completely different animals
As far as municipal defaults, sure it happens. But very infrequently. Even with piling up liabilities municipal entities generally are able to pay on their bonds even if it means issuing more bonds because if they default, all their liquidity dries up.