I recently read someone suggesting this, and it seemed like an interesting idea. Borrowing at a low tax-deductible rate on one’s equity line of credit, to invest in tax free municipal bonds or bond funds, which, after tax, would offer a higher return. One problem, the tax code doesn’t permit this.
From IRS Pub 936, page 4:
Mortgage proceeds invested in tax-exempt securities. You cannot deduct the home mortgage interest on grandfathered debt or home equity debt if you used the proceeds of the mortgage to buy securities or certificates that produce tax-free income.
So, an interesting idea, but not one permitted by the IRS.