Optimization of the Arbitrage Process in Advance Refunding of Municipal Bonds

States, municipalities, and other regional or local public bodies have the authority to issue debt securities, the interest on which is tax exempt under federal regulations. As a consequence, the interest which these entities must pay on their bonds is usually below the rate on U.S. government securities of identical maturity. Arbitrage bonds--issued by a municipality to take advantage of this differential--are not generally permitted, with the exception of Advance Refunding. Advance Refunding is the process by which the proceeds of a municipal bond issue are invested in Treasury securities and these securities placed in a trust fund to pay when due the principal and interest on debt previously outstanding. To limit the arbitrage profit to the municipality engaging in Advance Refunding, the U.S. government has strictly limited the amount of the new issue which may be invested at a yield rate greater than the rate obtained on the new municipal debt. This article, after discussing the appropriate government regulations, provides a simple example of Advance Refunding and a theoretical analysis of a simple refunding scheme. It then describes a two stage optimization procedure which will maximize the savings to the municipality which chooses to Advance Refund its debt. Results of this new procedure, which first minimizes the amount of Treasury securities and then provides an optimal maturity schedule for the new debt, are compared with actual refundings using other programs.