The Key Rate Durations of Municipal Bonds

Abstract

Effective duration, calculated by parallel shifts of the yield curve, is the standard measure of portfolio-based interest rate risk. Key rate durations, obtained by shifting individual key rates, describe how the risk is distributed along the term structure. Ordinarily the sum of the key rate durations equals the effective duration. However, in the case of tax-exempt municipal bonds the sum and the effective duration may differ. The reason is that the prices of discount munis are tax-affected, and the applicable tax rate depends on the size of the discount. The authors’ result has ramifications for the hedging of muni portfolios, and for the measurement of interest rate risk under the recently introduced SEC N-Port regulation.

TOPICS: Project finance, statistical methods, credit risk management

Key Findings

• • The tax effect on the price of a discount muni depends on the size of the discount (applicable tax rate around 20% if de minimis, 40% if not).

• • Because bumping individual key rates has smaller effects on price than shifting the entire yield curve, the applicable tax rates may differ.

• • Consequently key rate durations for munis may not add up to effective duration, creating challenges for portfolio hedging and SEC risk reporting.