Duration provides an accurate volatility measure for tax-exempt bonds selling above par, but it understates the volatility of discount municipals—especially those in the short to intermediate range. This is because discount municipal bonds are valued on the basis of after-tax yield relationships. A change in a bond’s after-tax yield will induce a larger yield to maturity adjustment and, in turn, a greater amount of volatility than would be suggested by applying duration to a given market move.

A modification of the duration concept leads to a “municipal volatility factor” calculation that captures this after-tax volatility effect for discount municipals. Par bonds will have two sets of volatility factors, since if yields decline they will trade on a yield to maturity basis as they move to premium, but if yields rise the subsequent discount instruments will be valued on the basis of their after-tax yields.

Volatility factors provide an invaluable measure of the risk inherent in individual bonds and in portfolio constructions. They illustrate, for example, the error inherent in using the average maturity of a portfolio as its risk measure. Three different portfolios having average maturities of 15 years—the first consisting of 15-year bonds, the second using equal weightings of 10- and 20-year bonds and the third using one-year and 30-year instruments—will have widely different volatilities. The downside volatility factor will be 9.59 for the first portfolio, but only 5.86 for the third, barbell portfolio.

A review of various volatility factors indicates that a combination of premium and discount bonds is likely to provide a better total return than a par bond regardless of the direction of market moves. Given a 50 basis point yield move over a six-month period, a 10-year, seven per cent par bond will return seven per cent if yields decline and a negative 0.85 per cent if yields increase. On the other hand, a combination of an eight per cent bond purchased to yield seven per cent and a six per cent bond purchased to yield 7.32 per cent (seven per cent after taxes) will return 7.69 per cent if yields decline and a negative 0.29 per cent if yields increase.