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1 November 1981 Financial Analysts Journal Volume 37, Issue 6

Volatility in Tax-Exempt Bonds: A Theoretical Model

  1. Martin L. Leibowitz, PhD

The duration concept provides an estimate of what the price movement in a bond of a specific maturity, coupon and starting yield will be for each basis point of yield change. However, duration essentially relates a bond’s price changes to changes in its gross yield. In many cases, a tax-exempt bond’s gross yield will not correspond to its net yield. For instance, tax-exempt par bonds will be subject to capital gains taxes when they move into the discount range as a result of adverse yield moves.

The “net yield factor”—the ratio of a bond’s gross yield movement to the corresponding movement in net yields—indicates how much a specific outstanding bond’s gross yield must increase above the movement in market rates in order to give the purchaser an after-tax yield equal to the current market yield on tax-exempts. The net yield factor will exceed one when a tax-exempt bond sells at a discount. Tax-exempts selling at a premium will have a factor of one; i.e., their gross yields will equal their net yields.

The net yield factor for adverse yield moves significantly increases the effective volatility of tax-exempt bonds, although its significance declines with maturity, since the capital gain has little impact in a present value sense at the longer maturities. Combining the effects of the net yield factor and duration shows that price volatility will be greater for adverse yield moves than for positive yield moves, and that the discrepancy will be greatest in the intermediate and shorter maturities.

Finally, one can relate movements in tax-exempt yields to movements in taxable yields via the “ratio model,” which states that tax-exempt yields at a given maturity represent some fraction of taxable (Treasury) yields—historically 75 and 54 per cent for 30-year and one-year maturities, respectively. Integrating this ratio model with duration and the net yield factor results in a general volatility model that will approximate the percentage price change in a given tax-exempt bond per change in general interest rates as represented by the Treasury yield curve.

The general volatility model indicates that tax-exempt par bonds will exhibit two general volatility factors, depending on the direction of yield moves. In the case of favorable yield moves, tax-exempts will exhibit less upside price volatility than corresponding Treasury bonds, especially at shorter maturities. For adverse yield moves, however, tax-exempt bonds across all maturities will experience virtually the same price volatility as corresponding Treasuries.

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