Creating a synthetic after-tax zero-coupon bond using US Treasury STRIP bonds: implications for the true after-tax spot rate

Abstract

For an individual or company that is subject to taxes, we develop a method that uses laddered Separate Trading of Registered Interest and Principal (STRIP) bonds to determine the value (and composition) of a portfolio that replicates a risk-free after-tax cash flow that will occur on a single future date. In contrast to previous approaches, our method does not require rebalancing or short sales. In addition, we show that the standard after-tax risk-free spot rate, defined as the after-tax yield on a US Treasury STRIP bond, is correct only for a flat-term structure. Using our method, we provide a true measure of the after-tax risk-free spot rate that applies to any term structure.

Notes

¹ In 1985, the US Treasury instituted the Separate Trading of Registered Interest and Principal of Securities (STRIPS) programme, which allows bond dealers to create zero-coupon securities by ‘stripping’ and selling separately the individual coupon and principal payments. These individual zero-coupon instruments are called STRIP bonds.

² See US Department of the Treasury, Internal Revenue Service (2010).

³ See Daves and Ehrhardt (1993) and the US Treasury's website at http://www.treasurydirect.gov/instit/marketables/strips/strips.htm for more information on STRIP bonds.

⁴ It is relatively simple to incorporate a deterministic time-varying tax rate, but the investor still will be exposed to risk due to unanticipated changes in the tax rate. These may result from changes in the statutory rate or, more likely, from varying levels of pre-tax income which put the investor into different tax brackets from year-to-year.

⁵ Barber and Copper (2006) extend the concept of immunization to a continuous time interest rate processes and show that immunization can guarantee a minimum loss, but not an exact match of the portfolio value with the liability value.

⁶ For a survey of methods used by forensic economists, see Brookshire (2006).

⁷ Note that this restriction eliminates municipal bonds. Munis have the desirable property of being tax-exempt, but they also have default risk. In addition, many municipal bonds are also relatively illiquid. Therefore, we exclude municipal bonds from our analyses.

⁸ The analysis is easily extended to the case of quarterly tax payments.

⁹ We replicated our analysis and incorporated a 4 basis-point commission, which caused our calculated values for the true after-tax risk-free rates to increase only by about 2 basis points. Even for long-term liabilities, the additional dollar cost to create the laddering portfolio was less than 0.6% of the laddered portfolio's cost.

¹⁰ We assume that the term structure does not change and that the tax rates shown in Table 1 do not change. See the Appendix for a detailed description of the calculations.

¹¹ Again, we assume that the term structure does not change and that the tax rates shown in Table 2 do not change. See the Appendix for a detailed description of the calculations.

¹² The upward and downward sloping term structures each have a 30-year pre-tax spot rate of 6.5% for the sake of comparability.

¹³ This expected price might be determined by a particular theory of the term structure. For example, the investor might assume that the term structure is not expected to change. Alternatively, the investor might assume that the pure expectations hypothesis holds, or that the term structure is determined by the Cox et al. (1985) model. Our derivation of the number of remaining bonds is applicable for any term structure model.

¹⁴ For mathematical convenience, we assume that STRIPs are divisible and that partial units in a STRIP may be sold. Because treasury bonds and notes now have redemption values in multiples of $100 rather than $1000, our assumption of divisibility is very reasonable.

¹⁵ For clarity of exposition, we ignore transactions costs. These can be easily included without changing the basic logic or effectiveness of the approach.

¹⁶ The logic of this example does not change if different term structure models are chosen.

¹⁷ A proof of this result is available from the authors.

¹⁸ Note that the required number of bonds to be purchased is a function of both τ _OI and τ _CG. Thus, the implied after-tax yield from this strategy also is a function of the combination of ordinary income and capital gains tax rates.