Incorporation of Tax Considerations Into the Computation of Duration

Abstract

In this paper, the immunization process is extended to protect after-tax income, and the duration indices for after-tax immunization are derived. Selection of the appropriate index depends on individual investor differences in tax regulations. Attention is focused on the mutually exclusive decisions to amortize or not to amortize premia or discounts. I. The ProblemThe process of immunization has received considerable attention in the finance literature. The literature is remiss, however, in focusing attention on the protection of pre-tax income. In this paper, the immunization process is adapted to protect after-tax income, with consideration given to individual investor differences in tax regulations.The immunization process requires the use of duration indices. Two indices are derived to reflect the mutually exclusive tax regulations confronting the investor. One index reflects the investor's decision to amortize any premium or discount for tax purposes as a result of purchasing the bond at a price different from face value. The second index reflects the decision of the investor not to amortize these premia or discounts. II. The AnalysisAt time t = 0, the investor is assumed to acquire an asset which yields the payment stream c(t), a positive cash flow continuously paid until maturity T. The investor is subject to an interest income tax rate, Yl, and a capital gain income tax rate, Y2. The value of the asset can be determined by the investor from the required after-tax holding period yields, h (O,t), where h(O,t) is the investor's after-tax growth rate on a (certain) investment held from°to t. The investor's planning period is of length m < T.Uncertainty arises from the possibility that the holding period yield structure, h(O,t), may have a single random shift immediately after the acquisition of the asset. Such a shift would produce two opposite effects. The first is the uncertainty in the value of the asset at any time prior to maturity. The second is the uncertainty in the after-tax yield at which the intermediate cash flows are reinvested.Immunization is defined by the following procedure: To insulate an investment from this single random disturbance to holding period yields, the investor selects the cash flowc(t) so that the after-tax portfolio value at m is at least as great as the after-tax portfolio value derived from purchasing an instrument unaffected by holding period yield changes (a discount bond).

Macaulay’s theory of duration: 80-year thematic bibliometric review of the literature

“…Negative cash flow is a case which arises sometimes due to tax adjustments and called after-tax duration strategies. The impact of tax adjustment was also addressed by Hessel and Huffman (1981,1981a) who opine that ignoring tax adjustment leads to erroneous duration.…”