Appendix: Path Return and Volatility
In this Appendix, we derive formulas for total return volatility, trendline volatility, and trendline tracking error. Under the assumption of a random walk model of interest rates, an initial investment is made in a D-year zero-coupon bond with nominal yield, Y0. Although we do not do so, we note that the model can easily be adjusted to accommodate rate drift.
We assume a duration-targeting (DT) strategy in which the same duration is maintained throughout the holding period by repricing the bond at the end of each year and rolling the proceeds into a new D-year bond.
For zero-coupon bonds, the time to maturity D is the same as the Macaulay duration. After one year, the aged bond duration is D − 1. The return ...