Bond Ladders and Rolling Yield Convergence

Most investment-grade bond portfolios have stable durations and can be regarded as “duration targeted” (DT). For DT portfolios, multiyear returns converge to the starting rolling yield if the yield curve undergoes a sequence of strictly parallel shifts. The theoretical convergence horizon is one year less than twice the duration target. The laddered portfolios favored by private investors are essentially DT, and surprisingly, their convergence return coincides with the starting yield of the ladder’s “top-rung” bond.This article addresses the expected performance of “duration-targeted” (DT) bond portfolios—those with a more or less stable duration—when the curvature of the starting yield curve is maintained but parallel curve shifts alter the level of the curve. According to historical data, most actively or passively managed diversified investment-grade bond funds and bond indexes have rather stable durations over long time periods. Thus, these portfolios undergo some form of duration-targeting process that maintains duration stability through either explicit or implicit portfolio rebalancing. For example, in the case of year-end rebalancing, the aged portfolio is repriced and bond positions are adjusted to insure that the portfolio duration is the same as it was at the start of the year. This rebalancing process stands in stark contrast to a buy-and-hold strategy in which there is no rebalancing and the duration simply declines over time.In this study, we extend previous results on flat yield curves to curves with a persistent curvature. A key finding is that when a shaped yield curve is subject to sequential “trendline” parallel shifts of equal magnitude, the theoretical convergence horizon is precisely the same as in the flat yield curve case—that is, one year less than twice the duration target. An important implication of this return convergence is that multiyear return volatility is likely to be much less than the volatility anticipated in traditional mean–variance models.In contrast to flat curves, with shaped curves, a DT portfolio converges not back to its initial yield but, rather, to its starting “rolling yield”—the hypothetical one-year return that would result as each bond ages to a shorter-maturity point along an unchanging yield curve. When the yield curve has a positive slope, the year-end yield of each bond will always be lower than its starting yield, so the rolling yield will incorporate a positive price gain from the roll down. Thus, in such (admittedly nonequilibrium) situations, the rolling yield for any bond will always be greater than the starting yield.In a general portfolio context, a positive curve slope implies that the portfolio’s average rolling yield will always be greater than the portfolio’s average yield. When such general DT portfolios are subject to parallel shifts, it will be this greater rolling yield that serves as the expected return over the convergence horizon.The rolling yield concept plays a key role in the important special case of bond ladders. A ladder is a bond portfolio that comprises roughly equal-weighted bond positions with maturities spaced one year apart. Laddered portfolios are widely used by private investors, especially in the municipal bond market. Although bond ladders are not typically viewed as DT portfolios, they are, in fact, a special case of duration targeting. The DT structure results because over time, the proceeds of maturing bonds are reinvested in such a way as to maintain the equal-weighted laddered structure—a process that at least roughly preserves the initial duration, which is approximately half the ladder’s length.Because bond ladders are implicitly DT, their multiyear returns under parallel shifts should converge toward the average rolling yield of the constituent bonds. One of our most surprising findings is that for any starting yield curve shape, the average rolling yield for any laddered portfolio corresponds to the starting yield of its “top-rung” bond. Therefore, with parallel shifts of any magnitude over the convergence horizon, a ladder’s annualized return should move back toward this starting top-rung yield.To empirically test these theoretical rolling yield results, we focused on the municipal bond market because its yield curves generally have a more persistently positive slope than taxable yield curves have. By using the Barclays Municipal Bond Index as a broadly diversified proxy portfolio, we found strong evidence that in markets with consistently positive yield curves, general DT portfolios do, in fact, converge back to their starting rolling yields rather than to their lower average yields. And for the special case of laddered portfolios, additional tests with historical municipal yield curves also confirm that a ladder’s annualized return converges back to its starting top-rung yield rather than to its lower average yield.