Long-Term Bond Returns under Duration Targeting

Although most bond portfolios maintain a relatively stable duration over time and are thus implicitly or explicitly “duration targeted,” the distinctive nature of duration targeting (DT) is underappreciated. The authors’ theoretical DT model demonstrates that over multi-year horizons, annualized DT returns converge back to the starting yield, regardless of the rate path. For example, for almost all six-year holding periods since 1985, Barclays bond index returns have converged to within 1% of the starting yield.The standard analyses of bond behavior (and common intuitions about it) are based on either short-term returns or some form of a hold-to-maturity model. However, the vast majority of bond portfolios actually follow a process known as duration targeting (DT), which maintains a relatively stable duration over time. A DT approach is central to the rebalancing procedures of most active and passive institutional bond funds, bond mutual funds, and the fixed-income components of multi-asset funds. Even laddered bond portfolios with illiquid holdings implicitly function in a DT mode.Despite this widespread presence of DT, there remains an underappreciation of the very distinctive and rather surprising nature of long-term DT returns. This situation is particularly striking given the persistence of historically low interest rates and corresponding concerns about rising rates. In fact, most of the existing literature on DT investing has focused on either short-term price sensitivity or longer-term liability management through immunization or liability-driven investments.In our study, in order to gain deeper insight into the DT process, we began with a simplified model of a flat yield curve, no default risk, annual rebalancing, and an investment in a zero-coupon bond. We also tested our results against 25–30 years of bond index return data. In our simplified model, the duration target is equal to the bond maturity (i.e., the Macaulay duration) and the year-end price factor is equal to the initial duration reduced by one year. This year-end effect stands in contrast to the instantaneous price sensitivity, which is measured by the modified duration.We found that along a trendline path from the initial yield to the terminal yield, the average return depends on only the annual yield change and the duration target. At the outset, annual price losses dominate the incremental accruals. However, because the annual price losses remain constant along the trendline whereas the annual accrual rate rises with each year’s higher level of yields, the cumulative accruals ultimately are sufficiently above the starting yield to fully offset the cumulative price loss. The incremental return is then reduced to zero, and the annualized return just equals the starting yield for an investment horizon that is one year less than twice the duration target.For the more general case of random rate paths, we partitioned the total return volatility into two distinct, independent components: trendline-based volatility and tracking error relative to trendline paths. In contrast to trendline volatility, tracking error increases gradually with the investment horizon and tends to stabilize within three years of the “convergence horizon.” For a typical DT fund with a five-year duration, the total return volatility declines over time until flattening out at around 1% by the sixth year. These findings suggest that a DT fund with a five-year target should have returns that converge, by the sixth year, to within 1% of the starting yield—regardless of the intervening rate paths!We first tested the theoretical DT models by using the 1977–2011 history of constant-maturity US Treasury yields to simulate returns for both point and ladder portfolios with five-year duration targets. We also used a more market-related test based on several bond indices that have had relatively stable durations over a recent span of years and, in effect, have functioned as DT funds. For example, the Barclays U.S. Aggregate Government/Credit Index has maintained a duration of 5.4 years since 1985, and the Barclays U.S. Credit Index duration has remained close to 6.1 years since 1981. In all cases, these tests confirmed that the starting yield does indeed estimate the six-year returns, with standard deviations close to the theoretical level of 1%.