Financial Analysts Journal Volume 70 Number 3 ©2014 CFA Institute
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PERSPECTIVES
Duration Targeting: No Magic for High-Yield Investors Martin S. Fridson, CFA, and Xiaoyi Xu Over time, the annualized return of a duration-targeting, investment-grade corporate bond portfolio will nearly match its initial yield. A high-yield bond portfolio’s performance is not similarly predictable. Furthermore, the difference between the high-yield universe’s initial yield and annualized return has a sharply negative bias. The absence of benefits from duration targeting has a bearing on valuation of the highyield asset class and helps explain the instability in its investor base.
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fascinating new section on duration targeting is a highlight of the recently published third edition of the fixed-income classic Inside the Yield Book,1 three of whose authors— Martin L. Leibowitz, Anthony Bova, and Stanley Kogelman—further explored the concept in a recent FAJ article, “Long-Term Bond Returns under Duration Targeting.”2 As Leibowitz, Bova, and Kogelman (LBK) explained in the article, a duration-targeting portfolio manager maintains an approximately constant duration by selling bonds as they approach maturity and replacing them with longer-dated issues. This strategy is in contrast to a buy-and-hold immunization strategy, in which duration shortens because bonds remain in the portfolio until they mature. In the article, LBK commented that aside from liability-driven immunizations, almost all actively and passively managed institutional portfolios use some form of stable duration targeting. Typically, the institution’s investment committee adopts a policy portfolio that reflects a desired risk–return trade-off. The policy portfolio’s components include stocks, bonds, and alternative assets. As market conditions change, the institution periodically rebalances its holdings to keep them in line with the policy portfolio’s risk profile. For the fixed-income portion of the institution’s holdings, defining the risk level is essentially equivalent to specifying the duration. Martin S. Fridson, CFA, is chief investment officer at Lehmann, Livian, Fridson Advisors, LLC, New York City. Xiaoyi Xu is quantitative research specialist at FridsonVision, LLC, New York City. 28 www.cfapubs.org
Significantly, for the purposes of our study, Leibowitz, Homer, Bova, and Kogelman (LHBK) observed, “For the high-grade bond component of the fund, this common rebalancing process tends to maintain a stable duration and, hence, is essentially tantamount to duration targeting.”3 That statement excludes high-yield bonds from the discussion—and properly so. As we demonstrate in this article, targeting duration in a high-yield portfolio does not provide a key benefit enjoyed by owners of duration-targeting investment-grade portfolios. The objective of our study was to figure out why.
Duration Targeting and Convergence of Returns A valuable benefit of duration targeting—the predictability of returns—is the key finding discussed by LBK in their article; they showed that given sufficient time, a duration-targeting portfolio will reliably produce an annualized return very close to its initial yield. Whether interest rates rise or fall in the interim, an investment-grade, durationtargeting bond portfolio’s excess return—the difference between initial yield and annualized total return—will approximate zero at a point somewhat beyond the portfolio’s duration. Knowing in advance, within a small tolerance, what a portfolio’s return will be is extremely valuable, considering that uncertainty is a hallmark of investing. Why do the returns of a duration-targeting portfolio, under a variety of interest rate scenarios, converge around the initial yield? If interest rates rise, the portfolio’s market value falls and thus its ©2014 CFA Institute
Duration Targeting
Investment-Grade and High-Yield Duration Targeting
total return declines. As these events occur, however, the reinvestment rate increases. Given sufficient time, reinvesting at the higher-than-initial rate offsets the loss in market value, leaving a net return equivalent to the initial yield. Conversely, if interest rates fall, the resulting gain in market value is eventually offset by a lower reinvestment rate. In their study, LBK began with a theoretical analysis. In the simplest case, the portfolio consists of one five-year, zero-coupon US Treasury bond. After one year, the bond’s duration (which is equivalent to its maturity) has aged down to four years; it is sold, and the proceeds, which include a gain or loss due to the change in interest rates, are reinvested in a new five-year bond. The authors also examined more-complex cases involving multiple bond portfolios and interest rate paths that fluctuate rather than rise or fall in a steady, unbroken (trendline) manner. LBK’s theoretical work demonstrates that convergence is mathematically bound to occur. If interest rates rise or fall in a trendline manner, the average return will equal the beginning yield after the number of years that is twice the duration minus 1 (2d – 1). The authors refer to this point in time as the bond’s effective maturity. LBK then put their theory to the test. They examined historical returns on the Barclays US Aggregate Government/Credit Index, which is effectively a duration-targeting portfolio. It is periodically rebalanced to eliminate bonds with less than one year remaining to maturity, while newly issued, longer-dated bonds are added. Since the late 1980s, this index’s duration has remained mostly within a band of five to six years. LBK found that significant convergence occurs well before the effective maturity of (5.4 × 2) – 1 = 9.8 years. They showed that returns over six-year holding periods are close to the beginning yields.
To examine the impact of credit quality on excessreturn convergence, we began by corroborating LBK’s key finding. Using a simple analysis of calendar-year returns, we confirmed that duration targeting produces meaningful convergence in an investment-grade bond portfolio. Figure 1 covers 1997–2012, the full period for which yield-toworst4 figures are available for The BofA Merrill Lynch US Corporate & Government Index, which includes issues in the blended-rating range of AAA to BBB3.5 Note that the number of observations per investment horizon decreases in later years. For example, no annualized return for five years or longer is available as of this writing for the period beginning 1 January 2009. In Year 1, excess return varies from –736 bps to 599 bps. That 1,335 bp range steadily tightens, reaching a minimum of 160 bps in Year 5. After Year 5, the range widens somewhat but never exceeds 214 bps. Portfolio managers who diversify widely and mimic the investment-grade index’s sector weightings can be reasonably confident of earning an annualized return approximately equal to the initial yield after five years. With respect to its mean effective duration over the observation period, The BofA Merrill Lynch US Corporate & Government Index has an effective maturity of 9.9 years. We found that extending the experiment to a high-yield bond portfolio produces a much smaller degree of convergence. Figure 2 shows a first-year excess-return range for The BofA Merrill Lynch US High Yield Index of 7,398 bps, versus 1,355 bps for The BofA Merrill Lynch US Corporate & Government Index. As with the investment-grade index, the range tapers to a minimum in Year 5, with an effective maturity of 8.8 years. The minimum
Figure 1. Range of Annualized Excess Returns for The BofA Merrill Lynch US Corporate & Government Index, 1997–2012 Percent 8 6 4 2 0 –2 –4 –6 –8 –10 1
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Source: Used with permission of Bank of America Merrill Lynch Global Research.
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pointed out, however, that the costs of rebalancing a portfolio of illiquid bonds can be mitigated by reinvesting coupons in longer-duration issues rather than by selling and replacing bonds that age down.
range of 899 bps, however, is more than five times greater than the investment-grade index’s 160 bps. The contrast in range of excess annual returns appears in sharp relief in Figure 3, which plots both series on the same scale. The BofA Merrill Lynch US High Yield Index’s fifth-year range of excess returns, from –8.42% to 0.57%, does not represent a convergence of any practical value to investors. For example, suppose a manager held a portfolio similar to the index on 31 December 2012, with a yield-to-worst of 6.11%, and then rebalanced with the same frequency as the index (monthly). On the basis of historical experience, the manager might realize an annualized return of anywhere from –2.31% to 6.68% over the succeeding five years. “Predictability” hardly seems an apt description of such a heterogeneous set of possible outcomes. Moreover, it is probably optimistic to count on an excess-return range as narrow as 899 bps for a real-world portfolio. In our analysis, we omitted the sizable transaction costs associated with rebalancing a high-yield portfolio. LBK
Explaining High Yield’s Relative Lack of Convergence One possible explanation for the large difference in excess-return ranges between investment-grade and high-yield bonds is the differing degrees of stability of duration. LHBK suggested that unstable duration interferes with convergence.6 In our example, however, we can reject that explanation. During our observation period, the monthly mean effective duration for the investment-grade index is 5.39 years, with a standard deviation of 0.27, or 5.0% of the mean. The comparable figures for the high-yield index are a mean of 4.43 years and a standard deviation of 0.19, or 4.3% of the mean. In short, the duration of the high-yield index is more
Figure 2. Range of Annualized Excess Returns for The BofA Merrill Lynch US High Yield Index, 1997–2012 Percent 50 40 30 20 10 0 –10 –20 –30 –40 1
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Source: Used with permission of Bank of America Merrill Lynch Global Research.
Figure 3. Range of Annual Excess Returns, 1997–2012 Percent 50 40 30 20 10 0 –10 –20 –30 –40 1
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Note: Gray bars represent The BofA Merrill Lynch US High Yield Index; white bars represent The BofA Merrill Lynch US Corporate & Government Index. Source: Used with permission of Bank of America Merrill Lynch Global Research.
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Duration Targeting
stable than that of the investment-grade index. It follows that the difference in volatility of duration does not explain the high-yield index’s wider range of excess returns. The true explanation of high yield’s less pronounced return convergence lies in its greater price volatility. As noted earlier, both investment-grade and high-yield bonds exhibit their narrowest range of excess returns in Year 5. During our observation period, prices on The BofA Merrill Lynch US Corporate & Government Index at the end of Year 5 range from 102.20 to 110.86. The comparable range for The BofA Merrill Lynch US High Yield Index is 61.15–104.35. It is more difficult for a change in the reinvestment rate to compensate for price swings over a 43.20-point range than for price swings over an 8.66-point range. Further support for price volatility as the most important determinant of the degree of convergence emerges from an expanded comparison of price range and convergence. Using the same analysis as before, we incorporated the key subdivisions of the US Corporate & Government Index7 into the analysis, as shown in Table 1. The relationship across the full spectrum of credit risk is clear: As the index price range widens, so does the range of excess returns.
Negative Bias in High-Yield Excess Returns In addition to exhibiting too wide a range to represent a useful level of predictability, the high-yield excess returns displayed in Figure 2 have a second disadvantage: They are heavily skewed to the negative, in sharp contrast to the strongly positive skew, after Year 1, for the investment-grade excess returns (Figure 1). LBK similarly found a positive bias in excess returns on the Barclays US Aggregate Government/ Credit Index, which they attributed to the downward trend of interest rates over their observation period. Rates also trended downward in our observation period, as shown in Figure 4. Despite this boost, the bias in high-yield excess returns is negative. We surmise that if future interest rates prove trendless, high-yield excess returns will be even more negatively biased than in our historical observation period. One explanation for the negative bias in high yield, which is not observed in investment grade, involves a substantial difference in default losses between the two categories. (Conceptually, the default loss rate is the default rate minus the recovery rate.)8 For 1982–2012, Moody’s Investors Service reports average annual default losses of
Table 1. Expanded Comparison of Price Range and Convergence
Category Governments Investment-grade corporates High yield
End of Year 5 Index Price Range (points) 10.56 22.54 40.20
Maximum Convergence Excess-Return Range (points) Year 3.11 4 3.71 6 8.99 5
Source: Used with permission of Bank of America Merrill Lynch Global Research.
Figure 4. Annual Yield History for The BofA Merrill Lynch Current 5-Year US Treasury Index, 31 December 1996 to 31 December 2012 Percent 7 6 5 4 3 2 1 0 96
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0.06% for investment grade and 2.73% for speculative grade (i.e., high yield).9 A second differentiator that lowers the highyield index’s range of excess returns, relative to that of the investment-grade index, is the degree of concentration in callable bonds. Early-redemption provisions—typically at modest premiums to par of about half the annual coupon—downwardly skew the distribution of potential returns. On the one hand, if an issuer’s credit quality improves, causing its spread versus Treasuries to decline, the investor’s upside will generally be limited to a few points above the call price.10 On the other hand, if the issuer’s credit quality deteriorates, the price may fall as low as the recovery level. The median recovery rate across all seniority levels over 1978– 2012 was 42.42%, according to a study published by the New York University Salomon Center.11 In contrast, noncallable (“bullet”) bonds with very long maturities sometimes trade 30 points or more above par. Early-redemption features can also skew returns in the context of large swings in interest rates. As rates fall, a callable bond trading near its current call price is likely to be called, forcing bondholders to reinvest at a lower rate without enjoying the compensating benefit of a substantial price gain. To some extent, this disadvantage vis-à-vis bullets is offset in periods of rising rates. Callable bonds trading above par are known as “cushion” bonds because they tend not to suffer large price declines under such circumstances. As of August 2013, just 20.1% of the issues in the US Corporate & Government Index were callable; in contrast, 73.3% of the issues in the US High Yield Index were callable. The resulting, more unfavorable skewing in the high-yield universe helps explain why that asset class—but not the investment-grade universe—showed predominantly negative excess returns during the observation period, despite the relentless decline of interest rates.
Conclusion Using returns on an investment-grade bond index, we confirmed that over a specified number of years, duration targeting ensures a cumulative annualized
return close to the portfolio’s initial yield. We also found that this valuable benefit of predictability is unavailable to high-yield investors. Excess returns (above the initial yield) on the high-yield index, like those on the investment-grade index, converge toward zero—but not enough to justify calling the five-year annualized return “predictable.” Furthermore, high-yield excess returns are strongly skewed toward the negative, reflecting the impact of default losses and call features that constrain price appreciation during interest rate declines. Our findings shed light on two aspects of highyield-market valuation and performance. First, the lack of meaningful predictability of returns for a duration-targeting high-yield portfolio represents a significant disadvantage visà-vis the investment-grade asset class. Investors demand compensation for uncertainty, as evidenced by their willingness to incur hedging costs to reduce it. Therefore, a value comparison of investment-grade and high-yield bonds should attribute a portion of high yield’s total return premium to the absence, practically speaking, of predictable performance in a duration-targeting high-yield portfolio. Second, the negative bias in high-yield excess returns helps explain the chronically destabilizing mix of investors in high-yield bonds. Some highyield buyers are perennial players who merely tweak their allocations to the asset class as market conditions change. Many others, however, are intermittent participants with very short investment horizons. They attempt to enter at a low point in prices, ride the market back up, and then take their profits so they can move on to another temporarily undervalued asset class. If high-yield investors could reliably earn a multi-year return close to their beginning yield, it seems likely that more long-term players would be attracted to that asset class. Because they cannot do so, however, high-yield prices are more heavily influenced by short-term traders—and are thus more volatile— than they would be if duration targeting worked the same magic in high yield as it does in investment grade. This article qualifies for 0.5 CE credit.
Notes 1. Martin L. Leibowitz and Sidney Homer, with Anthony Bova and Stanley Kogelman, Inside the Yield Book: The Classic That Created the Science of Bond Analysis, 3rd ed. (Hoboken, NJ: Wiley, 2013). Homer and Leibowitz coauthored the first edition in 1972; Homer died before the second edition’s publication, in 2004. In the latest edition, Leibowitz, Bova, and Kogelman acknowledged
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the seminal role of the late Terry Langetieg in discovering insights into the return characteristics of durationtargeting funds. 2. Financial Analysts Journal, vol. 70, no. 1 (January/February 2014):31–51. 3. Leibowitz, Homer, Bova, and Kogelman, Inside the Yield Book, p. 9.
©2014 CFA Institute
Duration Targeting 4. Yield-to-worst is the lowest in the set of a bond’s yields to maturity and to all premature redemption dates. 5. The Bank of America Merrill Lynch index system blends the credit opinions and notation systems of several rating agencies. For example, in lieu of the equivalent Aa3 (Moody’s Investors Service) and AA– (Standard & Poor’s) ratings, the system uses a rating of AA3. 6. Leibowitz, Homer, Bova, and Kogelman, Inside the Yield Book, p. 65. 7. A minor portion of The BofA Merrill Lynch US Corporate & Government Index consists of taxable municipal securities and dollar-denominated foreign government and supranational issues. 8. Here, recovery rate refers to the price shortly after default. That price is the market’s estimate of ultimate recovery, discounted for the expected length of resolution of the default, typically through a bankruptcy proceeding.
9. Albert Metz, David Chiu, Bo Wen, and Sharon Ou, “Annual Default Study: Corporate Default and Recovery Rates, 1920– 2012” (Moody’s Investors Service, 28 February 2013), p. 26. 10. A callable bond that is still in its noncall period may trade somewhat above its call price. Investors will price such a bond by comparing the sum of its current yield (Coupon ÷ Price) and its annualized loss through redemption at the current call price with yields on money market instruments. Still, the early-redemption provision will limit the upside. 11. Edward I. Altman and Brenda J. Kuehne, “Defaults and Returns in the High-Yield Bond and Distressed Debt Market: The Year 2012 in Review and Outlook” (New York University Salomon Center, 6 February 2013), p. 20.
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