*This post is available as a PDF download here.*

**Summary**

- In a rising rate environment, conventional wisdom says to shorten duration in bond portfolios.
- Even as rates rise in general, the influence of central banks and expectations for inflation can create short term movements in the yield curve that can be exploited using systematic style premia.
- Value, momentum, carry, and an explicit measure of the bond risk premium all produce strong absolute and risk-adjusted returns for timing duration.
- Since these methods are reasonably diversified to each other, combining factors using either a mixed or integrated approach can mitigate short-term underperformance in any given factor leading to more robust duration timing.

In past research commentaries, we have demonstrated that the current *level *of interest rates is much more important than the future *change *in interest rates when it comes to long-term bond index returns[1].

That said, short-term changes in rates may present an opportunity for investors to enhance return or mitigate risk. Specifically, by timing our duration exposure, we can try to increase duration during periods of falling rates and decrease duration during periods of rising rates.

In timing our duration exposure, we are effectively trying to time the *bond risk premium* (“BRP”). The BRP is the expected extra return earned from holding longer-duration government bonds over shorter-term government bonds.

In theory, if investors are risk neutral, the return an investor receives from holding a current long-duration bond to maturity should be equivalent to the expected return of rolling 1-period bonds over the same horizon. For example, if we buy a 10-year bond today, our return should be equal to the return we would expect from annually rolling 1-year bond positions over the next 10 years.

Risk averse investors will require a premium for the uncertainty associated with rolling over the short-term bonds at uncertain future interest rates.

In an effort to time the BRP, we explore the tried-and-true style premia: value, carry, and momentum. We also seek to explicitly measure BRP and use it as a timing mechanism.

To test these methods, we will create long/short portfolios that trade a 10-year constant maturity U.S. Treasury index and a 3-month constant maturity U.S. Treasury index. While we do not expect most investors to implement these strategies in a long/short fashion, a positive return in the strategy will imply successful duration timing. Therefore, instead of implementing these strategies directly, we can use them to inform how much duration risk we should take (e.g. if a strategy is long a 10-year index and short a 3-month index, it implies a long-duration position and would inform us to extend duration risk within our long-only portfolio). In evaluating these results as a potential overlay, the average profit, volatility, and Sharpe ratio can be thought of as alpha, tracking error, and information ratio, respectively.

As a general warning, we should be cognizant of the fact that we know *long duration* was the right trade to make over the last three decades. As such, hindsight bias can play a big role in this sort of research, as we may be subtly biased towards approaches that are naturally long duration. In effort to combat this effect, we will attempt to stick to standard academic measures of value, carry, and momentum within this space (see, for example, Ilmanen (1997)[2]).

**Timing with Value**

Following the standard approach in most academic literature, we will use “real yield” as our proxy of bond valuation. To estimate real yield, we will use the current 10-year rate minus a survey-based estimate for 10-year inflation (from the Philadelphia Federal Reserve’s Survey of Professional Forecasters)[3].

If the real yield is positive (negative), we will go long (short) the 10-year and short (long) the 3-month. We will hold the portfolio for 1 year (using 12 overlapping portfolios).

It is worth noting that the value model has been predominately long duration for the first 25 years of the sample period. While real yield may make an appropriate cross-sectional value measure, it’s applicability as a time-series value measure is questionable given the lack of trades made by this strategy.

One potential solution is to perform a rolling z-score on the value measure, to determine relative richness versus some normalized local history. In at least one paper, we have seen a long-term “normal” level established as an anchor point. With the complete benefit of hindsight, however, we know that such an approach would ultimately load to a short-duration position over the last 15 years during the period of secular decline in real rates.

For example, Ilmanen and Sayood (2002)[4] compare real yield versus its previous-decade average when trading 7- to 10-year German Bunds. Expectedly, the result is non-profitable.

**Timing with Momentum**

How to measure momentum within fixed income seems to be up for some debate. Some measures include:

- Change in bond yields (e.g. Ilmanen (1997))
- Total return of individual bonds (e.g. Kolanovic and Wei (2015)[5] and Brooks and Moskowitz (2017)[6])
- Total return of bond indices (or futures) (e.g. Asness, Moskowitz, and Pedersen (2013)[7], Durham (2013)[8], and Hurst, Ooi, Pedersen (2014)[9])

In our view, the approaches have varying trade-offs:

- While empirical evidence suggests that nominal interest rates can exhibit secular trends, rate evolution is most frequently modeled as mean-reversionary. Our research suggests that very short-term momentum can be effective, but leads to a significant amount of turnover.
- The total return of individual bonds makes sense if we plan on running a cross-sectional bond model (i.e. identifying individual bonds), but is less applicable if we want to implement with a constant maturity index.
- The total return of a bond index may capture past returns that are attributable to securities that have been recently removed.

We think it is worth noting that the latter two methods can capture yield curve effects beyond shift, including roll return, steepening and curvature changes. In fact, momentum in general may even be able to capture other effects such as flight-to-safety and liquidity (supply-demand) factors. This may be a positive or negative thing depending on your view of where momentum is originating from.

As our intention is to ultimately invest using products that follow constant maturity indices, we choose to compare the total return of bond indices.

Specifically, we will compute the 12-1 month return of the 10-year index and subtract the 12-1 month return of the 3-month index. If the return is positive (negative), we will go long (short) the 10-year and short (long) the 3-month.

**Timing with Carry**

We define the carry to be the term spread (or slope) of the yield curve, measured as the 5-year rate minus the 2-year rate.

A steeper curve has two implications. First, if there is a premium for bearing duration risk, longer-dated bonds should offer a higher yield than shorter-dated bonds. Hence, we would expect a steeper curve to be correlated with a higher BRP.

Second, all else held equal, a steeper curve implies a higher roll return for the constant maturity index. So long as the spread is positive, we will remain invested in the longer duration bonds.

Similar to the value strategy, we can see that term-spread was largely positive over the entire period, favoring a long-duration position. Again, this calls into question the efficacy of using term spread as a timing model since we didn’t see much timing.

Similar to value, we could employ a z-scoring method or compare the measure to a long-term average. Ilmanen and Sayood (2002) find such an approach profitable in 7- to 10-year German Bunds. We similarly find comparing current term-spread versus its 10-year average to be a profitable strategy, though annualized return falls by 200bp. The increased number of trades, however, may give us more confidence in the sustainability of the model.

One complicating factor to the carry strategy is that rate steepness simultaneously captures both the expectation of rising short rates as well as an embedded risk premium. In particular, evidence suggests that mean-reverting rate expectations dominate steepness when short rates are exceptionally low or high. Anecdotally, this may be due to the fact that the front end of the curve is determined by central bank policy while the back end is determined by inflation expectations. In *Expected Returns*, Antti Ilmanen highlights that the steepness of the yield curve and a de-trended short-rate have an astoundingly high correlation of -0.79.

While a steep curve may be a positive sign for the roll return that can be captured (and our carry strategy), it may simultaneously be a negative sign if flattening is expected (which would erode the roll return). The fact that the term spread simultaneously captures both of these effects can lead to confusing interpretations.

We can see that, generally, term spread does a good job of predicting forward 12-month realized returns for our carry strategy, particularly post 2000. However, having two sets of expectations embedded into a single measure can lead to potentially poor interpretations in the extreme.

**Explicitly Estimating the Bond Risk Premium**

While value, momentum, and carry strategies employ different measures that seek to exploit the time-varying nature of the BRP, we can also try to explicitly measure the BRP itself. We mentioned in the introduction that the BRP is compensation that an investor demands to hold a long-dated bond instead of simply rolling short-dated bonds.

One way of approximating the BRP, then, is to subtract the expected average 1-year rate over the next decade from the current 10-year rate.

While the current 10-year rate is easy to find, the expected average 1-year rate over the next decade is a bit more complicated. Fortunately, the Philadelphia Federal Reserve’s Survey of Professional Forecasters asks for that explicit data point. Using this information, we can extract the BRP.

When the BRP is positive (negative) – implying that we expect to earn a positive (negative) return for bearing term risk – we will go long (short) the 10-year index and short (long) the 3-month index. We will hold the position for one year (using 12 overlapping portfolios).

**Diversifying Style Premia**

A benefit of implementing multiple timing strategies is that we have the potential to benefit from process diversification. A simple correlation matrix shows us, for example, that the returns of the BRP model are well diversified against those of the Momentum and Carry models.

BRP | Momentum | Value | Carry | |

BRP | 1.00 | 0.35 | 0.76 | 0.37 |

Momentum | 0.35 | 1.00 | 0.68 | 0.68 |

Value | 0.76 | 0.68 | 1.00 | 0.73 |

Carry | 0.37 | 0.68 | 0.73 | 1.00 |

One simple method of embracing this diversification is simply using a composite multi-factor approach: just dividing our capital among the four strategies equally.

We can also explore combining the strategies through an *integrated *method. In the composite method, weights are averaged together, often resulting in allocations canceling out, leaving the strategy less than fully invested. In the integrated method, weights are averaged together and then the direction of the implied trade is fully implemented (e.g. if the composite method says be 25% long the 10-year index and -25% short the 3-month index, the integrated method would go 100% long the 10-year and -100% short the 3-month). If the weights fully cancel out, the integrated portfolio remains unallocated.

We can see that while the integrated method significantly increases full-period returns (adding approximately 150bp per year), it does so with a commensurate amount of volatility, leading to nearly identical information ratios in the two approaches.

**Did Timing Add Value?**

In quantitative research, it pays to be skeptical of your own results. A question worth asking ourselves is, “did timing actually add value or did we simply identify a process that happened to give us a good average allocation profile?” In other words, is it possible we just data-mined our way to good average exposures?

For example, the momentum strategy had an average allocation that was 55% long the 10-year index and -55% short the 3-month index. Knowing that long-duration was the right bet to make over the last 25 years, it is entirely possible that it was the average allocation that added the value: timing may actually be detrimental.

We can test for this by explicitly creating indices that represent the average long-term allocations. Our timing models are labeled “Timing” while the average weight models are labeled “Strategic.”

CAGR | Volatility | Sharpe Ratio | Max Drawdown | |

BRP Strategic | 2.75% | 3.36% | 0.82 | 7.17% |

BRP Timing | 3.89% | 5.48% | 0.71 | 14.00% |

Momentum Strategic | 3.54% | 4.32% | 0.82 | 9.09% |

Momentum Timing | 3.62% | 7.20% | 0.50 | 17.68% |

Value Strategic | 4.37% | 5.38% | 0.81 | 11.27% |

Value Timing | 5.75% | 6.84% | 0.84 | 15.17% |

Carry Strategic | 4.71% | 5.80% | 0.81 | 12.11% |

Carry Timing | 5.47% | 6.97% | 0.79 | 12.03% |

While timing appears to add value from an absolute return perspective, in many cases it significantly increases volatility, reducing the resulting risk-adjusted return.

Attempting to rely on process diversification does not alleviate the issue either.

CAGR | Volatility | Sharpe Ratio | Max Drawdown | |

Composite Strategic | 3.78% | 4.63% | 0.82 | 9.71% |

Composite Timing | 4.03% | 5.26% | 0.77 | 9.15% |

** **As a more explicit test, we can also construct a long/short portfolio that goes long the timing strategy and short the strategic strategy. Statistically significant positive expectancy of this long/short would imply value added by timing above and beyond the average weights.

Unfortunately, in conducting such a test, we find that *none *of the timing models conclusively offer statistically significant benefits.

We want to be clear here that this does not mean timing did not add value. Rather, in this instance, timing does not seem to add value *beyond *the average strategic weights the timing models harvested.

One explanation for this result is that there was largely one regime over our testing period where long-duration was the correct bet. Therefore, there was little room for models to add value beyond just being net long duration – and in that sense, the models succeeded. However, this predominately long-duration position created strategic benchmark bogeys that were harder to beat. This test could really only show if the models detracted significantly from a long-duration benchmark. Ideally, we need to test these models in other market environments (geographies or different historical periods) to further assess their efficacy.** **

**Robustness Testing: International Markets**

We can try to allay our fears of overfitting by testing these methods on a different dataset. For example, we can run the momentum, value, and carry strategies on German Bund yields and see if the models are still effective.

Due to data accessibility, instead of switching between 10-year and 3-month indices, we will use 10-year and 2-year indices. We also slightly alter our strategy definitions:

- Momentum: 12-1 month 10-year index return versus 12-1 month 2-year index return.
- Value: 10-year yield minus trailing 1-year CPI change
- Carry: 10-year yield minus 2-year yield

Given the regime concerns highlighted above, we will also test two other measures:

- Value #2: Demeaned (using prior 10-year average) 10-year yield minus trailing 1-year CPI change
- Carry #2: Demeaned (using prior 10-year average) 10-year yield minus 2-year yield

We can see similar results applying these methods with German rates as we saw with U.S. rates: momentum and both carry strategies remain successful while value fails when demeaned.

However, given that developed rates around the globe post-2008 were largely dominated by similar policies and factors, a healthy dose of skepticism is still well deserved.

**Robustness Testing: Different Time Period**

While success of these methods in an international market may bolster our confidence, it would be useful to test them during a period with very different interest rate and inflation evolutions. If we are again willing to slightly alter our definitions, we can take our U.S. tests back to the 1960s – 1980s.

Instead of switching between 10-year and 3-month indices, we will use 10-year and 1-year indices. Furthermore, we use the following methodology definitions:

- Momentum: 12-1 month 10-year index return versus 12-1 month 1-year index return.
- Value: 10-year yield minus trailing 1-year CPI change
- Carry: 10-year yield minus 1-year yield
- Value #2: Demeaned (using prior 10-year average) 10-year yield minus trailing 1-year CPI change
- Carry #2: Demeaned (using prior 10-year average) 10-year yield minus 1-year yield

Over this period, *all* of the strategies exhibit statistically significant (95% confidence) positive annualized returns.[10]

That said, the value strategy suffers out of the gate, realizing a drawdown exceeding -25% during the 1960s through 6/1970, as 10-year rates climbed from 4% to nearly 8%. Over that period, prior 1-year realized inflation climbed from less than 1% to over 5%. With the nearly step-for-step increase in rates and inflation, the spread remained positive – and hence the strategy remained long duration. Without a better estimate of *expected *inflation (e.g. 5-year, 5-year forward inflation expectations, TIPs, or survey estimates)[11], value may be a failed methodology.

On the other hand, there is nothing that says that inflation expectations would have necessarily been more accurate in forecasting actual inflation. It is entirely plausible that future inflation was an unexpected surprise, and a more accurate model of inflation expectations would have kept real-yield elevated over the period.

Again, we find the power in diversification. While value had a loss of approximately -25% during the initial hikes, momentum was up 12% and carry was flat. Diversifying across all three methods would leave an investor with a loss of approximately -4.3%: certainly not a confidence builder for a decade of (mis-)timing decisions, but not catastrophic from a portfolio perspective.[12]

**Conclusion**

With fear of rising rates high, shortening bond during might be a gut reaction. However, even as rates rise in general, the influence of central banks and expectations for inflation can create short term movements in the yield curve that can potentially be exploited using style premia.

We find that value, momentum, carry, and an explicit measure of the bond risk premium all produce strong absolute and risk-adjusted returns for timing duration. The academic and empirical evidence of these factors in a variety of asset classes gives us confidence that there are behavioral reasons to expect that style premia will persist over long enough periods. Combining multiple factors into a portfolio can harness the benefits of diversification and smooth out the short-term fluctuations that can lead to emotion-driven decisions.

Our in-sample testing period, however, leaves much to be desired. Dominated largely by a single regime that benefited long-duration trades, all of the timing models harvested average weights that were net-long duration. Our research shows that the timing models did not add any statistically meaningful value above-and-beyond these average weights. Caveat emptor: without further testing in different geographies or interest rate regimes – and despite our best efforts to use simple, industry-standard models – these results may be the result of data mining.

As a robustness test, we run value, momentum, and carry strategies for German Bund yields and over the period of the 1960s-1980s within the United States. While we continue to see success to momentum and carry, we find that the value method may prove to be too blunt an instrument for timing (or we may simply need a better measure as our anchor for value).

Nevertheless, we believe that utilizing systematic, factor-based methods for making duration changes in a portfolio can be a way to adapt to the market environment and manage risk without relying solely on our own judgements or those we hear in the media.

As inspiration for future research, Brooks and Moskowitz (2017)[13] recently demonstrated that style premia – i.e. momentum, value, and carry strategies – provide a better description of bond risk premia than traditional model factors. Interestingly, they find that not only are momentum, value, and carry predictive when applied to the level of the yield curve, but also when applied to slope and curvature positions. While this research focuses on the *cross-section *of government bond returns across 13 countries, there may be important implications for timing models as well.

[1] https://blog.thinknewfound.com/2017/04/declining-rates-actually-matter/

[2] https://www.aqr.com/library/journal-articles/forecasting-us-bond-returns

[3] https://www.philadelphiafed.org/research-and-data/real-time-center/survey-of-professional-forecasters

[4] https://www.aqr.com/library/journal-articles/quantitative-forecasting-models-and-active-diversification-for-international-bonds

[5] http://www.cmegroup.com/education/files/jpm-momentum-strategies-2015-04-15-1681565.pdf

[6] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2956411

[7] https://www.aqr.com/library/journal-articles/value-and-momentum-everywhere

[8] https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr657.pdf

[9] https://www.aqr.com/library/aqr-publications/a-century-of-evidence-on-trend-following-investing

[10] While not done here, these strategies should be further tested against their average allocations as well.

[11] It is worth noting that The Cleveland Federal Reserve does offers model-based inflation expectations going back to 1982 (https://www.clevelandfed.org/our-research/indicators-and-data/inflation-expectations.aspx) and The New York Federal Reserve also offers model-based inflation expectations going back to the 1970s (http://libertystreeteconomics.newyorkfed.org/2013/08/creating-a-history-of-us-inflation-expectations.html).

[12] Though certainly a long enough period to get a manager fired.

[13] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2956411

## 5 Pingbacks