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

# Summary

- The bond risk premium is the return that investors earn by investing in longer duration bonds.
- While the most common way that investors can access this return stream is through investing in bond portfolios, bonds often significantly de-risk portfolios and scale back returns.
- Investors who desire more equity-like risk can tap into the bond risk premium by overlaying bond exposure on top of equities.
- Through the use of a leveraged ETP strategy, we construct a long-only bond risk premium factor and investigate its characteristics in terms of rebalance frequency and timing luck.
- By balancing the costs of trading with the risk of equity overexposure, investors can incorporate the bond risk premium as a complementary factor exposure to equities without sacrificing return potential from scaling back the overall risk level unnecessarily.

The discussion surrounding factor investing generally pertains to either equity portfolios or bond portfolios in isolation. We can calculate value, momentum, carry, and quality factors for each asset class and invest in the securities that exhibit the best characteristics of each factor or a combination of factors.

There are also ways to use these factors to shift allocations between stocks and bonds (e.g. trend and standardizing based on historical levels). However, we do not typically discuss bonds as their own standalone factor.

The bond risk premium – or term premium – can be thought of as the premium investors earn from holding longer duration bonds as opposed to cash. In a sense, it is a measure of carry. Its theoretical basis is generally seen to be related to macroeconomic factors such as inflation and growth expectations.^{1}

While timing the term premium using factors within bond duration buckets is definitely a possibility, this commentary will focus on the term premium in the context of an equity investor who wants long-term exposure to the factor.

**The Term Premium as a Factor**

For the term premium, we can take the usual approach and construct a self-financing long/short portfolio of 100% intermediate (7-10 year) U.S. Treasuries that borrows the entire portfolio value at the risk-free rate.

This factor, shown in bold in the chart below, has exhibited a much tamer return profile than common equity factors.

*Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

*Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

But over the entire time period, its returns have been higher than those of both the Size and Value factors. Its maximum drawdown has been less than 40% of that of the next best factor (Quality), and it is worth acknowledging that its volatility – which is generally correlated to drawdown for highly liquid assets with non-linear payoffs – has also been substantially lower.

The term premium also has exhibited very low correlation with the other equity factors.

*Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

**A Little Free Lunch**

Whether we are treating bonds as factor or not, they are generally the primary way investors seek to diversify equity portfolios.

The problem is that they are also a great way to reduce returns during most market environments through their inherently lower risk.

Anytime that an asset with lower volatility is added to a portfolio, the risk will be reduced. Unless the asset class also has a particularly high Sharpe ratio, maintaining the same level of return is virtually impossible even if risk-adjusted returns are improved.

In a 2016 paper^{2}, Salient broke down this reduction in risk into two components: de-risking and the “free lunch” affect.

The reduction in risk form the free lunch effect is desirable, but the risk reduction from de-risking may or may not be desirable, depending on the investor’s target risk profile.

The following chart shows the volatility breakdown of a range of portfolios of the S&P 500 (IVV) and 7-10 Year U.S. Treasuries (IEF).

*Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

Moving from an all equity portfolio to a 50/50 equity reduces the volatility from 14.2% to 7.4%. But only 150 bps of this reduction is from the free lunch effect that stems from the lower correlation between the two assets (-0.18). The remaining 530 bps of volatility reduction is simply due to lower risk.

In this case, annualized returns were dampened from 9.6% to 7.8%. While the Sharpe ratio climbed from 0.49 to 0.70, an investor seeking higher risk would not benefit without the use of leverage.

Despite the strong performance of the term premium factor, risk-seeking investors (e.g. those early in their careers) are generally reluctant to tap into this factor too much because of the de-risking effect.

How do investors who want to bear risk commensurate with equities tap into the bond risk premium without de-risking their portfolio?

One solution is using leveraged ETPs.

**Long-Only Term Premium**

By taking a 50/50 portfolio of the 2x Levered S&P 500 ETF (SSO) and the 2x Levered 7-10 Year U.S. Treasury ETF (UST), we can construct a portfolio that has 100% equity exposure and 100% of the term premium factor.^{3}

But managing this portfolio takes some care.

Left alone to drift, the allocations can get very far away from their target 50/50, spanning the range from 85/15 to 25/75. Periodic rebalancing is a must.

*Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

Of course, now the question is, “How frequently should we rebalance the portfolio?”

This boils down to a balancing act between performance and costs (e.g. ticket charges, tax impacts, operational burden, etc.).

On one hand, we would like to remain as close to the 50/50 allocation as possible to maintain the desired exposure to each asset class. However, this could require a prohibitive amount of trading.

From a performance standpoint, we see improved results with longer holding periods (take note of the y-axes in the following charts; they were scaled to highlight the differences).

*Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

The returns do not show a definitive pattern based on rebalance frequency, but the volatility decreases with increasing time between rebalances. This seems like it would point to waiting longer between rebalances, which would be corroborated by a consideration of trading costs.

The issues with waiting longer between the rebalance are twofold:

- Waiting longer is essentially a momentum trade. The better performing asset class garners a larger allocation as time progresses. This can be a good thing – especially in hindsight with how well equities have done – but it allows the portfolio to become overexposed to factors that we are not necessarily intending to exploit.
- Longer rebalances are more exposed to timing luck. For example, a yearly rebalance may have done well from a performance perspective, but the short-term performance could vary by as much as 50,000 bps between the best performing rebalance month and the worst! The chart below shows the performance of each iteration relative to the median performance of the 12 different monthly rebalance strategies.

*Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

As the chart also shows, tranching can help mitigate timing luck. Tranching also gives the returns of the strategies over the range of rebalance frequencies a more discernible pattern, with longer rebalance period strategies exhibiting slightly higher returns due to their higher average equity allocations.

Under the assumption that we can tranche any strategy that we choose, we can now compare only the tranched strategies at different rebalance frequencies to address our concern with taking bets on momentum.

Pausing for a minute, we should be clear that we do not actually *know* what the true factor construction should be; it is a moving target. We are more concerned with robustness than simply trying to achieve outperformance. So we will compare the strategies to the median performance of the previously monthly offset annual rebalance strategies.

The following charts shows the aggregate risk of short-term performance deviations from this benchmark.

The first one shows the aggregate deviations, both positive and negative, and the second focuses on only the downside deviation (i.e. performance that is worse than the median).^{4}

Both charts support a choice of rebalance frequency somewhere in the range of 3-6 months.

With the rebalance frequency set based on the construction of the factor, the last part is a consideration of costs.

Unfortunately, this is more situation-specific (e.g. what commissions does your platform charge for trades?).

From an asset manager point-of-view, where we can trade with costs proportional to the size of the trade, execute efficiently, and automate much of the operational burden, tranching is our preferred approach.

We also prefer this approach over simply rebalancing back to the static 50/50 allocation more frequently.

In our previous commentary on constructing value portfolios to mitigate timing luck, we described how tranching monthly is a different decision than rebalancing monthly and that tranching frequency and rebalance frequency are distinct decisions.

We see the same effect here where we plot the monthly tranched annually rebalanced strategy (blue line) and the strategy rebalanced back to 50/50 every month (orange line).

Tranching wins out.

However, since the target for the term premium factor is a 50/50 static allocation, running a simple allocation filter to keep the portfolio weights within a certain tolerance can be a way to implement a more dynamic rebalancing model while reducing costs.

For example, rebalancing when the allocations for SSO and UST we outside a 5% band (i.e. the portfolio was beyond a 55/45 or 45/55) achieved better performance metrics than the monthly rebalanced version with an average of only 3 rebalances per year.

**Conclusion**

The bond term premium does not have to be reserved for risk-averse investors. Investors desiring portfolios tilted heavily toward equities can also tap into this diversifying return stream as a factor within their portfolio.

Utilizing leveraged ETPs is one way to maintaining exposure to equities while capturing a significant portion of the bond risk premium. However, it requires more oversight than investing in other factors such as value, momentum, and quality, which are typically packaged in easy-to-access ETFs.

If a fixed frequency rebalance approach is used, tranching is an effective way to reduce timing risk, especially when markets are volatile. Aside from tranching, we find that, historically, holding periods between 3 and 6 months yield results close in line with the median rolling short-term performance of the individual strategies. Implementing a methodology like this can reduce the risk of poor luck in choosing the rebalance frequency or starting the strategy at an unfortunate time.

If frequent rebalances – like those seen with tranching – are infeasible, a dynamic schedule based on a drift in allocations is also a possibility.

Leveraged ETPs are often seen as risk trading instruments that are not fit for retail investors who are more focused on buy-and-hold systems. However, given the right risk management, these investment vehicles can be a way for investors to access the bond term premium, getting a larger free lunch, and avoiding undesired de-risking along the way.

## Yield Curve Trades with Trend and Momentum

By Corey Hoffstein

On October 14, 2019

In Momentum, Term, Weekly Commentary

This post is available as a PDF download here.## Summary

It has been well established in fixed income literature that changes to the U.S. Treasury yield curve can be broken down into three primary components: a level shift, a slope change, and a curvature twist.

A level change occurs when rates increase or decrease across the entire curve at once. A slope change occurs when short-term rates decrease (increase) while long-term rates increase (decrease). Curvature defines convexity and concavity changes to the yield curve, capturing the bowing that occurs towards the belly of the curve.

Obviously these three components do not capture 100% of changes in the yield curve, but they do capture a significant portion of them. From 1962-2019 they explain 99.5% of the variance in daily yield curve changes.

We can even decompose longer-term changes in the yield curve into these three components. For example, consider how the yield curve has changed in the three years from 6/30/2016 to 6/30/2019.

Source: Federal Reserve of St. Louis.We can see that there was generally a positive increase across the entire curve (i.e. a positive level shift), the front end of the curve increased more rapidly (i.e. a flattening slope change) and the curve flipped from concave to convex (i.e. an inverted bowing of the curve).

Using the historical yield curve changes, we can mathematically estimate these stylized changes using principal component analysis. We plot the loadings of the first three components below for this three-year change.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.We can see that

–PC1–has generally positive loadings across the entire curve, and therefore captures our level shift component.–PC2–exhibits negative loadings on the front end of the curve and positive loadings on the back, capturing our slope change. Finally,–PC3–has positive loadings from the 1-to-5-year part of the curve, capturing the curvature change of the yield curve itself.Using a quick bit of linear algebra, we can find the combination of these three factors that closely matches the change in the curve from 6/30/2016 to 6/30/2019. Comparing our model versus the actual change, we see a reasonably strong fit.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.So why might this be useful information?

First of all, we can interpret our principal components as if they are portfolios. For example, our first principal component is saying, “buy a portfolio that is long interest rates across the entire curve.” The second component, on the other hand, is better expressed as, “go short rates on the front end of the curve and go long rates on the back end.”

Therefore, insofar as we believe changes to the yield curve may exhibit absolute or relative momentum, we may be able to exploit this momentum by constructing a portfolio that profits from it.

As a more concrete example, if we believe that the yield curve will generally steepen over the next several years, we might buy 2-year U.S. Treasury futures and short 10-year U.S. Treasury futures. The biggest wrinkle we need to deal with is the fact that 2-year U.S. Treasury futures will exhibit very different sensitivity to rate changes than 10-year U.S. Treasury futures, and therefore we must take care to duration-adjust our positions.

Why might such changes exhibit trends or relative momentum?

In related literature, Fan et al (2019) find that the net hedging or speculative position has strong cross-sectional explanatory power for agricultural and currency futures returns, but

notin fixed income markets. To quote,Interestingly, Markowitz et al. (2012) suggest that speculators may be profiting from time-series momentum at the expense of hedgers, suggesting that they earn a premium for providing liquidity. Such does not appear to be the case for fixed income futures, however.

As far as we are aware, it has not yet been tested in the literature whether the net speculator versus hedger position has been tested for yield curve trades, and it may be possible that a risk transfer does not exist at the individual maturity basis, but rather exists for speculators willing to bear level, slope, or curvature risk.

Stylized Component TradesWhile we know the exact loadings of our principal components (i.e. which maturities make up the principal portfolios), to avoid the risk of overfitting our study we will capture level, slope, and curvature changes with three different stylized portfolios.

To implement our portfolios, we will buy a basket of 2-, 5-, and 10-year U.S. Treasury futures contracts (“UST futures”). We will assume that the 5-year contract has 2.5x the duration of the 2-year contract and the 10-year contract has 5x the duration of the 2-year contract.

To capture a level shift in the curve, we will go long across all the contracts. Specifically, for every dollar of 2-year UST futures exposure we purchase, we will buy $0.4 of 5-year UST futures and $0.20 of 10-year UST futures. This creates equal duration exposure across the entire curve.

To capture slope change, we will go short 2-year UST futures and long the 10-year UST futures, holding zero position in the 5-year UST futures. As before, we will duration-adjust our positions such that for each $1 short of the 2-year UST futures position, we are $0.20 long the 10-year UST futures.

Finally, to capture curvature change we will construct a butterfly trade where we short the 2- and 10-year UST futures and go long the 5-year UST futures. For each $1 long in the 5-year UST futures, we will short $1.25 of 2-year UST futures and $0.25 of 10-year UST futures.

Note that the slope and curvature portfolios are implemented such that they are duration neutral (based upon our duration assumptions) so a level shift in the curve will generate no profit or loss.

An immediate problem with our approach arises when we actually construct these portfolios. Unless adjusted, the volatility exhibited across these trades will be meaningfully different. Therefore, we target a constant 10% volatility for all three portfolios by adjusting the notional exposure of each portfolio based upon an exponentially-weighted estimate of prior 3-month realized volatility.

Source: Stevens Futures. Calculations by Newfound Research.Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.It appears, at least to the naked eye, that changes in the yield curve – and therefore the returns of these portfolios – may indeed exhibit positive autocorrelation. For example,

–Slope–appears to exhibit significant trends from 2000-2004, 2004-to 2007, and 2007-2012.Whether those trends can be identified and exploited is another matter entirely. Thus, with our stylized portfolios in hand, we can begin testing.

Trend SignalsWe begin our analysis by exploring the application of time-series momentum signals across all three of the portfolios. We evaluate lookback horizons ranging from 21-to-294 trading days (or, approximately 1-to-14 months). Portfolios assume a 21-trading-day holding period and are implemented using 21 overlapping portfolios to control for timing luck.

Source: Stevens Futures. Calculations by Newfound Research.Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.Some observations:

Here we should pause to acknowledge that we are blindly throwing strategies at data without much forethought. If we consider, however, that we might reasonably expect duration to be a positively compensated risk premium, as well as the fact that we would expect the futures to capture a generally positive roll premium (due to a generally upward sloping yield curve), then explicitly shorting duration risk may not be a keen idea.

In other words, it may make more sense to implement our level trade as a long/flat rather than a long/short. When implemented in this fashion, we see that the annualized return versus buy-and-hold is much more closely maintained while volatility and maximum drawdown are significantly reduced.

Source: Stevens Futures. Calculations by Newfound Research.Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.Taken together, it would appear that time-series momentum may be effective for trading the persistence in Level and Slope changes, though not in Curvature.

Momentum SignalsIf we treat each stylized portfolio as a separate asset, we can also consider the returns of a cross-sectional momentum portfolio. For example, each month we can rank the portfolios based upon their prior returns. The top-ranking portfolio is held long; the 2

^{nd}ranked portfolio is held flat; and the 3^{rd}ranked portfolio is held short.As before, we will evaluate lookback horizons ranging from 21-to-294 trading days (approximately 1-to-14 months) and assuming a 21-trading-day holding period, implemented with 21 overlapping portfolios.

Results – as well as example allocations from the 7-month lookback portfolio – are plotted below.

Source: Stevens Futures. Calculations by Newfound Research.Here we see very strong performance results except in the 1- and 2-month lookback periods. The allocation graph appears to suggest that results are not merely the byproduct of consistently being long or short a particular portfolio and the total return level appears to suggest that the portfolio is able to simultaneously profit from both legs.

If we return back to the graph of the stylized portfolios, we can see a significant negative correlation between the Level and Slope portfolios from 1999 to 2011. The negative correlation appears to disappear after this point, almost precisely coinciding with a 6+ year drawdown in the cross-sectional momentum strategy.

This is due to a mixture of construction and the economic environment.

From a construction perspective, consider that the Level portfolio is long the 2-, the 5-, and the 10-year UST futures while the Slope portfolio is short 2-year and long the 10-year UST futures. Since the positions are held in a manner that targets equivalent duration exposure, when the 2-year rate moves more than the 10-year rate, we end up in a scenario where the two trades have negative correlation, since one strategy is short and the other is long the 2-year position. Conversely, if the 10-year rate moves more than the 2-year rate, we end up in a scenario of positive correlation, since both strategies are long the 10-year.

Now consider the 1999-2011 environment. We had an easing cycle during the dot-com bust, a tightening cycle during the subsequent economic expansion, and another easing cycle during the 2008 crisis. This caused significantly more directional movement in the 2-year rate than the 10-year rate. Hence, negative correlation.

After 2008, however, the front end of the curve became pinned to zero. This meant that there was significantly more movement in the 10-year than the 2-year, leading to positive correlation in the two strategies. With positive correlation there is less differentiation among the two strategies and so we see a considerable increase in strategy turnover – and effectiveness – as momentum signals become less differentiated.

With that in mind, had we designed our Slope portfolio to be long 2-year UST futures and short 10-year UST futures (i.e. simply inverted the sign of our allocations), we would have seen

positivecorrelation between Level and Slope from 1999 to 2011, resulting in a very different set of allocations and returns. In actually testing this step, we find that the 1999-2011 period is no longer dominated by Level versus Slope trades, but rather Slope versus Curvature. Performance of the strategy is still largely positive, but the spread among specifications widens dramatically.Taken all together, it is difficult to conclude that the success of this strategy was not, in essence, driven almost entirely by autocorrelation in easing and tightening cycles with a relatively stable back end of the curve.

^{1}Given that there have only been a handful of full rate cycles in the last 20 years, we’d be reluctant to rely too heavily on the equity curve of this strategy as evidence of a robust strategy.ConclusionIn this research note, we explored the idea of generating stylized portfolios designed to isolate and profit from changes to the form of the yield curve. Specifically, using 2-, 5-, and 10-year UST futures we design portfolios that aim to profit from level, slope, and curvature changes to the US Treasury yield curve.

With these portfolios in hand, we test whether we can time exposure to these changes using time-series momentum.

We find that while time-series momentum generates positive performance for the Level portfolio, it fails to keep up with buy & hold. Acknowledging that level exposure may offer a positive long-term risk premium, we adjust the strategy from long/short to long/flat and are able to generate a substantially improved risk-adjusted return profile.

Time-series momentum also appears effective for the Slope portfolio, generating meaningful excess returns above the buy-and-hold portfolio.

Applying time-series momentum to the Curvature portfolio does not appear to offer any value.

We also tested whether the portfolios can be traded employing cross-sectional momentum. We find significant success in the approach but believe that the results are an artifact of (1) the construction of the portfolios and (2) a market regime heavily influenced by monetary policy. Without further testing, it is difficult to determine if this approach has merit.

Finally, even though our study focused on portfolios constructed using U.S. Treasury futures, we believe the results have potential application for investors who are simply trying to figure out how to position their duration exposure. For example, a signal to be short (or flat) the Level portfolio and long the Slope portfolio may imply a view of rising rates with a flattening curve. Translating these quantitative signals into a forecast about yield-curve behavior may allow investors to better position their fixed income portfolios.

Since this study utilized U.S. Treasury futures, these results translate well to implementing a portable beta strategy. For example, if you were an investor with a desired risk profile on par with 100% equities, you could add bond exposure

on topof the higher risk portfolio. This would add a (generally) diversifying return source with only a minor cash drag to the extent that margin requirements dictate.