Tag: carry Page 1 of 2

Quantitative Styles and Multi-Sector Bonds

On June 10, 2019

In Carry, Defensive, Momentum, Risk & Style Premia, Value

This post is available as a PDF download here.

Summary

In this commentary we explore the application of several quantitative signals to a broad set of fixed income exposures.
Specifically, we explore value, momentum, carry, long-term reversals, and volatility signals.
We find that value, 3-month momentum, carry, and 3-year reversals all create attractive quantile profiles, potentially providing clues for how investors might consider pursuing higher returns or lower risk.
This study is by no means comprehensive and only intended to invite further research and conversation around the application of quantitative styles across fixed income exposures.

In Navigating Municipal Bonds with Factors, we employed momentum, value, carry, and low-volatility signals to generate a sector-based approach to navigating municipal bonds.

In this article, we will introduce an initial data dive into applying quantitative signals to a broader set of fixed income exposures. Specifically, we will incorporate 17 different fixed income sectors, spanning duration, credit, and geographic exposure.

U.S. Treasuries: Near (3-Month), short (1-3 Year), mid (3-5 Year) intermediate (7-10 Year), and long (20+ Year).
Investment-Grade Corporates: Short-term, intermediate-term, and Floating Rate corporate bonds.
High Yield: Short- and intermediate-term high yield.
International Government Bonds: Currency hedged and un-hedged government bonds.
Emerging Market: Local and US dollar denominated.
TIPs: Short- and intermediate-term TIPs.
Mortgage-Backed: Investment grade mortgage-backed bonds.

In this study, each exposure is represented by a corresponding ETF. We extend our research prior to ETF launch by employing underlying index data the ETF seeks to track.

The quantitative styles we will explore are:

Momentum: Buy recent winners and sell recent losers.
Value: Buy cheap and sell expensive.
Carry: Buy high carry and sell low carry.
Reversal: Buy long-term losers and sell long-term winners.
Volatility: Buy high volatility and sell low volatility.¹

The details of each style are explained in greater depth in each section below.

Note that the analysis herein is by no means meant to be prescriptive in any manner, nor is it a comprehensive review. Rather, it is meant as a launching point for further commentaries we expect to write.

At the risk of spoiling the conclusion, below we plot the annualized returns and volatility profiles of dollar-neutral long-short portfolios.² We can see that short-term Momentum, Value, Carry, and Volatility signals generate positive excess returns over the testing period.

Curiously, longer-term Momentum does not seem to be a profitable strategy, despite evidence of this approach being rather successful for many other asset classes.

Source: Bloomberg; Tiingo. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.

However, these results are not achievable by most investors who may be constrained to a long-only implementation. Even when interpreted as over- and under-weight signals, the allocations in the underlying long/short portfolios differ so greatly from benchmark exposures, they would be nearly impossible to implement.

For a long-only investor, then, what is more relevant is how these signals forecast performance of different rank orderings of portfolios. For example, how does a portfolio of the best-ranking 3-month momentum exposures compare to a portfolio of the worst-ranking?

In the remainder of this commentary, we explore the return and risk profiles of quintile portfolios formed on each signal. To construct these portfolios, we rank order our exposures based on the given quantitative signal and equally-weight the exposures falling within each quintile.

Momentum

We generate momentum signals by computing 12-, 6- and 3- month prior total returns to reflect slow, intermediate, and fast momentum signals. Low-ranking exposures are those with the lowest prior total returns, while high ranking exposures have the highest total returns.

The portfolios assume a 1-month holding period for momentum signals. To avoid timing luck, four sub-indexes are used, each rebalancing on a different week of the month.

Annualized return and volatility numbers for the quintiles are plotted below.

A few interesting data-points stand out:

For 12-month prior return, the lowest quintile actually had the highest total return.However, it has a dramatically lower Sharpe ratio than the highest quintile, which only slightly underperforms it.
Total returns among the highest quintile increase by 150 basis points (“bps”) from 12-month to 3-month signals, and 3-month rankings create a more consistent profile of increasing total return and Sharpe ratio. This may imply that short-term signals are more effective for fixed income.

Carry

Carry is the expected excess return of an asset assuming price does not change. For our fixed income universe, we proxy carry using yield-to-worst minus the risk-free rate. For non-Treasury holdings, we adjust this figure for expected defaults and recovery.

For reasonably efficient markets, we would expect higher carry to imply higher return, but not necessarily higher risk-adjusted returns. In other words, we earn higher carry as a reward for bearing more risk.

Therefore, we also calculate an alternate measure of carry: carry-to-risk. Carry-to-risk is calculated by taking our carry measure and dividing it by recent realized volatility levels. One way of interpreting this figure is as forecast of Sharpe ratio. Our expectation is that this signal may be able to identify periods when carry is episodically cheap or rich relative to prevailing market risk.

The portfolios assume a 12-month holding period for carry signals. To avoid timing luck, 52 sub-indexes are used, each rebalancing on a different week of the year.

We see:

Higher carry implies a higher return as well as a higher volatility. As expected, no free lunch here.
Carry-to-risk does not seem to provide a meaningful signal. In fact, low carry-to-risk outperforms high carry-to-risk by 100bps annualized.
Volatility meaningfully declines for carry-to-risk quintiles, potentially indicating that this integrated carry/volatility signal is being too heavily driven by volatility.

Value

In past commentaries, we have used real yield as our value proxy in fixed income. In this commentary, we deviate from that methodology slightly and use a time-series z-score of carry as our value of measure. Historically high carry levels are considered to be cheap while historically low carry levels are considered to be expensive.

The portfolios assume a 12-month holding period for value signals. To avoid timing luck, 52 sub-indexes are used, each rebalancing on a different week of the year.

We see not only a significant increase in total return in buying cheap versus expensive holdings, but also an increase in risk-adjusted returns.

Reversal

Reversal signals are the opposite of momentum: we expect past losers to outperform and past winners to underperform. Empirically, reversals tend to occur over very short time horizons (e.g. 1 month) and longer-term time horizons (e.g. 3- to 5-years). In many ways, long-term reversals can be thought of as a naive proxy for value, though there may be other behavioral and structural reasons for the historical efficacy of reversal signals.

We must be careful implementing reversal signals, however, as exposures in our universe have varying return dynamics (e.g. expected return and volatility levels).

To illustrate this problem, consider the simple two-asset example of equities and cash. A 3-year reversal signal would sell the asset that has had the best performance over the prior 3-years and buy the asset that has performed the worst. The problem is that we expect stocks to outperform cash due to the equity risk premium. Naively ranking on prior returns alone would have us out of equities during most bull markets.

Therefore, we must be careful in ranking assets with meaningfully different return dynamics.

(Why, then, can we do it for momentum? In a sense, momentum is explicitly trying to exploit the relative time-series properties over a short-term horizon. Furthermore, in a universe that contains low-risk, low-return assets, cross-sectional momentum can be thought of as an integrated process between time-series momentum and cross-sectional momentum, as the low-risk asset will bubble to the top when absolute returns are negative.)

To account for this, we use a time-series z-score of prior returns to create a reversal signal. For example, at each point in time we calculate the current 3-year return and z-score it against all prior rolling 3-year periods.

Note that in this construction, high z-scores will reflect higher-than-normal 3-year numbers and low z-scores will reflect lower-than-normal 3-year returns. Therefore, we negate the z-score to generate our signal such that low-ranked exposures reflect those we want to sell and high-ranked exposures reflect those we want to buy.

The portfolios assume a 12-month holding period for value signals. To avoid timing luck, 52 sub-indexes are used, each rebalancing on a different week of the year.

Plotting the results below for 1-, 3-, and 5-year reversal signals, we see that 3- and 5-year signals see a meaningful increase in both total return and Sharpe ratio between the lowest quintile.

Volatility

Volatility signals are trivial to generate: we simply sort assets based on prior realized volatility. Unfortunately, exploiting the low-volatility anomaly is difficult without leverage, as the empirically higher risk-adjusted return exhibited by low-volatility assets typically coincides with lower total returns.

For example, in the tests below the low quintile is mostly comprised of short-term Treasuries and floating rate corporates. The top quintile is allocated across local currency emerging market debt, long-dated Treasuries, high yield bonds, and unhedged international government bonds.

As a side note, for the same reason we z-scored reversal signals, we also hypothesized that z-scoring may work on volatility. Beyond these two sentences, the results were nothing worth writing about.

Nevertheless, we can still attempt to confirm the existence of the low-volatility anomaly in our investable universe by ranking assets on their past volatility.

The portfolios assume a 1-month holding period for momentum signals. To avoid timing luck, four sub-indexes are used, each rebalancing on a different week of the month.

Indeed, in plotting results we see that the lowest volatility quintiles have significantly higher realized Sharpe ratios.

Of the results plotted above, our eyes might be drawn to the results in the short-term volatility measure. It would appear that the top quintile has both a lower total return and much higher volatility than the 3^rdand 4^thquintiles. This might suggest that we could improve our portfolios risk-adjusted returns without sacrificing total return by avoiding those top-ranked assets.

Unfortunately, this is not so clear cut. Unlike the other signals where the portfolios had meaningful turnover, these quintiles are largely stable. This means that the results are driven more by the composition of the portfolios than the underlying signals. For example, the 3^rdand 4^thquintiles combine both Treasuries and credit exposure, which allows the portfolio to realize lower volatility due to correlation. The highest volatility quintile, on the other hand, holds both local currency emerging market debt and un-hedged international government bonds, introducing (potentially uncompensated) currency risk into the portfolio.

Thus, the takeaway may be more strategic than tactical: diversification is good and currency exposure is going to increase your volatility.

Oh – and allocating to zero-to-negatively yielding foreign bonds isn’t going to do much for your return unless currency changes bail you out.

Conclusion

In this study, we explored the application of value, momentum, carry, reversal, and volatility signals across fixed income exposures. We found that value, 3-month momentum, carry, and 3-year reversal signals may all provide meaningful information about forward expected returns and risk.

Our confidence in this analysis, however, is potentially crippled by several points:

The time horizon covered is, at best, two decades, and several economic variables are constant throughout it.
The inflation regime over the time period was largely uniform.
A significant proportion of the period covered had near-zero short-term Treasury yields and negative yields in foreign government debt.
Reversal signals require a significant amount of formation data. For example, the 3-year reversal signal requires 6 years (i.e. 3-years of rolling 3-year returns) of data before a signal can be generated. This represents nearly 1/3^rdof the data set.
The dispersion in return dynamics (e.g. volatility and correlation) of the underlying assets can lead to the emergence of unintended artifacts in the data that may speak more to portfolio composition than the value-add from the quantitative signal.
We did not test whether certain exposures or certain time periods had an outsized impact upon results.
We did not thoroughly test stability regions for different signals.
We did not test the impact of our holding period assumptions.
Holdings within quantile portfolios were assumed to be equally weighted.

Some of these points can be addressed simply. Stability concerns, for example, can be addressed by testing the impact of varying signal parameterization.

Others are a bit trickier and require more creative thinking or more computational horsepower.

Testing for the outsized impact of a given exposure or a given time period, for example, can be done through sub-sampling and cross-validation techniques. We can think of this as the application of randomness to efficiently cover our search space.

For example, below we re-create our 3-month momentum quintiles, but do so by randomly selecting only 10 of the exposures and 75% of the return period to test. We repeat this resampling 10,000 times for each quintile and plot the distribution of annualized returns below.

Even without performing an official difference-in-means test, the separation between the low and high quintile annualized return distributions provides a clue that the performance difference between these two is more likely to be a pervasive effect rather than due to an outlier holding or outlier time period.

We can make this test more explicit by using this subset resampling technique to bootstrap a distribution of annualized returns for a top-minus-bottom quintile long/short portfolio. Specifically, we randomly select a subset of assets and generate our 3-month momentum signals. We construct a dollar-neutral long/short portfolio by going long assets falling in the top quintile and short assets falling in the bottom quintile. We then select a random sub-period and calculate the annualized return.

Only 207 of the 10,000 samples fall below 0%, indicating a high statistical likelihood that the outperformance of recent winners over recent losers is not an effect dominated by a specific subset of assets or time-periods.

While this commentary provides a first step towards analyzing quantitative style signals across fixed income exposures, more tests need to be run to develop greater confidence in their efficacy.

Tactical Portable Beta

By Corey Hoffstein

On May 6, 2019

In Carry, Portfolio Construction, Risk & Style Premia, Term, Trend, Value, Weekly Commentary

This post is available as a PDF download here.

Summary

In this commentary, we revisit the idea of portable beta: utilizing leverage to overlay traditional risk premia on existing strategic allocations.
While a 1.5x levered 60/40 portfolio has historically out-performed an all equity blend with similar risk levels, it can suffer through prolonged periods of under-performance.
Positive correlations between stocks and bonds, inverted yield curves, and rising interest rate environments can make simply adding bond exposure on top of equity exposure a non-trivial pursuit.
We rely on prior research to introduce a tactical 90/60 model, which uses trend signals to govern equity exposure and value, momentum, and carry signals to govern bond exposure.
We find that such a model has historically exhibited returns in-line with equities with significantly lower maximum drawdown.

In November 2017, I was invited to participate in a Bloomberg roundtable discussion with Barry Ritholtz, Dave Nadig, and Ben Fulton about the future of ETFs. I was quoted as saying,

Most of the industry agrees that we are entering a period of much lower returns for stocks and fixed income. That’s a problem for younger generations. The innovation needs to be around efficient use of capital. Instead of an ETF that holds intermediate-term Treasuries, I would like to see a U.S. Treasury ETF that uses Treasuries as collateral to buy S&P 500 futures, so you end up getting both stock and bond exposure. By introducing a modest amount of leverage, you can take $1 and trade it as if the investor has $1.50. After 2008, people became skittish around derivatives, shorting, and leverage. But these aren’t bad things when used appropriately.

Shortly after the publication of the discussion, we penned a research commentary titled Portable Beta which extolled the potential virtues of employing prudent leverage to better exploit diversification opportunities. For investors seeking to enhance returns, increasing beta exposure may be a more reliable approach than the pursuit of alpha.

In August 2018, WisdomTree introduced the 90/60 U.S. Balanced Fund (ticker: NTSX), which blends core equity exposure with a U.S. Treasury futures ladder to create the equivalent of a 1.5x levered 60/40 portfolio. On March 27, 2019, NTSX was awarded ETF.com’s Most Innovative New ETF of 2018.

The idea of portable beta was not even remotely uniquely ours. Two anonymous Twitter users – “Jake” (@EconomPic) and “Unrelated Nonsense” (@Nonrelatedsense) – had discussed the idea several times prior to my round-table in 2017. They argued that such a product could be useful to free up space in a portfolio for alpha-generating ideas. For example, an investor could hold 66.6% of their wealth in a 90/60 portfolio and use the other 33.3% of their portfolio for alpha ideas. While the leverage is technically applied to the 60/40, the net effect would be a 60/40 portfolio with a set of alpha ideas overlaid on the portfolio. Portable beta becomes portable alpha.

Even then, the idea was not new. After NTSX launched, Cliff Asness, co-founder and principal of AQR Capital Management, commented on Twitter that even though he had a “22-year head start,” WisdomTree had beat him to launching a fund. In the tweet, he linked to an article he wrote in 1996, titled Why Not 100% Equities, wherein Cliff demonstrated that from 1926 to 1993 a 60/40 portfolio levered to the same volatility as equities achieved an excess return of 0.8% annualized above U.S. equities. Interestingly, the appropriate amount of leverage utilized to match equities was 155%, almost perfectly matching the 90/60 concept.

Source: Asness, Cliff. Why Not 100% Equities. Journal of Portfolio Management, Winter 1996, Volume 22 Number 2.

Following up on Cliff’s Tweet, Jeremy Schwartz from WisdomTree extended the research out-of-sample, covering the quarter century that followed Cliff’s initial publishing date. Over the subsequent 25 years, Jeremy found that a levered 60/40 outperformed U.S. equities by 2.6% annualized.

NTSX is not the first product to try to exploit the idea of diversification and leverage. These ideas have been the backbone of managed futures and risk parity strategies for decades. The entire PIMCO’s StocksPLUS suite – which traces its history back to 1986 – is built on these foundations. The core strategy combines an actively managed portfolio of fixed income with 100% notional exposure in S&P 500 futures to create a 2x levered 50/50 portfolio.

The concept traces its roots back to the earliest eras of modern financial theory. Finding the maximum Sharpe ratio portfolio and gearing it to the appropriate risk level has always been considered to be the theoretically optimal solution for investors.

Nevertheless, after 2008, the words “leverage” and “derivatives” have largely been terms non gratisin the realm of investment products. But that may be to the detriment of investors.

90/60 Through the Decades

While we are proponents of the foundational concepts of the 90/60 portfolio, frequent readers of our commentary will not be surprised to learn that we believe there may be opportunities to enhance the idea through tactical asset allocation. After all, while a 90/60 may have out-performed over the long run, the short-run opportunities available to investors can deviate significantly. The prudent allocation at the top of the dot-com bubble may have looked quite different than that at the bottom of the 2008 crisis.

To broadly demonstrate this idea, we can examine the how the realized efficient frontier of stock/bond mixes has changed shape over time. In the table below, we calculate the Sharpe ratio for different stock/bond mixes realized in each decade from the 1920s through present.

Source: Global Financial Data. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees, transaction costs, and taxes. Returns assume the reinvestment of all distributions. Bonds are the GFD Indices USA 10-Year Government Bond Total Return Index and Stocks are the S&P 500 Total Return Index (with GFD Extension). Sharpe ratios are calculated with returns excess of the GFD Indices USA Total Return T-Bill Index. You cannot invest in an index. 2010s reflect a partial decade through 4/2019.

We should note here that the original research proposed by Asness (1996) assumed a bond allocation to an Ibbotson corporate bond series while we employ a constant maturity 10-year U.S. Treasury index. While this leads to lower total returns in our bond series, we do not believe it meaningfully changes the conclusions of our analysis.

We can see that while the 60/40 portfolio has a higher realized Sharpe ratio than the 100% equity portfolio in eight of ten decades, it has a lower Sharpe ratio in two consecutive decades from 1950 – 1960. And the 1970s were not a ringing endorsement.

In theory, a higher Sharpe ratio for a 60/40 portfolio would imply that an appropriately levered version would lead to higher realized returns than equities at the same risk level. Knowing the appropriate leverage level, however, is non-trivial, requiring an estimate of equity volatility. Furthermore, leverage requires margin collateral and the application of borrowing rates, which can create a drag on returns.

Even if we conveniently ignore these points and assume a constant 90/60, we can still see that such an approach can go through lengthy periods of relative under-performance compared to buy-and-hold equity. Below we plot the annualized rolling 3-year returns of a 90/60 portfolio (assuming U.S. T-Bill rates for leverage costs) minus 100% equity returns. We can clearly see that the 1950s through the 1980s were largely a period where applying such an approach would have been frustrating.

Source: Global Financial Data. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees, transaction costs, and taxes. Bonds are the GFD Indices USA 10-Year Government Bond Total Return Index and Stocks are the S&P 500 Total Return Index (with GFD Extension). The 90/60 portfolio invests 150% each month in the 60/40 portfolio and -50% in the GFD Indices USA Total Return T-Bill Index. You cannot invest in an index.

Poor performance of the 90/60 portfolio in this era is due to two effects.

First, 10-year U.S. Treasury rates rose from approximately 4% to north of 15%. While a constant maturity index would constantly roll into higher interest bonds, it would have to do so by selling old holdings at a loss. Constantly harvesting price losses created a headwind for the index.

This is compounded in the 90/60 by the fact that the yield curve over this period spent significant time in an inverted state, meaning that the cost of leverage exceeded the yield earned on 40% of the portfolio, leading to negative carry. This is illustrated in the chart below, with –T-Bills– realizing a higher total return over the period than –Bonds–.

Source: Global Financial Data. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees, transaction costs, and taxes. Returns assume the reinvestment of all distributions. T-Bills are the GFD Indices USA Total Return T-Bill Index, Bonds are the GFD Indices USA 10-Year Government Bond Total Return Index, and Stocks are the S&P 500 Total Return Index (with GFD Extension). You cannot invest in an index.

This is all arguably further complicated by the fact that while a 1.5x levered 60/40 may closely approximate the risk level of a 100% equity portfolio over the long run, it may be a far cry from it over the short-run. This may be particularly true during periods where stocks and bonds exhibit positive realized correlations as they did during the 1960s through 1980s. This can occur when markets are more pre-occupied with inflation risk than economic risk. As inflationary fears abated and economic risk become the foremost concern in the 1990s, correlations between stocks and bonds flipped.

Thus, during the 1960s-1980s, a 90/60 portfolio exhibited realized volatility levels in excess of an all-equity portfolio, while in the 2000s it has been below.

This all invites the question: should our levered allocation necessarily be static?

Getting Tactical with a 90/60

We might consider two approaches to creating a tactical 90/60.

The first is to abandon the 90/60 model outright for a more theoretically sound approach. Specifically, we could attempt to estimate the maximum Sharpe ratio portfolio, and then apply the appropriate leverage such that we either hit a (1) constant target volatility or (2) the volatility of equities. This would require us to not only accurately estimate the expected excess returns of stocks and bonds, but also their volatilities and correlations. Furthermore, when the Sharpe optimal portfolio is highly conservative, notional exposure far exceeding 200% may be necessary to hit target volatility levels.

In the second approach, equity and bond exposure would each be adjusted tactically, without regard for the other exposure. While less theoretically sound, one might interpret this approach as saying, “we generally want exposure to the equity and bond risk premia over the long run, and we like the 60/40 framework, but there might be certain scenarios whereby we believe the expected return does not justify the risk.” The downside to this approach is that it may sacrifice potential diversification benefits between stocks and bonds.

Given the original concept of portable beta is to increase exposure to the risk premia we’re already exposed to, we prefer the second approach. We believe it more accurately reflects the notion of trying to provide long-term exposure to return-generating risk premia while trying to avoid the significant and prolonged drawdowns that can be realized with buy-and-hold approaches.

Equity Signals

To manage exposure to the equity risk premium, our preferred method is the application of trend following signals in an approach we call trend equity. We will approximate this class of strategies with our Newfound Research U.S. Trend Equity Index.

To determine whether our signals are able to achieve their goal of “protect and participate” with the underlying risk premia, we will plot their regime-conditional betas. To do this, we construct a simple linear model:

We define a bear regime as the worst 16% of monthly returns, a bull regime as the best 16% of monthly returns, and a normal regime as the remaining 68% of months. Note that the bottom and top 16^thpercentiles are selected to reflect one standard deviation.

Below we plot the strategy conditional betas relative to U.S. equity

We can see that trend equity has a normal regime beta to U.S. equities of approximately 0.75 and a bear market beta of 0.5, in-line with expectations that such a strategy might capture 70-80% of the upside of U.S. equities in a bull market and 40-50% of the downside in a prolonged bear market. Trend equity beta of U.S. equities in a bull regime is close to the bear market beta, which is consistent with the idea that trend equity as a style has historically sacrificed the best returns to avoid the worst.

Bond Signals

To govern exposure to the bond risk premium, we prefer an approach based upon a combination of quantitative, factor-based signals. We’ve written about many of these signals over the last two years; specifically in Duration Timing with Style Premia (June 2017), Timing Bonds with Value, Momentum, and Carry (January 2018), and A Carry-Trend-Hedge Approach to Duration Timing (October 2018). In these three articles we explore various mixes of value, momentum, carry, flight-to-safety, and bond risk premium measures as potential signals for timing duration exposure.

We will not belabor this commentary unnecessarily by repeating past research. Suffice it to say that we believe there is sufficient evidence that value (deviation in real yield), momentum (prior returns), and carry (term spread) can be utilized as effective timing signals and in this commentary are used to construct bond indices where allocations are varied between 0-100%. Curious readers can pursue further details of how we construct these signals in the commentaries above.

As before, we can determine conditional regime betas for strategies based upon our signals.

We can see that our value, momentum, and carry signals all exhibit an asymmetric beta profile with respect to 10-year U.S. Treasury returns. Carry and momentum exhibit an increase in bull market betas while value exhibits a decrease in bear market beta.

Combining Equity and Bond Signals into a Tactical 90/60

Given these signals, we will construct a tactical 90/60 portfolio as being comprised of 90% trend equity, 20% bond value, 20% bond momentum, and 20% bond carry. When notional exposure exceeds 100%, leverage cost is assumed to be U.S. T-Bills. Taken together, the portfolio has a large breadth of potential configurations, ranging from 100% T-Bills to a 1.5x levered 60/40 portfolio.

But what is the appropriate benchmark for such a model?

In the past, we have argued that the appropriate benchmark for trend equity is a 50% stock / 50% cash benchmark, as it not only reflects the strategic allocation to equities empirically seen in return decompositions, but it also allows both positive and negative trend calls to contribute to active returns.

Similarly, we would argue that the appropriate benchmark for our tactical 90/60 model is not a 90/60 itself – which reflects the upper limit of potential capital allocation – but rather a 45% stock / 30% bond / 25% cash mix. Though, for good measure we might also consider a bit of hand-waving and just use a 60/40 as a generic benchmark as well.

Below we plot the annualized returns versus maximum drawdown for different passive and active portfolio combinations from 1974 to present (reflecting the full period of time when strategy data is available for all tactical signals). We can see that not only does the tactical 90/60 model (with both trend equity and tactical bonds) offer a return in line with U.S. equities over the period, it does so with significantly less drawdown (approximately half). Furthermore, the tactical 90/60 exceeded trend equity and 60/40 annualized returns by 102 and 161 basis points respectively.

These improvements to the return and risk were achieved with the same amount of capital commitment as in the other allocations. That’s the beauty of portable beta.

Source: Federal Reserve of St. Louis, Kenneth French Data Library, and Newfound Research. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees, transaction costs, and taxes. Returns assume the reinvestment of all distributions. You cannot invest in an index.

Of course, full-period metrics can deceive what an investor’s experience may actually be like. Below we plot rolling 3-year annualized returns of U.S. equities, the 60/40 mix, trend equity, and the tactical 90/60.

The tactical 90/60 model out-performed a 60/40 in 68% of rolling 3-year periods and the trend equity model in 71% of rolling 3-year periods. The tactical 90/60, however, only out-performs U.S. equities in 35% of rolling 3-year periods, with the vast majority of relative out-performance emerging during significant equity drawdown periods.

For investors already allocated to trend equity strategies, portable beta – or portable tactical beta – may represent an alternative source of potential return enhancement. Rather than seeking opportunities for alpha, portable beta allows for an overlay of more traditional risk premia, which may be more reliable from an empirical and academic standpoint.

The potential for increased returns is illustrated below in the rolling 3-year annualized return difference between the tactical 90/60 model and the Newfound U.S. Trend Equity Index.

From Theory to Implementation

In practice, it may be easier to acquire leverage through the use of futures contracts. For example, applying portable bond beta on-top of an existing trend equity strategy may be achieved through the use of 10-year U.S. Treasury futures.

Below we plot the growth of $1 in the Newfound U.S. Trend Equity Index and a tactical 90/60 model implemented with Treasury futures. Annualized return increases from 7.7% to 8.9% and annualized volatility declines from 9.7% to 8.5%. Finally, maximum drawdown decreases from 18.1% to 14.3%.

We believe the increased return reflects the potential return enhancement benefits from introducing further exposure to traditional risk premia, while the reduction in risk reflects the benefit achieved through greater portfolio diversification.

Source: Quandl and Newfound Research. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees, transaction costs, and taxes. Returns assume the reinvestment of all distributions. You cannot invest in an index.

It should be noted, however, that a levered constant maturity 10-year U.S. Treasury index and 10-year U.S. Treasury futures are not the same. The futures contracts are specified such that eligible securities for delivery include Treasury notes with a remaining term to maturity of between 6.5 and 10 years. This means that the investor short the futures contract has the option of which Treasury note to deliver across a wide spectrum of securities with potentially varying characteristics.

In theory, this investor will always choose to deliver the bond that is cheapest. Thus, Treasury futures prices will reflect price changes of this so-calledcheapest-to-deliver bond, which often does not reflect an actual on-the-run 10-year Treasury note.

Treasury futures therefore utilize a “conversion factor” invoicing system referenced to the 6% futures contract standard. Pricing also reflects a basis adjustment that reflects the coupon income a cash bond holder would receive minus financing costs (i.e. the cost of carry) as well as the value of optionality provided to the futures seller.

Below we plot monthly returns of 10-year U.S. Treasury futures versus the excess returns of a constant maturity 10-year U.S. Treasury index. We can see that the futures had a beta of approximately 0.76 over the nearly 20-year period, which closely aligns with the conversion factor over the period.

Source: Quandl and the Federal Reserve of St. Louis. Calculations by Newfound Research.

Despite these differences, futures can represent a highly liquid and cost-effective means of implementing a portable beta strategy. It should be further noted that having a lower “beta” over the last two decades has not necessarily implied a lower return as the basis adjustment can have a considerable impact. We demonstrate this in the graph below by plotting the returns of continuously-rolled 10-year U.S. Treasury futures (rolled on open interest) and the excess return of a constant maturity 10-year U.S. Treasury index.

Conclusion

In a low return environment, portable beta may be a necessary tool for investors to generate the returns they need to hit their financial goals and reduce their risk of failing slow.

Historically, a 90/60 portfolio has outperformed equities with a similar level of risk. However, the short-term dynamics between stocks and bonds can make the volatility of a 90/60 portfolio significantly higher than a simple buy-and-hold equity portfolio. Rising interest rates and inverted yield curves can further confound the potential benefits versus an all-equity portfolio.

Since constant leverage is not a guarantee and we do not know how the future will play out, moving beyond standard portable beta implementations to tactical solutions may augment the potential for risk management and lead to a smoother ride over the short-term.

Getting over the fear of using leverage and derivatives may be an uphill battle for investors, but when used appropriately, these tools can make portfolios work harder. Risks that are known and compensated with premiums can be prudent to take for those willing to venture out and bear them.

If you are interested in learning how Newfound applies the concepts of tactical portable beta to its mandates, please reach out (info@thinknewfound.com).

A Carry-Trend-Hedge Approach to Duration Timing

By Corey Hoffstein

On October 15, 2018

In Carry, Risk & Style Premia, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

In this paper we discuss simple rules for timing exposure to 10-year U.S. Treasuries.
We explore signals based upon the slope of the yield curve (“carry”), prior returns (“trend”), and prior equity returns (“hedge”).
We implement long/short implementations of each strategy covering the time period of 1962-2018.
We find that all three methods improve both total and risk-adjusted returns when compared to long-only exposure to excess bond returns.
Naïve combination of both strategies and signals appears to improve realized risk-adjusted returns, promoting the benefits of process diversification.

Introduction

In this strategy brief, we discuss three trading rules for timing exposure to duration. Specifically, we seek to time the excess returns generated from owning 10-year U.S. Treasury bonds over short rates. This piece is meant as a companion to our prior, longer-form explorations Duration Timing with Style Premiaand Timing Bonds with Value, Momentum, and Carry. In contrast, the trading rules herein are simplistic by design in an effort to highlight the efficacy of the signals.

We explore three different signals in this piece:

The slope of the yield curve (“term spread”);
Prior realized excess bond returns; and
Prior realized equity market returns.

In contrast to prior studies, we do not consider traditional value measures, such as real yields, or explicit estimates of the bond risk premium, as they are less easily calculated. Nevertheless, the signals studied herein capture a variety of potential influences upon bond markets, including inflation shocks, economic shocks, policy shocks, marginal utility shocks, and behavioral anomalies.

The strategies based upon our signals are implemented as dollar-neutral long/short portfolios that go long a constant maturity 10-year U.S. Treasury bond index and short a short-term U.S. Treasury index (assumed to be a 1-year index prior to 1982 and a 3-month index thereafter). We compare these strategies to a “long-only” implementation that is long the 10-year U.S. Treasury bond index and short the short-term U.S. Treasury index in order to capture the excess realized return associated with duration.

Implementing our strategies as dollar-neutral long/short portfolios allows them to be interpreted in a variety of useful manners. For example, one obvious interpretation is an overlay implemented on an existing bond portfolio using Treasury futures. However, another interpretation may simply be to guide investors as to whether to extend or contract their duration exposure around a more intermediate-term bond portfolio (e.g. a 5-year duration).

At the end of the piece, we explore the potential diversification benefits achieved by combining these strategies in both an integrated (i.e. signal combination) and composite (i.e. strategy combination) fashion.

Slope of the Yield Curve

In past research on timing duration, we considered explicit measures of the bond risk premium as well as valuation. In Duration Timing with Style Premiawe used a simple signal based upon real yield, which had the problem of being predominately long over the last several decades. In Timing Bonds with Value, Momentum, and Carry we compared a de-trended real yield against recent levels in an attempt to capture more short-term valuation fluctuations.

In both of these prior research pieces, we also explicitly considered the slope of the yield curve as a predictor of future excess bond returns. One complicating factor to carry signals 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.

Thus, despite being a rather blunt measure, steepness may simultaneously be related to business cycles, credit cycles and monetary policy cycles. To quote Ilmanen (2011):

A steep [yield curve] coincides with high unemployment rate (correlation +0.45) and predictsfast economic growth. [Yield curve] countercyclicality may explain its ability to predict near-term bond and stock returns: high required premia near business cycle troughs result in a steep [yield curve], while low required premia near business cycle peaks result in an inverted [yield curve].

Therefore, while estimates of real yield may seek to be explicit measures of value, we may consider carry to be an ancillary measure as well, as a high carry tends to be associated with a high term premium. In Figure 1 we plot the annualized next month excess bond return based upon the quartile (using the prior 10 years of information) that the term spread falls into. We can see a significant monotonic improvement from the 1^stto the 4^thquartiles, indicating that higher levels of carry, relative to the past, are positive indicators of future returns.

Therefore, we construct our carry strategy as follows:

At the end of each month, calculate the term spread between 10- and 1-year U.S. Treasuries.
Calculate the realized percentile of this spread by comparing it against the prior 10-years of daily term spread measures.
If the carry score is in the top two thirds, go long excess bond returns. If the carry score is in the bottom third, go short excess bond returns.
Trade at the close of the 1^sttrading day of the month.

Returns for this strategy are plotted in Figure 2. Our research suggests that the backtested results of this model can be significantly improved through the use of longer holding periods and portfolio tranching. Another potential improvement is to scale exposure linearly to the current percentile. We will leave these implementations as exercises to readers.

Figure 1

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Carry Long/Short strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Figure 2

Data from 1972-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	2.1%	7.6%	0.27
CARRY L/S	2.6%	7.7%	0.33

Trend in Bond Returns

Momentum, in both its relative and absolute (i.e. “trend”) forms, has a long history among both practitioners and academics (see our summary piece Two Centuries of Momentum).

The literature covering momentum in bond returns, however, varies in precisely whatprior returns matter. There are three primary categories: (1) change in bond yields (e.g. Ilmanen (1997)), (2) total return of individual bonds (e.g. Kolanovic and Wei (2015) and Brooks and Moskowitz (2017)), and (3) total return of bond indices (or futures) (e.g. Asness, Moskowitz, and Pedersen (2013), Durham (2013), and Hurst, Ooi, Pedersen (2014))

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.

In this piece, we elect to measure momentum as an exponentially-weighting average of prior log returns of the total return excess between long and short bond indices. We measure this average at the end of each month and go long duration when it is positive and short duration when it is negative. In Figure 4 we plot the results of this method based upon a variety of lookback periods that approximate 1-, 3-, 6-, and 12-month formation periods.

Figure 3

	MOM 21	MOM 63	MOM 126	MOM 252
MOM 21	1.00	0.87	0.65	0.42
MOM 63	0.87	1.00	0.77	0.53
MOM 126	0.65	0.77	1.00	0.76
MOM 252	0.42	0.53	0.76	1.00

We see varying success in the methods, with only MOM 63 and MOM 256 exhibiting better risk-adjusted return profiles. Despite this long-term success, we can see that MOM 63 remains in a drawdown that began in the early 2000s, highlighting the potential risk of relying too heavily on a specific measure or formation period. In Figure 3 we calculate the correlation between the different momentum strategies. As we found in Measuring Process Diversification in Trend Following, diversification opportunities appear to be available by mixing both short- and long-term formation periods.

With this in mind, we elect for the following momentum implementation:

At the end of each month, calculate both a 21- and 252-day exponentially-weighted moving average of realized daily excess log returns.
When both signals are positive, go long duration; when both signals are negative, go short duration; when signals are mixed, stay flat.
Rebalance at the close of the next trading day.

The backtested results of this strategy are displayed in Figure 5.

As with carry, we find that there are potential craftsmanship improvements that can be made with this strategy. For example, implementing with four tranches, weekly rebalances appears to significantly improve backtested risk-adjusted returns. Furthermore, there may be benefits that can be achieved by incorporating other means of measuring trends as well as other lookback periods (see Diversifying the What, When, and How of Trend Following and Measuring Process Diversification in Trend Following).

Figure 4

Data from 1963-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	1.5%	7.3%	0.21
MOM 21	1.4%	7.5%	0.19
MOM 63	1.8%	7.4%	0.25
MOM 128	1.3%	7.4%	0.18
MOM 252	1.9%	7.4%	0.26

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Momentum strategies do not reflect any strategies offered or managed by Newfound Research and were constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Figure 5

Data from 1963-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	1.5%	7.2%	0.21
MOM L/S	1.7%	6.3%	0.28

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Momentum Long/Short strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Safe-Haven Premium

Stocks and bonds generally exhibit a positive correlation over time. One thesis for this long-term relationship is the present value model, which argues that declining yields, and hence increasing bond prices, increase the value of future discounted cash flows and therefore the fair value of equities. Despite this long-term relationship, shocks in economic growth, inflation, and even monetary policy can overwhelm the discount rate thesis and create a regime-varying correlation structure.

For example, empirical evidence suggests that high quality bonds can exhibit a safe haven premium during periods of economic stress. Using real equity prices as a proxy for wealth, Ilmanen (1995) finds that “wealth-dependent relative risk aversion appears to be an important source of bond return predictability.” Specifically, inverse wealth is a significant positive predictor of future excess bond returns at both world and local (U.S., Canada, Japan, Germany, France, and United Kingdom) levels. Ilmanen (2003) finds that, “stock-bond correlations are more likely to be negative when inflation is low, growth is slow, equities are weak, and volatility is high.”

To capitalize on this safe-haven premium, we derive a signal based upon prior equity returns. Specifically, we utilize an exponentially weighted average of prior log returns to estimate the underlying trend of equities. We then compare this estimate to a 10-year rolling window of prior estimates, calculating the current percentile.

In Figure 6 we plot the annualized excess bond return for the month following, assuming signals are generated at the close of each month and trades are placed at the close of the following trading day. We can see several effects. First, next month returns for 1^stquartile equity momentum – i.e. very poor equity returns – tends to be significantly higher than other quartiles. Second, excess bond returns in the month following very strong equity returns tend to be poor. We would posit that these two effects are two sides of the same coin: the safe-haven premium during 1^stquartile periods and an unwind of the premium in 4^thquartile periods. Finally, we can see that 2^ndand 3^rdquartile returns tend to be positive, in line with the generally positive excess bond return over the measured period.

In an effort to isolate the safe-haven premium, we construct the following strategy:

At the end of each month, calculate an equity momentum measure by taking a 63-day exponentially weighted average of prior daily log-returns.
Calculate the realized percentile of this momentum measure by comparing it against the prior 10-years of daily momentum measures.
If the momentum score is in the bottom quartile, go long excess bond returns. If the momentum score is in the top quartile, go short excess bond returns. Otherwise, remain flat.
Trade at the close of the 1^sttrading day of the month.

Returns for this strategy are plotted in Figure 7. As expected based upon the quartile design, the strategy only spends 24% of its time long, 23% of its time short, and the remainder of its time flat. Despite this even split in time, approximately 2/3^rdsof the strategy’s return comes from the periods when the strategy is long.

Figure 6

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Equity Momentum Long/Short strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Figure 7

Data from 1962-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	1.5%	7.2%	0.21
Equity Mom L/S	1.9%	5.7%	0.34

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Equity Momentum Long/Short strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Combining Signals

Despite trading the same underlying instrument, variation in strategy construction means that we can likely benefit from process diversification in constructing a combined strategy. Figure 8 quantifies the available diversification by measuring full-period correlations among the strategies from joint inception (1972). We can also see that the strategies exhibit low correlation to the Long Only implementation, suggesting that they may introduce diversification benefits to a strategic duration allocation as well.

Figure 8

	LONG ONLY	CARRY L/S	MOM L/S	EQ MOM L/S
LONG ONLY	1.00	0.42	0.33	-0.09
CARRY L/S	0.42	1.00	0.40	-0.09
MOM L/S	0.33	0.40	1.00	-0.13
EQ MOM L/S	-0.10	-0.10	-0.19	1.00

We explore two different implementations of a diversified strategy. In the first, we simply combine the three strategies in equal-weight, rebalancing on a monthly basis. This implementation can be interpreted as three sleeves of a larger portfolio construction. In the second implementation, we combine underlying long/short signals. When the net signal is positive, the strategy goes 100% long duration and when the signal is negative, it goes 100% short. This can be thought of as an integrated approach that takes a majority-rules voting approach. Results for these strategies are plotted in Figure 9. We note the substantial increase in the backtested Sharpe Ratio of these diversified approaches in comparison to their underlying components outlined in prior sections.

It is important to note that despite strong total and risk-adjusted returns, the strategies spend only approximately 54% of their time net-long duration, with 19% of their time spent flat and 27% of their time spent short. While slightly biased long, this breakdown provides evidence that strategies are not simply the beneficiaries of a bull market in duration over the prior several decades.

Figure 9

Data from 1972-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	2.1%	7.6%	0.27
Combined L/S	2.5%	4.3%	0.58
Integrated L/S	3.5%	7.1%	0.49

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. Neither the Combined Long/Short or Integrated Long/Short strategies reflect any strategy offered or managed by Newfound Research and were constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Conclusion

In this research brief, we continued our exploration of duration timing strategies. We aimed to implement several signals that were simple by construction. Specifically, we evaluated the impact of term spread, prior excess bond returns, and prior equity returns on next month’s excess bond returns. Despite their simplicity, we find that all three signals can potentially offer investors insight for tactical timing decisions.

While we believe that significant craftsmanship improvements can be made in all three strategies, low hanging improvement may simply come from combining the approaches. We find a meaningful improvement in Sharpe Ratio by naively combining these strategies in both a sleeve-based and integrated signal fashion.

Bibliography

Asness, Clifford S. and Moskowitz, Tobias J. and Pedersen, Lasse Heje, Value and Momentum Everywhere (June 1, 2012). Chicago Booth Research Paper No. 12-53; Fama-Miller Working Paper. Available at SSRN: https://ssrn.com/abstract=2174501 or http://dx.doi.org/10.2139/ssrn.2174501

Brooks, Jordan and Moskowitz, Tobias J., Yield Curve Premia (July 1, 2017). Available at SSRN: https://ssrn.com/abstract=2956411 or http://dx.doi.org/10.2139/ssrn.2956411

Durham, J. Benson, Momentum and the Term Structure of Interest Rates (December 1, 2013). FRB of New York Staff Report No. 657. Available at SSRN: https://ssrn.com/abstract=2377379 or http://dx.doi.org/10.2139/ssrn.2377379

Hurst, Brian and Ooi, Yao Hua and Pedersen, Lasse Heje, A Century of Evidence on Trend-Following Investing (June 27, 2017). Available at SSRN: https://ssrn.com/abstract=2993026 or http://dx.doi.org/10.2139/ssrn.2993026

Ilmanen, Antti, Time-Varying Expected Returns in International Bond Markets, Journal of Finance, Vol. 50, No. 2, 1995, pp. 481-506.

Ilmanen, Antti, Forecasting U.S. Bond Returns, Journal of Fixed Income, Vol. 7, No. 1, 1997, pp. 22-37.

Ilmanen, Antti, Stock-Bond Correlations, Journal of Fixed Income, Vol. 13, No. 2, 2003, pp. 55-66.

Ilmanen, Antti. Expected Returns an Investor’s Guide to Harvesting Market Rewards. John Wiley, 2011.

Kolanovic, Marko, and Wei, Zhen, Momentum Strategies Across Asset Classes (April 2015). Available at https://www.cmegroup.com/education/files/jpm-momentum-strategies-2015-04-15-1681565.pdf

Timing Bonds with Value, Momentum, and Carry

By Corey Hoffstein

On January 29, 2018

In Carry, Momentum, Popular, Risk & Style Premia, Value, Weekly Commentary

This post is available as a PDF download here.

Summary

Bond timing has been difficult for the past 35 years as interest rates have declined, especially since bonds started the period with high coupons.
With low current rates and higher durations, the stage may be set for systematic, factor-based bond investing.
Strategies such as value, momentum, and carry have done well historically, especially on a risk-adjusted basis.
Diversifying across these three strategies and employing prudent leverage takes advantage of differences in the processes and the information contained in their joint decisions.

This commentary is a slight re-visit and update to a commentary we wrote last summer, Duration Timing with Style Premia[1]. The models we use here are similar in nature, but have been updated with further details and discussion, warranting a new piece.

Historically Speaking, This is a Bad Idea

Let’s just get this out of the way up front: the results of this study are probably not going to look great.

Since interest rates peaked in September 1981, the excess return of a constant maturity 10-year U.S. Treasury bond index has been 3.6% annualized with only 7.3% volatility and a maximum drawdown of 16.4%. In other words, about as close to a straight line up and to the right as you can get.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

With the benefit of hindsight, this makes sense. As we demonstrated in Did Declining Rates Actually Matter?[2], the vast majority of bond index returns over the last 30+ years have been a result of the high average coupon rate. High average coupons kept duration suppressed, meaning that changes in rates produced less volatile movements in bond prices.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

Ultimately, we estimate that roll return and benefits from downward shifts in the yield curve only accounted for approximately 30% of the annualized return.

Put another way, whenever you got “out” of bonds over this period, there was a very significant opportunity cost you were experiencing in terms of foregone interest payments, which accounted for 70% of the total return.

If we use this excess return as our benchmark, we’ve made the task nearly impossible for ourselves. Consider that if we are making “in or out” tactical decisions (i.e. no leverage or shorting) and our benchmark is fully invested at all times, we can only outperform due to our “out” calls. Relative to the long-only benchmark, we get no credit for correct “in” calls since correct “in” calls mean we are simply keeping up with the benchmark. (Note: Broadly speaking, this highlights the problems with applying traditional benchmarks to tactical strategies.) In a period of consistently positive returns, our “out” calls must be very accurate, in fact probably unrealistically accurate, to be able to outperform.

When you put this all together, we’re basically asking, “Can you create a tactical strategy that can only outperform based upon its calls to get out of the market over a period of time when there was never a good time to sell?”

The answer, barring some serious data mining, is probably, “No.”

**This Might Now be a Good Idea**

Yet this idea might have legs.

Since the 10-year rate peaked in 1981, the duration of a constant maturity 10-year U.S. bond index has climbed from 4.8 to 8.7. In other words, bonds are now 1.8x more sensitive to changes in interest rates than they were 35 years ago.

If we decompose bond returns in the post-crisis era, we can see that shifts in the yield curve have played a large role in year-to-year performance. The simple intuition is that as coupons get smaller, they are less effective as cushions against rate volatility.

Higher durations and lower coupons are a potential double whammy when it comes to fixed income volatility.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

With rates low and durations high, strategies like value, momentum, and carry may afford us more risk-managed access to fixed income.

Timing Bonds with Value

Following the standard approach taken in most literature, we will use real yields as our measure of value. Specifically, we will estimate real yield by taking the current 10-year U.S. Treasury rate minus the 10-year forecasted inflation rate from Philadelphia Federal Reserve’s Survey of Professional Forecasters.[3]

To come up with our value timing signal, we will compare real yield to a 3-year exponentially weighted average of real yield.

Here we need to be a bit careful. With a secular decline in real yields over the last 30 years, comparing current real yield against a trailing average of real yield will almost surely lead to an overvalued conclusion, as the trailing average will likely be higher.

Thus, we need to de-trend twice. We first subtract real yield from the trailing average, and then subtract this difference from a trailing average of differences. Note that if there is no secular change in real yields over time, this second step should have zero impact. What this is measuring is the deviation of real yields relative to any linear trend.

After both of these steps, we are left with an estimate of how far our real rates are away from fair value, where fair value is defined by our particular methodology rather than any type of economic analysis. When real rates are below our fair value estimate, we believe they are overvalued and thus expect rates to go up. Similarly, when rates are above our fair value estimate, we believe they are undervalued and thus expect them to go down.

Source: Federal Reserve of St. Louis. Philadelphia Federal Reserve. Calculations by Newfound Research.

Before we can use this valuation measure as our signal, we need to take one more step. In the graph above, we see that the deviation from fair value in September 1993 was approximately the same as it was in June 2003: -130bps (implying that rates were 130bps below fair value and therefore bonds were overvalued). However, in 1993, rates were at about 5.3% while in 2003 rates were closer to 3.3%. Furthermore, duration was about 0.5 higher in 2003 than it was 1993.

In other words, a -130bps deviation from fair value does not mean the same thing in all environments.

One way of dealing with this is by forecasting the actual bond return over the next 12 months, including any coupons earned, by assuming real rates revert to fair value (and taking into account any roll benefits due to yield curve steepness). This transformation leaves us with an actual forecast of expected return.

We need to be careful, however, as our question of whether to invest or not is not simply based upon whether the bond index has a positive expected return. Rather, it is whether it has a positive expected return in excess of our alternative investment. In this case, that is “cash.” Here, we will proxy cash with a constant maturity 1-year U.S. Treasury index.

Thus, we need to net out the expected return from the 1-year position, which is just its yield. [4]

Source: Federal Reserve of St. Louis. Philadelphia Federal Reserve. Calculations by Newfound Research.

While the differences here are subtle, had our alternative position been something like a 5-year U.S. Treasury Index, we may see much larger swings as the impact of re-valuation and roll can be much larger.

Using this total expected return, we can create a simple timing model that goes long the 10-year index and short cash when expected excess return is positive and short the 10-year index and long cash when expected excess return is negative. As we are forecasting our returns over a 1-year period, we will employ a 1-year hold with 52 overlapping portfolios to mitigate the impact of timing luck.

We plot the results of the strategy below.

Source: Federal Reserve of St. Louis. Philadelphia Federal Reserve. Calculations by Newfound Research. Results are hypothetical and backtested. Past performance is not a guarantee of future results. Returns are gross of all fees (including management fees, transaction costs, and taxes). Returns assume the reinvestment of all income and distributions.

The value strategy return matches the 10-year index excess return nearly exactly (2.1% vs 2.0%) with just 70% of the volatility (5.0% vs 7.3%) and 55% of the max drawdown (19.8% versus 36.2%).

Timing Bonds with Momentum

For all the hoops we had to jump through with value, the momentum strategy will be fairly straightforward.

We will simply look at the trailing 12-1 month total return of the index versus the alternative (e.g. the 10-year index vs. the 1-year index) and invest in the security that has outperformed and short the other. For example, if the 12-1 month total return for the 10-year index exceeds that of the 1-year index, we will go long the 10-year and short the 1-year, and vice versa.

Since momentum tends to decay quickly, we will use a 1-month holding period, implemented with four overlapping portfolios.

(Note that this backtest starts earlier than the value backtest because it only requires 12 months of returns to create a trading signal versus 6 years of data – 3 for the value anchor and 3 to de-trend the data – for the value score.)

Compared to the buy-and-hold approach, the momentum strategy increases annualized return by 0.5% (1.7% versus 1.2%) while closely matching volatility (6.7% versus 6.9%) and having less than half the drawdown (20.9% versus 45.7%).

Of course, it cannot be ignored that the momentum strategy has largely gone sideways since the early 1990s. In contrast to how we created our bottom-up value return expectation, this momentum approach is a very blunt instrument. In fact, using momentum this way means that returns due to differences in yield, roll yield, and re-valuation are all captured simultaneously. We can really think of decomposing our momentum signal as:

10-Year Return – 1-Year Return = (10-Year Yield – 1-Year Yield) + (10-Year Roll – 1-Year Roll) + (10-Year Shift – 1-Year Shift)

Our momentum score is indiscriminately assuming momentum in all the components. Yet when we actually go to put on our trade, we do not need to assume momentum will persist in the yield and roll differences: we have enough data to measure them explicitly.

With this framework, we can isolate momentum in the shift component by removing yield and roll return expectations from total returns.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

Ultimately, the difference in signals is minor for our use of 10-year versus 1-year, though it may be far less so in cases like trading the 10-year versus the 5-year. The actual difference in resulting performance, however, is more pronounced.

Ironically, by doing worse mid-period, the adjusted momentum long/short strategy appears to be more consistent in its return from the early 1990s through present. We’re certain this is more noise than signal, however.

Timing Bonds with Carry

Carry is the return we earn by simply holding the investment, assuming everything else stays constant. For a bond, this would be the yield-to-maturity. For a constant maturity bond index, this would be the coupon yield (assuming we purchase our bonds at par) plus any roll yield we capture.

Our carry signal, then, will simply be the difference in yields between the 10-year and 1-year rates plus the difference in expected roll return.

For simplicity, we will assume roll over a 1-year period, which makes the expected roll of the 1-year bond zero. Thus, this really becomes, more or less, a signal to be long the 10-year when the yield curve is positively sloped, and long the 1-year when it is negatively sloped.

As we are forecasting returns over the next 12-month period, we will use a 12-month holding period and implement with 52 overlapping portfolios.

Again, were we comparing the 10-year versus the 5-year instead of the 10-year versus the 1-year, the roll can have a large impact. If the curve is fairly flat between the 5- and 10-year rates, but gets steep between the 5- and the 1-year rates, then the roll expectation from the 5-year can actually overcome the yield difference between the 5- and the 10-year rates.

Building a Portfolio of Strategies

With three separate methods to timing bonds, we can likely benefit from process diversification by constructing a portfolio of the approaches. The simplest method to do so is to simply give each strategy an equal share. Below we plot the results.

Indeed, by looking at per-strategy performance, we can see a dramatic jump in Information Ratio and an exceptional reduction in maximum drawdown. In fact, the maximum drawdown of the equal weight approach is below that of any of the individual strategies, highlighting the potential benefit of diversifying away conflicting investment signals.

Strategy	Annualized Return	Annualized Volatility	Information Ratio	Max Drawdown
10-Year Index Excess Return	2.0%	7.3%	0.27	36.2%
Value L/S	2.0%	5.0%	0.41	19.8%
Momentum L/S	1.9%	6.9%	0.27	20.9%
Carry L/S	2.5%	6.6%	0.38	20.1%
Equal Weight	2.3%	4.0%	0.57	10.2%

One potential way to improve upon the portfolio construction is by taking into account the actual covariance structure among the strategies (correlations shown in the table below). We can see that, historically, momentum and carry have been fairly positively correlated while value has been independent, if not slightly negatively correlated. Therefore, an equal-weight approach may not be taking full advantage of the diversification opportunities presented.

	Value L/S	Momentum L/S	Carry L/S
Value L/S	1.0	-0.2	-0.1
Momentum L/S	-0.2	1.0	0.6
Carry L/S	-0.1	0.6	1.0

To avoid making any assumptions about the expected returns of the strategies, we will construct a portfolio where each strategy contributes equally to the overall risk profile (“ERC”). So as to avoid look-ahead bias, we will use an expanding window to compute our covariance matrix (seeding with at least 5 years of data). While the weights vary slightly over time, the result is a portfolio where the average weights are 43% value, 27% momentum, and 30% carry.

The ERC approach matches the equal-weight approach in annualized return, but reduces annualized volatility from 4.2% to 3.8%, thereby increasing the information ratio from 0.59 to 0.64. The maximum drawdown also falls from 10.2% to 8.7%.

A second step we can take is to try to use the “collective intelligence” of the strategies to set our risk budget. For example, we can have our portfolio target the long-term volatility of the 10-year Index Excess Return, but scale this target between 0-2x depending on how invested we are.

For example, if the strategies are, in aggregate, only 20% invested, then our target volatility would be 0.4x that of the long-term volatility. If they are 100% invested, though, then we would target 2x the long-term volatility. When the strategies are providing mixed signals, we will simply target the long-term volatility level.

Unfortunately, such an approach requires going beyond 100% notional exposure, often requiring 2x – if not 3x – leverage when current volatility is low. That makes this system less useful in the context of “bond timing” since we are now placing a bet on current volatility remaining constant and saying that our long-term volatility is an appropriate target.

One way to limit the leverage is to increase how much we are willing to scale our risk target, but truncate our notional exposure at 100% per leg. For example, we can scale our risk target between 0-4x. This may seem very risky (indeed, an asymmetric bet), but since we are clamping our notional exposure to 100% per leg, we should recognize that we will only hit that risk level if current volatility is greater than 4x that of the long-term average and all the strategies recommend full investment.

With a little mental arithmetic, the approach it is equivalent to saying: “multiply the weights by 4x and then scale based on current volatility relative to historical volatility.” By clamping weights between -100% and +100%, the volatility targeting really does not come into play until current volatility is 4x that of long-term volatility. In effect, we leg into our trades more quickly, but de-risk when volatility spikes to abnormally high levels.

Compared to the buy-and-hold model, the variable risk ERC model increases annualized returns by 90bps (2.4% to 3.3%), reduces volatility by 260bps (7.6% to 5.0%), doubles the information ratio (0.31 to 0.66) and halves the maximum drawdown (30% to 15%).

There is no magic to the choice of “4” above: it is just an example. In general, we can say that as the number goes higher, the strategy will approach a binary in-or-out system and the volatility scaling will have less and less impact.

Conclusion

Bond timing has been hard for the past 35 years as interest rates have declined. Small current coupons do not provide nearly the cushion against rate volatility that investors have been used to, and these lower rates mean that bonds are also exposed to higher duration.

These two factors are a potential double whammy when it comes to fixed income volatility.

This can open the door for systematic, factor-based bond investing.

Value, momentum, and carry strategies have all historically outperformed a buy-and-hold bond strategy on a risk adjusted basis despite the bond bull market. Diversifying across these three strategies and employing prudent leverage takes advantage of differences in the processes and the information contained in their joint decisions.

We should point out that in the application of this approach, there were multiple periods of time in the backtest where the strategy went years without being substantially invested. A smooth, nearly 40-year equity curve tells us very little about what it is actually like to sit on the sidelines during these periods and we should not underestimate the emotional burden of using such a timing strategy.

Even with low rates and high rate movement sensitivity, bonds can still play a key role within a portfolio. Going forward, however, it may be prudent for investors to consider complementary risk-management techniques within their bond sleeve.

[1] https://blog.thinknewfound.com/2017/06/duration-timing-style-premia/

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

[3] Prior to the availability of the 10-year inflation estimate, the 1-year estimate is utilized; prior to the 1-year inflation estimate availability, the 1-year GDP price index estimate is utilized.

[4] This is not strictly true, as it largely depends on how the constant maturity indices are constructed. For example, if they are rebalanced on a monthly basis, we would expect that re-valuation and roll would have impact on the 1-year index return. We would also have to alter the horizon we are forecasting over as we are assuming we are rolling into new bonds (with different yields) more frequently.

Duration Timing with Style Premia

By Corey Hoffstein

On June 26, 2017

In Carry, Risk & Style Premia, Trend, Value, Weekly Commentary

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.

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

Tag: carry Page 1 of 2

Quantitative Styles and Multi-Sector Bonds

Summary­

Momentum

Carry

Value

Reversal

Volatility

Conclusion

Tactical Portable Beta

Summary­

90/60 Through the Decades

Getting Tactical with a 90/60

Equity Signals

Bond Signals

Combining Equity and Bond Signals into a Tactical 90/60

From Theory to Implementation

Conclusion

A Carry-Trend-Hedge Approach to Duration Timing

Summary­

Introduction

Slope of the Yield Curve

Trend in Bond Returns

Safe-Haven Premium

Combining Signals

Conclusion

Bibliography

Timing Bonds with Value, Momentum, and Carry

Summary­­

Historically Speaking, This is a Bad Idea

This Might Now be a Good Idea

Timing Bonds with Value

Timing Bonds with Momentum

Timing Bonds with Carry

Building a Portfolio of Strategies

Conclusion

Duration Timing with Style Premia

Summary­­

Timing with Value

Timing with Momentum

Timing with Carry

Explicitly Estimating the Bond Risk Premium

Diversifying Style Premia

Did Timing Add Value?

Robustness Testing: International Markets

Robustness Testing: Different Time Period

Conclusion

Summary

Summary

Summary

Summary

**This Might Now be a Good Idea**

Summary