Tag: momentum Page 2 of 4

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).

Tightening the Uncertain Payout of Trend-Following

By Nathan Faber

On January 28, 2019

In Craftsmanship, Portfolio Construction, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

Long/flat trend-following strategies have historically delivered payout profiles similar to those of call options, with positive payouts for larger positive underlying asset returns and slightly negative payouts for near-zero or negative underlying returns.
However, this functional relationship contains a fair amount of uncertainty for any given trend-following model and lookback period.
In portfolio construction, we tend to favor assets that have a combination of high expected returns or diversifying return profiles.
Since broad investor behavior provides a basis for systematic trend-following models to have positive expected returns, taking a multi-model approach to trend-following can be used to reduce the variance around the expected payout profile.

Introduction

Over the past few months, we have written much about model diversification as a tactic for managing specification risk, even with specific case studies. When we consider the three axes of diversification, model diversification pertains to the “how” axis, which focuses on strategies that have the same overarching objective but go about achieving it in different ways.

Long/flat trend-following, especially with equity investments, aims to protect capital on the downside while maintaining participation in positive markets. This leads to a payout profile that looks similar to that of a call option.¹

However, while a call option offers a defined payout based on the price of an underlying asset and a specific maturity date, a trend-following strategy does not provide such a guarantee. There is a degree of uncertainty.

The good news is that uncertainty can potentially be diversified given the right combinations of assets or strategies.

In this commentary, we will dive into a number of trend-following strategies to see what has historically led to this benefit and the extent that diversification would reduce the uncertainty around the expected payoff.

Diversification in Trend-Following

The justification for a multi-model approach boils down to a simple diversification argument.

Say you would like to include trend-following in a portfolio as a way to manage risk (e.g. sequence risk for a retiree). There is academic and empirical evidence that trend-following works over a variety of time horizons, generally ranging from 3 to 12 months. And there are many ways to measure trends, such as moving average crossovers, trailing returns, deviations from moving averages, risk adjusted returns, etc.

The basis for deciding ex-ante which variant will be the best over our own investment horizon is tenuous at best. Backtests can show one iteration outperforming over a given time horizon, but most of the differences between strategies are either noise from a statistical point of view or realized over a longer time period than any investor has the lifespan (or mettle) to endure.

However, we expect each one to generate positive returns over a sufficiently long time horizon. Whether this is one year, three years, five years, 10 years, 50 years… we don’t know. What we do know is that out of the multitude the variations of trend-following, we are very likely to pick one that is not the best or even in the top segment of the pack in the short-term.

From a volatility standpoint, when the strategies are fully invested, they will have volatility equal to the underlying asset. Determining exactly when the diversification benefits will come in to play – that is, when some strategies are invested and others are not – is a fool’s errand.

Modern portfolio theory has done a disservice in making correlation seem like an inherent trait of an investment. It is not.

Looking at multiple trend-following strategies that can coincide precisely for stretches of time before behaving completely differently from each other, makes many portfolio construction techniques useless. We do not expect correlation benefits to always be present. These are nonlinear strategies, and fitting them into a linear world does not make sense.

If you have pinned up ReSolve Asset Management’s flow chart of portfolio choice above your desk (from Portfolio Optimization: A General Framework for Portfolio Choice), then the decision on this is easy.

Source: ReSolve Asset Management. Reprinted with permission

From this simple framework, we can break the different performance regimes down as follows:

The Math Behind the Diversification

The expected value of a trend-following strategy can be thought of as a function of the underlying security return:

Where the subscript i is used to indicate that the function is dependent on the specific trend-following strategy.

If we combine multiple trend-following strategies into a portfolio, then the expectation is the average of these functions (assuming an equal weight portfolio per the ReSolve chart above):

What’s left to determine is the functional form of f.

Continuing in the vein of the call option payoff profile, we can use the Black-Scholes equation as the functional form (with the risk-free rate set to 0). This leaves three parameters with which to fit the formula to the data: the volatility (with the time to expiration term lumped in, i.e. sigma * sqrt(T-t)), the strike, and the initial cost of the option.

where d₁ and d₂ are defined in the standard fashion and N is the cumulative normal distribution function.

r_K is the strike price in the option formula expressed as a percent relative to the current value of the underlying security.

In the following example, we will attempt to provide some meaning to the fitted parameters. However, keep in mind that any mapping is not necessarily one-to-one with the option parameters. The functional form may apply, but the parameters are not ones that were set in stone ex-ante.²

An Example: Trend-Following on the S&P 500

As an example, we will consider a trend-following model on the S&P 500 using monthly time-series momentum with lookback windows ranging from 4 to 16 months. The risk-free rate was used when the trends were negative.

The graph below shows an example of the option price fit to the data using a least-squares regression for the 15-month time series momentum strategy using rolling 3-year returns from 1927 to 2018.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The volatility parameter was 9.5%, the strike was 2.3%, and the cost was 1.7%.

What do these parameters mean?

As we said before this can be a bit tricky. Painting in broad strokes:

The volatility parameter describes how “elbowed” payoff profile is. Small values are akin to an option close to expiry where the payoff profile changes abruptly around the strike price. Larger values yield a more gentle change in slope.
The strike represents the point at which the payoff profile changes from participation to protection using trend-following lingo. In the example where the strike is 2.3%, this means that the strategy would be expected to start protecting capital when the S&P 500 return is less than 2.3%. There is some cost associated with this value being high.
The cost is the vertical shift of the payoff profile, but it is not good to think of it as the insurance premium of the trend-following strategy. It is only one piece. To see why this is the case, consider that the fitted volatility may be large and that the option price curve may be significantly above the final payout curve (i.e. if the time-scaled volatility went to zero).

So what is the actual “cost” of the strategy?

With trend-following, since whipsaw is generally the largest potential detractor, we will look at the expected return on the strategy when the S&P 500 is flat, that is, an absence of an average trend. It is possible for the cost to be negative, indicating a positive expected trend-following return when the market was flat.

Looking at the actual fit of the data from a statistical perspective, the largest deviations from the expected value (the residuals from the regression) are seen during large positive returns for the S&P 500, mainly coming out of the Great Depression. This characteristic of individual trend-following models is generally attributable to the delay in getting back into the market after a prolonged, severe drawdown due to the time it takes for a new positive trend to be established.

Part of the seemingly large number of outliers is simply due to the fact that these returns exhibit autocorrelation since the periods are rolling, which means that the data points have some overlap. If we filtered the data down into non-overlapping periods, some of these outliers would be removed.

The outliers that remain are a fact of trend-following strategies. While this fact of trend-following cannot be totally removed, some of the outliers may be managed using multiple lookback periods.

The following chart illustrates the expected values for the trend-following strategies over all the lookback periods.

The shorter-term lookback windows have the expected value curves that are less horizontal on the left side of the chart (higher volatility parameter).

As we said before the cost of the trend-following strategy can be represented by the strategy’s expected return when the S&P 500 is flat. This can be thought of as the premium for the insurance policy of the trend-following strategies.

The blend does not have the lowest cost, but this cost is only one part of the picture. The parameters for the expected value functions do nothing to capture the distribution of the data around – either above or below – these curves.

The diversification benefits are best seen in the distribution of the rolling returns around the expected value functions.

Now with a more comprehensive picture of the potential outcomes, a cost difference of even 3% is less than one standard deviation, making the blended strategy much more robust to whipsaw for the potential range of S&P 500 returns.

As a side note, the cost of the short window (4 and 5 month) strategies is relatively high. However, since there are many rolling periods when these models are the best performing of the group, there can still be a benefit to including them. With them in the blend, we still see a reduction in the dispersion around the expected value function.

Expanding the Multitude of Models

To take the example even further down the multi-model path, we can look at the same analysis for varying lookback windows for a price-minus-moving-average model and an exponentially weighted moving average model.

And finally, we can combine all three trend-following measurement style blends into a final composite blend.

As with nearly every study on diversification, the overall blend is not the best by all metrics. In this case, its cost is higher than the EWMA blended model and its dispersion is higher than the TS blended model. But it exhibits the type of middle-of-the-road characteristics that lead to results that are robust to an uncertain future.

Conclusion

Long/flat trend-following strategies have payoff profiles similar to call options, with larger upsides and limited downsides. Unlike call options (and all derivative securities) that pay a deterministic amount based on the underlying securities prices, the payoff of a trend-following strategy is uncertain,

Using historical data, we can calculate the expected payoff profile and the dispersion around it. We find that by blending a variety of trend-following models, both in how they measure trend and the length of the lookback window, we can often reduce the implied cost of the call option and the dispersion of outcomes.

A backtest of an individual trend-following model can look the best over a given time period, but there are many factors that play into whether that performance will be valid going forward. The assets have to behave similarly, potentially both on an absolute and relative basis, and an investor has to hold the investment for a long enough time to weather short-term underperformance.

A multi-model approach can address both of these.

It will reduce the model specification risk that is present ex-ante. It will not pick the best model, but then again, it will not pick the worst.

From an investor perspective, this diversification reduces the spread of outcomes which can lead to an easier product to hold as a long-term investment. Diversification among the models may not always be present (i.e. when style risk dominates and all trend-following strategies do poorly), but when it is, it reduces the chance of taking on uncompensated risks.

Taking on compensated risks is a necessary part of investing, and in the case of trend-following, the style risk is something we desire. Removing as many uncompensated risks as possible leads to more pure forms of this style risk and strategies that are robust to unfavorable specifications.

Fragility Case Study: Dual Momentum GEM

By Corey Hoffstein

On January 14, 2019

In Craftsmanship, Momentum, Popular, Portfolio Construction, Risk Management, Trend

This post is available as a PDF download here.

Summary

Recent market volatility has caused many tactical models to make sudden and significant changes in their allocation profiles.
Periods such as Q4 2018 highlight model specification risk: the sensitivity of a strategy’s performance to specific implementation decisions.
We explore this idea with a case study, using the popular Dual Momentum GEM strategy and a variety of lookback horizons for portfolio formation.
We demonstrate that the year-to-year performance difference can span hundreds, if not thousands, of basis points between the implementations.
By simply diversifying across multiple implementations, we can dramatically reduce model specification risk and even potentially see improvements in realized metrics such as Sharpe ratio and maximum drawdown.

Introduction

Among do-it-yourself tactical investors, Gary Antonacci’s Dual Momentum is the strategy we tend to see implemented the most. The Dual Momentum approach is simple: by combining both relative momentum and absolute momentum (i.e. trend following), Dual Momentum seeks to rotate into areas of relative strength while preserving the flexibility to shift entirely to safety assets (e.g. short-term U.S. Treasury bills) during periods of pervasive, negative trends.

In our experience, the precise implementation of Dual Momentum tends to vary (with various bells-and-whistles applied) from practitioner to practitioner. The most popular benchmark model, however, is the Global Equities Momentum (“GEM”), with some variation of Dual Momentum Sector Rotation (“DMSR”) a close second.

Recently, we’ve spoken to several members in our extended community who have bemoaned the fact that Dual Momentum kept them mostly aggressively positioned in Q4 2018 and signaled a defensive shift at the beginning of January 2019, at which point the S&P 500 was already in a -14% drawdown (having peaked at over -19% on December 24^th). Several DIYers even decided to override their signal in some capacity, either ignoring it entirely, waiting a few days for “confirmation,” or implementing some sort of “half-and-half” rule where they are taking a partially defensive stance.

Ignoring the fact that a decision to override a systematic model somewhat defeats the whole point of being systematic in the first place, this sort of behavior highlights another very important truth: there is a significant gap of risk that exists between the long-term supporting evidence of an investment style (e.g. momentum and trend) and the precise strategy we attempt to implement with (e.g. Dual Momentum GEM).

At Newfound, we call that gap model specification risk. There is significant evidence supporting both momentum and trend as quantitative styles, but the precise means by which we measure these concepts can lead to dramatically different portfolios and outcomes. When a portfolio’s returns are highly sensitive to its specification – i.e. slight variation in returns or model parameters lead to dramatically different return profiles – we label the strategy as fragile.

In this brief commentary, we will use the Global Equities Momentum (“GEM”) strategy as a case study in fragility.

Global Equities Momentum (“GEM”)

To implement the GEM strategy, an investor merely needs to follow the decision tree below at the end of each month.

From a practitioner stand-point, there are several attractive features about this model. First, it is based upon the long-run evidence of both trend-following and momentum. Second, it is very easy to model and generate signals for. Finally, it is fairly light-weight from an implementation perspective: only twelve potential rebalances a year (and often much less), with the portfolio only holding one ETF at a time.

Despite the evidence that “simple beats complex,” the simplicity of GEM belies its inherent fragility. Below we plot the equity curves for GEM implementations that employ different lookback horizons for measuring trend and momentum, ranging from 6- to 12-months.

Source: CSI Analytics. Calculations by Newfound Research. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees except for underlying ETF expense ratios. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

We can see a significant dispersion in potential terminal wealth. That dispersion, however, is not necessarily consistent with the notion that one formation period is inherently better than another. While we would argue, ex-ante, that there should be little performance difference between a 9-month and 10-month lookback – they both, after all, capture the notion of “intermediate-term trends” – the former returned just 43.1% over the period while the latter returned 146.1%.

These total return figures further hide the year-to-year disparity that exists. The 9-month model, for example, was not a consistent loser. Below we plot these results, highlighting both the best (blue) and worst (orange) performing specifications. We see that the yearly spread between these strategies can be hundreds-to-thousands of basis points; consider that in 2010, the strategy formed using a 10-month lookback returned 12.2% while the strategy formed using a 9-month lookback returned -9.31%.

Same thesis. Same strategy. Slightly different specification. Dramatically different outcomes. That single year is likely the difference between hired and fired for most advisors and asset managers.

☞ Explore a diversified approach with the Newfound/ReSolve Robust Equity Momentum Index.

For those bemoaning their 2018 return, note that the 10-month specification would have netted a positive result! That specification turned defensive at the end of October.

Now, some may cry “foul” here. The evidence for trend and momentum is, after all, centuries in length and the efficacy of all these horizons is supported. Surely the noise we see over this ten-year period would average out over the long run, right?

The unfortunate reality is that these performance differences are not expected to mean-revert. The gambler’s fallacy would have us believe that bad luck in one year should be offset by good luck in another and vice versa. Unfortunately, this is not the case. While we would expect, at any given point in time, that each strategy has equal likelihood of experiencing good or bad luck going forward, that luck is expected to occur completely independently from what has happened in the past.

The implication is that performance differences due to model specification are not expected to mean-revert and are therefore expected to be random, but very permanent, return artifacts.¹

The larger problem at hand is that none of us have a hundred years to invest. In reality, most investors have a few decades. And we act with the temperament of having just a few years. Therefore, bad luck can have very permanent and very scarring effects not only upon our psyche, but upon our realized wealth.

But consider what happens if we try to neutralize the role of model specification risk and luck by diversifying across the seven different models equally (rebalanced annually). We see that returns closer in line with the median result, a boost to realized Sharpe ratio, and a reduction in the maximum realized drawdown.

These are impressive results given that all we employed was naïve diversification.

Conclusion

The odd thing about strategy diversification is that it guarantees we will be wrong. Each and every year, we will, by definition, allocate at least part of our capital to the worst performing strategy. The potential edge, however, is in being vaguely wrong rather than precisely wrong. The former is annoying. The latter can be catastrophic.

In this commentary we use the popular Dual Momentum GEM strategy as a case study to demonstrate how model specification choices can lead to performance differences that span hundreds, if not thousands, of basis points a year. Unfortunately, we should not expect these performance differences to mean revert. The realizations of good and bad luck are permanent, and potentially very significant, artifacts within our track records.

By simply diversifying across the different models, however, we can dramatically reduce specification risk and thereby reduce strategy fragility.

To be clear, no amount of diversification will protect you from the risk of the style. As we like to say, “risk cannot be destroyed, only transformed.” In that vein, trend following strategies will always incur some sort of whipsaw risk. The question is whether it is whipsaw related to the style as a whole or to the specific implementation.

For example, in the graphs above we can see that Dual Momentum GEM implemented with a 10-month formation period experienced whipsaw in 2011 when few of the other implementations did. This is more specification whipsaw than style whipsaw. On the other hand, we can see that almost all the specifications exhibited whipsaw in late 2015 and early 2016, an indication of style whipsaw, not specification whipsaw.

Specification risk we can attempt to control for; style risk is just something we have to bear.

At Newfound, evidence such as this informs our own trend-following mandates. We seek to diversify ourselves across the axes of what (“what are we investing in?”), how (“how are we making the decisions?”), and when (“when are we making those decisions?”) in an effort to reduce specification risk and provide the greatest style consistency possible.

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

Tag: momentum Page 2 of 4

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

Tightening the Uncertain Payout of Trend-Following

Summary­

Introduction

Diversification in Trend-Following

The Math Behind the Diversification

An Example: Trend-Following on the S&P 500

Expanding the Multitude of Models

Conclusion

Fragility Case Study: Dual Momentum GEM

Summary­

Introduction

Global Equities Momentum (“GEM”)

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

Summary

Summary

Summary

Summary

Summary