Category: Risk & Style Premia Page 14 of 16

Duration Timing with Style Premia

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.

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

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

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

Timing with Carry

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

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

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

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

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

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

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

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

Explicitly Estimating the Bond Risk Premium

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

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

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

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

Diversifying Style Premia

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

	BRP	Momentum	Value	Carry
BRP	1.00	0.35	0.76	0.37
Momentum	0.35	1.00	0.68	0.68
Value	0.76	0.68	1.00	0.73
Carry	0.37	0.68	0.73	1.00

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

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

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

Did Timing Add Value?

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

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

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

	CAGR	Volatility	Sharpe Ratio	Max Drawdown
BRP Strategic	2.75%	3.36%	0.82	7.17%
BRP Timing	3.89%	5.48%	0.71	14.00%
Momentum Strategic	3.54%	4.32%	0.82	9.09%
Momentum Timing	3.62%	7.20%	0.50	17.68%
Value Strategic	4.37%	5.38%	0.81	11.27%
Value Timing	5.75%	6.84%	0.84	15.17%
Carry Strategic	4.71%	5.80%	0.81	12.11%
Carry Timing	5.47%	6.97%	0.79	12.03%

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

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

	CAGR	Volatility	Sharpe Ratio	Max Drawdown
Composite Strategic	3.78%	4.63%	0.82	9.71%
Composite Timing	4.03%	5.26%	0.77	9.15%

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

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

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

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

Robustness Testing: International Markets

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

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

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

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

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

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

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

Robustness Testing: Different Time Period

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

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

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

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

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

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

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

Conclusion

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Navigating Municipal Bonds With Factors

By Justin Sibears

On May 15, 2017

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

This post is available as a PDF download here.

Summary

In this case study, we explore building a simple, low cost, systematic municipal bond portfolio.
The portfolio is built using the low volatility, momentum, value, and carry factors across a set of six municipal bond sectors. It favors sectors with lower volatility, better recent performance, cheaper valuations, and higher yields. As with other factor studies, a multi-factor approach is able to harvest major benefits from active strategy diversification since the factors have low correlations to one another.
The factor tilts lead to over- and underweights to both credit and duration through time. Currently, the portfolio is significantly underweight duration and modestly overweight credit.
A portfolio formed with the low volatility, value, and carry factors has sufficiently low turnover that these factors may have value in setting strategic allocations across municipal bond sectors.

Recently, we’ve been working on building a simple, ETF-based municipal bond strategy. Probably to the surprise of nobody who regularly reads our research, we are coming at the problem from a systematic, multi-factor perspective.

For this exercise, our universe consists of six municipal bond indices:

Bloomberg Barclays AMT-Free Short Continuous Municipal Index
Bloomberg Barclays AMT-Free Intermediate Continuous Municipal Index
Bloomberg Barclays AMT-Free Long Continuous Municipal Index
Bloomberg Barclays Municipal Pre-Refunded-Treasury-Escrowed Index
Bloomberg Barclays Municipal Custom High Yield Composite Index
Bloomberg Barclays Municipal High Yield Short Duration Index

These indices, all of which are tracked by VanEck Vectors ETFs, offer access to municipal bonds across a range of durations and credit qualities.

Source: VanEck

Before we get started, why are we writing another multi-factor piece after addressing factors in the context of a multi-asset universe just two weeks ago?

The simple answer is that we find the topic to be that pressing for today’s investors. In a world of depressed expected returns and elevated correlations, we believe that factor-based strategies have a role as both return generators and risk mitigators.

Our confidence in what we view as the premier factors (value, momentum, low volatility, carry, and trend) stems largely from their robustness in out-of-sample tests across asset classes, geographies, and timeframes. The results in this case study not only suggest that a factor-based approach is feasible in muni investing, but also in our opinion strengthens the case for factor investing in other contexts (e.g. equities, taxable fixed income, commodities, currencies, etc.).

Constructing Long/Short Factor Portfolios

For the municipal bond portfolio, we consider four factors:

Value: Buy undervalued sectors, sell overvalued sectors
Momentum: Buy strong recent performers, sell weak recent performers
Low Volatility: Buy low risk sectors, sell high risk sectors
Carry: Buy higher yielding sectors, sell lower yielding sectors

As a first step, we construct long/short single factor portfolios. The weight on index i at time t in long/short factor portfolio f is equal to:

In this formula, c is a scaling coefficient, S is index i’s time t score on factor f, and N is the number of indices in the universe at time t.

We measure each factor with the following metrics:

Value: Normalized deviation of real yield from the 5-year trailing average yield[1]
Momentum: Trailing twelve month return
Low Volatility: Historical standard deviation of monthly returns[2]
Carry: Yield-to-worst

For the value, momentum, and carry factors, the scaling coefficient is set so that the portfolio is dollar neutral (i.e. we are long and short the same dollar amount of securities). For the low volatility factor, the scaling coefficient is set so that the volatilities of the long and short portfolios are approximately equal. This is necessary since a dollar neutral construction would be perpetually short “beta” to the overall municipal bond market.

All four factors are profitable over the period from June 1998 to April 2017. The value factor is the top performer both from an absolute return and risk-adjusted return perspective.

Data Source: Blooomberg. Calculations by Newfound Research. All returns are hypothetical and backtested. Returns reflect the reinvestment of all distributions and are gross of all fees (including any management fees and transaction costs). The hypothetical indices start on June 30, 1998. The start date was chosen based on data availability of the underlying indices and the time necessary to calibrate the factor models. Data is through April 30, 2017. The portfolios are reconstituted monthly. Past performance does not guarantee future results. The benchmark is an equal-weight portfolio of all indices in the universe adjusted for the indices that are calibrated and included in each long/short factor index based on data availability.

There is significant variation in performance over time. All four factors have years where they are the best performing factor and years where they are the worst performing factor. The average annual spread between the best performing factor and the worst performing factor is 11.3%.

The individual long/short factor portfolios are diversified to both each other (average pairwise correlation of -0.11) and to the broad municipal bond market.

Moving From Single Factor to Multi-Factor Portfolios

The diversified nature of the long/short return streams makes a multi-factor approach hard to beat in terms of risk-adjusted returns. This is another example of the type of strategy diversification that we have long lobbied for.

As evidence of these benefits, we have built two versions of a portfolio combining the low volatility, value, carry, and momentum factors. The first version targets an equal dollar allocation to each factor. The second version uses a naïve risk parity approach to target an approximately equal risk contribution from each factor.

Both approaches outperform all four individual factors on a risk-adjusted basis, delivering Sharpe Ratios of 1.19 and 1.23, respectively, compared to 0.96 for the top single factor (value).

Data Source: Bloomberg. Calculations by Newfound Research. All returns are hypothetical and backtested. Returns reflect the reinvestment of all distributions and are gross of all fees (including any management fees and transaction costs). The hypothetical indices start on June 30, 1998. The start date was chosen based on data availability of the underlying indices and the time necessary to calibrate the factor models. Data is through April 30, 2017. The portfolios are reconstituted monthly. Past performance does not guarantee future results. The benchmark is an equal-weight portfolio of all indices in the universe adjusted for the indices that are calibrated and included in each long/short factor index based on data availability. The factor risk parity construction uses a simple inverse volatility methodology. Volatility estimates are shrunk in the early periods when less data is available.

To stress this point, diversification is so plentiful across the factors that even the simplest portfolio construction methodologies outperforms an investor who was able to identify the best performing factor with perfect foresight. For additional context, we constructed a “Look Ahead Mean-Variance Optimization (“MVO”) Portfolio” by calculating the Sharpe optimal weights using actual realized returns, volatilities, and correlations. The Look Ahead MVO Portfolio has a Sharpe Ratio of 1.43, not too far ahead of our two multi-factor portfolios. The approximate weights in the Look Ahead MVO Portfolio are 49% to Low Volatility, 25% to Value, 15% to Carry, and 10% to Momentum. While the higher Sharpe Ratio factors (Low Volatility and Value) do get larger allocations, Momentum and Carry are still well represented due to their diversification benefits.

From a risk perspective, both multi-factor portfolios have lower volatility than any of the individual factors and a maximum drawdown that is within 1% of the individual factor with the least amount of historical downside risk. It’s also worth pointing out that the risk parity construction leads to a return stream that is very close to normally distributed (skew of 0.1 and kurtosis of 3.0).

In the graph on the next page, we present another lens through which we can view the tremendous amount of diversification that can be harvested between factors. Here we plot how the allocation to a specific factor, using MVO, will change as we vary that factor’s Sharpe Ratio. We perform this analysis for each factor individually, holding all other parameters fixed at their historical levels.

As an example, to estimate the allocation to the Low Volatility factor at a Sharpe Ratio of 0.1, we:

Assume the covariance matrix is equal to the historical covariance over the full sample period.
Assume the excess returns for the other three factors (Carry, Momentum, and Value) are equal to their historical averages.
Assume the annualized excess return for the Low Volatility factor is 0.16% so that the Sharpe Ratio is equal to our target of 0.1 (Low Volatility’s annualized volatility is 1.6%).
Calculate the MVO optimal weights using these excess return and risk assumptions.

As expected, Sharpe Ratios and allocation sizes are positively correlated. Higher Sharpe Ratios lead to higher allocations.

That being said, three of the factors (Low Volatility, Carry, and Momentum) would receive allocations even if their Sharpe Ratios were slightly negative.

The allocations to carry and momentum are particularly insensitive to Sharpe Ratio level. Momentum would receive an allocation of 4% with a 0.00 Sharpe, 9% with a 0.25 Sharpe, 13% with a 0.50 Sharpe, 17% with a 0.75 Sharpe, and 20% with a 1.00 Sharpe. For the same Sharpe Ratios, the allocations to Carry would be 10%, 15%, 19%, 22%, and 24%, respectively.

Holding these factors provides a strong ballast within the multi-factor portfolio.

Moving From Long/Short to Long Only

Most investors have neither the space in their portfolio for a long/short muni strategy nor sufficient access to enough affordable leverage to get the strategy to an attractive level of volatility (and hence return). A more realistic approach would be to layer our factor bets on top of a long only strategic allocation to muni bonds.

In a perfect world, we could slap one of our multi-factor long/short portfolios right on top of a strategic municipal bond portfolio. The results of this approach (labeled “Benchmark + Equal Weight Factor Long/Short” in the graphics below) are impressive (Sharpe Ratio of 1.17 vs. 0.93 for the strategic benchmark and return to maximum drawdown of 0.72 vs. 0.46 for the strategic benchmark). Unfortunately, this approach still requires just a bit of shorting. The size of the total short ranges from 0% to 19% with an average of 5%.

We can create a true long only portfolio (“Long Only Factor”) by removing all shorts and normalizing so that our weights sum to one. Doing so modestly reduces risk, return, and risk-adjusted return, but still leads to outperformance vs. the benchmark.

Below we plot both the historical and current allocations for the long only factor portfolio. Currently, the portfolio would have approximately 25% in each short-term investment grade, pre-refunded, and short-term high yield with the remaining 25% split roughly 80/20 between high yield and intermediate-term investment grade. There is currently no allocation to long-term investment grade.

Data Source: Blooomberg. Calculations by Newfound Research. All allocations are backtested and hypothetical. The hypothetical indices start on June 30, 1998. The start date was chosen based on data availability of the underlying indices and the time necessary to calibrate the factor models. Data is through April 30, 2017. The portfolios are reconstituted monthly. Past performance does not guarantee future results.

A few interesting observations relating to the long only portfolio and muni factor investing in general:

The factor tilts lead to clear duration and credit bets over time. Below we plot the duration and a composite credit score for the factor portfolio vs. the benchmark over time.
Data source: Calculations by Newfound Research. All allocations are backtested and hypothetical. The hypothetical indices start on June 30, 1998. The start date was chosen based on data availability of the underlying indices and the time necessary to calibrate the factor models. Data is through April 30, 2017. The portfolios are reconstituted monthly. Past performance does not guarantee future results. Weighted average durations are estimated using current constituent durations.
Data source: Calculations by Newfound Research. All allocations are backtested and hypothetical. The hypothetical indices start on June 30, 1998. The start date was chosen based on data availability of the underlying indices and the time necessary to calibrate the factor models. Data is through April 30, 2017. The portfolios are reconstituted monthly. Past performance does not guarantee future results. Weighted average credit scores are estimated using current constituent credit scores. Credit scores use S&P’s methodology to aggregate scores based on the distribution of credit scores of individual bonds.
Currently, the portfolio is near an all-time low in terms of duration and is slightly titled towards lower credit quality sectors relative to the benchmark. Historically, the factor portfolio was most often overweight both duration and credit, having this positioning in 53.7% of the months in the sample. The second and third most common tilts were underweight duration / underweight credit (22.0% of sample months) and underweight duration / overweight credit (21.6% of sample months). The portfolio was overweight duration / underweight credit in only 2.6% of sample months.
Even for more passive investors, a factor-based perspective can be valuable in setting strategic allocations. The long only portfolio discussed above has annualized turnover of 77%. If we remove the momentum factor, which is by far the biggest driver of turnover, and restrict ourselves to a quarterly rebalance, we can reduce turnover to just 18%. This does come at a cost, as the Sharpe Ratio drops from 1.12 to 1.04, but historical performance would still be strong relative to our benchmark. This suggests that carry, value, and low volatility may be valuable in setting strategic allocations across municipal bond ETFs with only periodic updates at a normal strategic rebalance frequency.
We ran regressions with our long/short factors on all funds in the Morningstar Municipal National Intermediate category with a track record that extended over our full sample period from June 1998 to April 2017. Below, we plot the betas of each fund to each of our four long/short factors. Blue bars indicate that the factor beta was significant at a 5% level. Gray bars indicate that the factor beta was not significant at a 5% level. We find little evidence of the active managers following a factor approach similar to what we outline in this post. Part of this is certainly the result of the constrained nature of the category with respect to duration and credit quality. In addition, these results do not speak to whether any of the managers use a factor-based approach to pick individual bonds within their defined duration and credit quality mandates.
Data source: Calculations by Newfound Research. Analysis over the period from June 1998 to April 2017.
The average beta to the low volatility factor, ignoring non-statistically significant values, is -0.23. This is most likely a function of category since the category consists of funds with both investment grade credit quality and durations ranging between 4.5 and 7.0 years. In contrast, our low volatility factor on average has short exposure to the intermediate and long-term investment grade sectors.
Data source: Calculations by Newfound Research. Analysis over the period from June 1998 to April 2017.
Only 14 of the 33 funds in the universe have statistically significant exposure to the value factor with an average beta of -0.03.
Data source: Calculations by Newfound Research. Analysis over the period from June 1998 to April 2017.
The average beta to the carry factor, ignoring non-statistically significant values, is -0.23. As described above with respect to low volatility, this is most likely function of category as our carry factor favors the long-term investment grade and high yield sectors.
Data source: Calculations by Newfound Research. Analysis over the period from June 1998 to April 2017.
Only 9 of the 33 funds in the universe have statistically significant exposure to the momentum factor with an average beta of 0.02.

Conclusion

Multi-factor investing has generated significant press in the equity space due to the (poorly named) “smart beta” movement. The popular factors in the equity space have historically performed well both within other asset classes (rates, commodities, currencies, etc.) and across asset classes. The municipal bond market is no different. A simple, systematic multi-factor process has the potential to improve risk-adjusted performance relative to static benchmarks. The portfolio can be implemented with liquid, low cost ETFs.

Moving beyond active strategies, factors can also be valuable tools when setting strategic sector allocations within a municipal bond sleeve and when evaluating and blending municipal bond managers.

Perhaps more importantly, the out-of-sample evidence for the premier factors (momentum, value, low volatility, carry, and trend) across asset classes, geographies, and timeframes continues to mount. In our view, this evidence can be crucial in getting investors comfortable to introducing systematic active premia into their portfolios as both return generators and risk mitigators.

[1] Computed using yield-to-worst. Inflation estimates are based on 1-year and 10-year survey-based expected inflation. We average the value score over the last 2.5 years, allowing the portfolio to realize a greater degree of valuation mean reversion before closing out a position.

[2] We use a rolling 5-year (60-month) window to calculate standard deviation. We require at least 3 years of data for an index to be included in the low volatility portfolio. The standard deviation is multiplied by -1 so that higher values are better across all four factor scores.

Did Declining Rates Actually Matter?

By Corey Hoffstein

On April 10, 2017

This post is available as a PDF here.

Summary

From 1981 to 2017, 10-year U.S. Treasury rates declined from north of 15% to below 2%.
Since bond prices appreciate when rates decline, many have pointed towards this secular decline as a tailwind that created an unprecedented bull market in bonds.
Exactly how much declining rates contributed, however, is rarely quantified. An informal poll, however, tells us that people generally believe the impact was significant (explaining >50% of bond returns).
We find that while, in theory, investors should be indifferent to rate changes, high turnover in bond portfolios means that a structural mis-estimation of rate changes could be harvested.
Despite the positive long-term impact of declining rates, coupon yield had a much more significant impact on long-term returns.
The bull market in bonds was caused more by the high average rates over the past 30 years than declining rates.

On 9/30/1981, the 10-year U.S. Treasury rate peaked at an all-time high of 15.84%. Over the next 30 years, it deflated to an all-time low of 1.37% on 7/5/2016.

Source: Federal Reserve of St. Louis

It has been repeated in financial circles that this decline in rates caused a bull market in bond returns that makes past returns a particularly poor indicator of future results.

But exactly how much did those declining rates contribute?

We turned to our financial circle on Twitter[1] with a question: For a constant maturity, 10-year U.S. Treasury index, what percent of total return from 12/1981 through 12/2012 could be attributed to declining rates?

Little consensus was found.

Clearly there is a large disparity in views about exactly how much declining rates actually contributed to bond returns over the last 30 years. What we can see is that people generally think it is a lot: over 50% of people said over 50% of returns can be attributed to declining rates.

Well let’s dig in and find out.

Rates Down, Bonds Up

To begin, let’s remind ourselves why the bond / rate relationship exists in the first place.

Imagine you buy a 10-year U.S. Treasury bond for $100 at the prevailing 5% rate. Immediately after you buy, interest rates drop: all available 10-year U.S. Treasury bonds – still selling for $100 – are now offering only a 4% yield.

In every other way, except the yield being offered, the bond you now hold and the bonds being offered in the market are identical. Except yours provides a higher yield.

Therefore, it should be more valuable. After all, you are getting more return for your investment. And hence we get the inverse relationship between bonds and interest rates. As rates fall, existing bond values go up and as rates rise, existing bond values go down.

With rates falling by an average of 42 basis points a year over the last 35 years, we can imagine a pretty steady, and potentially sizable tailwind to returns.

Just How Much More Valuable?

In our example, exactly how much did our bond appreciate when rates fell? Or, to ask the question another way: how much would someone now be willing to buy our bond for?

The answer arises from the fact that markets loathe an arbitrage opportunity. Scratch that: markets love arbitrage. So much so that they are quickly wiped away as market participants jump to exploit them.

We mentioned that in the example, the bond you held and the bonds now being offered by the market were identical in every fashion except the coupon yield they offer.

Consider what would happen if the 4% bonds and your 5% bonds were both still selling for $100. Someone could come to the market, short-sell a 4% bond and use the $100 to buy your 5% bond from you. Each coupon period, they would collect $5 from the bond they bought from you, pay $4 to cover the coupon payment they owe from the short-sale, and pocket $1.

Effectively, they’ve created a free stream of $1 bills.

Knowing this to be the case, someone else might step in first and try to offer you $101 for your bond to sweeten the deal. Now they must finance by short-selling 1.01 shares of the 4% bonds, owing $4.04 each period and $101 at maturity. While less profitable, they would still pocket a free $0.86 per coupon payment.[2]

The scramble to sweeten the offer continues until it reaches the magic figure of $108.11. At this price, the arbitrage disappears: the cost of financing exactly offsets the extra yield earned by the bond.

Another way of saying this is that the yield-to-maturity of both bonds is identical. If someone pays $108.11 for the 5% coupon bond, they may receive a $5 coupon each period, but there will be a “pull-to-par” effect as the bond matures, causing the bond to decline in value. This effect occurs because the bond has a pre-defined payout stream: at maturity, you are only going to receive your $100 back.

Therefore, while your coupon yield may be 5%, your effective yield – which accounts for this loss in value over time – is 4%, perfectly matching what is available to other investors.

And so everyone becomes indifferent[3] to which bond they hold. The bond you hold may be worth more on paper, but if we try to sell it to lock in our profit, we have to reinvest at a lower yield and offsets our gain.

In a strange way, then, other than mark-to-market gains and losses, we should be largely indifferent to rate changes.

The Impact of Time

One very important aspect ignored by our previous example is time. Interest rates rarely gap up or down instantaneously: rather they move over time.

We therefore need to consider the yield curve. The yield curve tells us what rate is being offered for bonds of different maturities.

Source: Federal Reserve of St. Louis.

In the yield curve plotted above, we see an upward sloping trend. Buying a 7-year U.S. Treasury earns us a 2.25% rate, while the 10-year U.S. Treasury offers 2.45%.

Which introduces an interesting dynamic: if rates do not change whatsoever, if we buy a 10-year bond today and wait three years, our bond will appreciate in value.

Why?

The answer is because it is now a 7-year bond, and compared to other 7-year bonds it is offering 0.20% more yield.

In fact, depending on the shape of the yield curve, it can continue to appreciate until the pull-to-par effect becomes too strong. Below we plot the value of a 10-year U.S. Treasury as it matures, assuming that the yield curve stays entirely constant over time.

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

Unfortunately, like in our previous example, the amount of the bond gains in value is exactly equal to the level required to make us indifferent to holding the bond to maturity or selling it and reinvesting at the prevailing rate. For all intents and purposes, we could simply pretend we bought a 7-year bond at 2.45% and rates fell instantly to 2.25%. By the same logic as before, we’re no better off.

We simply cannot escape the fact that markets are not going to give us a free return.

The Impact of Choice

Again, reality is more textured than theory. We are ignoring an important component: choice.

In our prior examples, our choice was between continuing to hold our bond, or selling it and reinvesting in the equivalent bond. What if we chose to reinvest in something else?

For example:

We buy a 2.45% 10-year U.S. Treasury for $100
We wait three years
We sell the now 7-year U.S. Treasury for $101.28 (assuming the yield curve did not change)
We reinvest in 2.45% 10-year U.S. Treasuries, sold at $100

If the yield curve never changes, we can keep capturing this roll return by simply waiting, selling, and buying what we previously owned.

What’s the catch? The catch, of course, is that we’re assuming rates won’t change. If we stop for a moment, however, and consider what the yield curve is telling us, we realize this assumption may be quite poor.

The yield curve provides several rates at which we can invest. What if we are only interested in investing over the next year? Well, we can buy a 1-year U.S. Treasury at 0.85% and just hold it to maturity, or we could buy a 10-year U.S. Treasury for 2.45% and sell it after a year.

That is a pretty remarkable difference in 1-year return potential.

If the market is even reasonably efficient, then the expected 1-year return, no matter where we buy on the curve, should be the same. Therefore, the only way the 10-year U.S. Treasury yield should be so much higher than the 1-year is if the market is predicting that rates are going to go up such that the extra yield is exactly offset by the price loss we take when we sell the bond.

Hence a rising yield curve tells us the market is expecting rising rates. At least, that’s what the pure expectations hypothesis (“PEH”) says. Competing theories argue that investors should earn at least some premium for bearing term risk. Nevertheless, there should be some component of a rising yield curve that tells us rates should go up.

However, over the past 35 years, the average slope of the yield curve (measured as 10-year yields minus 2-year yields) has been over 100bp. The market was, in theory, was consistently predicting rising rates over a period rates fell.

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

Not only could an investor potentially harvest roll-yield, but also the added bump from declining rates.

Unfortunately, doing so would require significant turnover. We would have to constantly sell our bonds to harvest the gains.

While this may have created opportunity for active bond managers, a total bond market index typically holds bonds until maturity.

Turnover in a Bond Index

Have you ever looked at the turnover in a total bond market index fund? You might be surprised.

While the S&P 500 has turnover of approximately 5% per year, the Bloomberg Barclay’s U.S. Aggregate often averages between 40-60% per year.

Where is all that turnover coming from?

Index additions (e.g. new issuances)
Index deletions (e.g. maturing bonds)
Paydowns
Coupon reinvestment

If the general structure of the fixed income market does not change considerably over time, this level of turnover implies that a total bond market index will behave very similarly to a constant duration bond fund.

Bonds are technically held to maturity, but roll return and profit/loss from shifts in interest rates are booked along the way as positions are rebalanced.

Which means that falling rates could matter. Even better, we can test how much falling rates mattered by proxying a total bond index with a constant maturity bond index[4].

Specifically, we will look at a constant maturity 10-year U.S. Treasury index. We will assume 10-year Treasuries are bought at the beginning of each year, held for a year, and sold as 9-year Treasuries[5]. The proceeds will then be reinvested back into the new 10-year Treasuries. We will also assume that coupons are paid annually.

We ran the test from 12/1981 to 12/2012, since those dates represented both the highest and lowest end-of-year rates.

We will then decompose returns into three components:

Coupon yield (“Coupon”)
Roll return (“Roll”)
Rate changes (“Shift”)

Coupon yield is, simply, the return we get from the coupon itself. Roll return is equal to the slope between 10-year and 9-year U.S. Treasuries at the point of purchase adjusted by the duration of the bond. Rate changes are measured as price return we achieve due to shifts in the 9-year rate from the point at which we purchased the bond and the point at which we are selling it.

This allows us to create a return stream for each component as well as identify each component’s contribution to the total return of the index.

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

What we can see is that coupon return dominates roll and shift. On an annualized basis, coupon was 6.24%, while roll only contributed 0.24% and shift contributed 2.22%.

Which leaves us with a final decomposition: coupon yield accounted for 71% of return, roll accounted for 3%, and shift accounted for 26%.

We can perform a similar test for constant maturity indices constructed at different points on the curve as well.

	Total Return			% Contribution
	Coupon	Roll	Shift	Coupon	Roll	Shift
10-year	6.24%	0.24%	2.22%	71.60%	2.84%	25.55%
7-year	6.08%	0.62%	1.72%	72.16%	7.37%	20.47%
5-year	5.81%	0.65%	1.29%	75.01%	8.38%	16.61%

Conclusion: Were Declining Rates Important?

A resounding yes. An extra 2.22% per year over 30+ years is nothing to sneeze at. Especially when you consider that this was the result of a very unique period unlikely to be repeated over the next 30 years.

Just as important to consider, however, is that it was not the most important contributor to total returns. While most people in our poll answered that decline in rates would account for 50%+ of total return, the shift factor only came in at 26%.

The honor of the highest contributor goes to coupon yield. Even though rates deflated over 30 years, the average yield was high enough to be, by far and away, the biggest contributor to returns.

The bond bull was not due to declining rates, in our opinion, but rather the unusually high rates we saw over the period.

A fact which is changing today. We can see this by plotting the annual sources of returns year-by-year.

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

Note that while coupon is always a positive contributor, its role has significantly diminished in recent years compared to the influence of rate changes.

The consistency of coupon and the varying influence of shift on returns (i.e. both positive and negative) means that coupon yield actually makes an excellent predictor of future returns. Lozada (2015)[6] finds that the optimal horizon to use yield as a predictor of return in constant duration or constant-maturity bond funds is at twice the duration.

Which paints a potentially bleak picture for fixed income investors.

Fund	Asset	Duration	TTM Yield	Predicted Return
AGG	U.S. Aggregate Bonds	5.74	2.37%	2.37% per year through 2028
IEI	3-7 Year U.S. Treasuries	4.48	1.31%	1.31% per year through 2025
IEF	7-10 Year U.S. Treasuries	7.59	1.77%	1.77% per year through 2032
TLT	20+ Year U.S. Treasuries	17.39	2.56%	2.56% per year through 2051
LQD	Investment Grade Bonds	8.24	3.28%	3.28% per year through 2033

Source: iShares. Calculations by Newfound Research.

Note that we are using trailing 12-month distribution yield for the ETFs here. We do this because ETF issuers often amortize coupon yield to account for pull-to-par effects, making it an approximation of yield-to-worst. It is not perfect, but we don’t think the results materially differ in magnitude with any other measure: it’s still ugly.

The story remains largely the same as we’ve echoed over the past year: when it comes to fixed income, your current yield will be a much better predictor of returns than trying to guess about changing rates.

Coupon yield had 3x the influence on total return over the last 30 years than changes in rates did.

What we should be concerned about today is not rising rates: rather, we should be concerned about the returns that present low rates imply for the future.

And we should be asking ourselves: are there other ways we can look to manage risk or find return?

[1] Find us on Twitter! Newfound is @thinknewfound and Corey is @choffstein.

[2] It is $0.86 instead of $0.96 because they need to set aside $0.10 to cover the extra dollar they owe at maturity.

[3] This is a bit of a simplification as the bonds will have different risk characteristics (e.g. different durations and convexity) which could cause investors, especially those with views on future rate changes, to prefer one bond over the other.

[4] We made the leap here from total bond index to constant duration index to constant maturity index. Each step introduces some error, but we believe for our purposes the error is de minimis and a constant maturity index allows for greater ease of implementation.

[5] Since no 9-year U.S. Treasury is offered, we create a model for the yield curve using cubic splines and then estimate the 9-year rate.

[6] http://content.csbs.utah.edu/~lozada/Research/IniYld_6.pdf

Diversification in Multi-Factor Portfolios

By Corey Hoffstein

On March 20, 2017

In Craftsmanship, Portfolio Construction, Risk & Style Premia

This blog post is available as a PDF here.

Summary

The debate rages on over the application of valuation in factor-timing methods. Regardless, diversification remains a prudent recommendation.
How to diversify multi-factor portfolios, however, remains up for debate.
The ActiveBeta team at Goldman Sachs finds new evidence that composite diversification approaches can offer a higher information ratio than integrated approaches due to interaction effects at low-to-moderate factor concentration levels.
At high levels, they find that integrated approaches have higher information ratios due to high levels of idiosyncratic risks in composite approaches.
We return to old research and explore empirical evidence in FTSE Russell’s tilt-tilt approach to building an integrated multi-factor portfolio to determine if this multi-factor approach does deliver greater factor efficiency than a comparable composite approach.

The debate over factor timing between Cliff Asness and Rob Arnott rages on. This week saw Cliff publish a blog post titled Factor Timing is Hard providing an overview of his recently co-authored work Contrarian Factor Timing is Deceptively Difficult. Generally in academic research, you find a certain level of hedged decorum: authors rarely insult the quality of work, they just simply refute it with their own evidence.

This time, Cliff pulled no punches.

“In multiple online white papers, Arnott and co-authors present evidence in support of contrarian factor timing based on a plethora of mostly inapplicable, exaggerated, and poorly designed tests that also flout research norms.”

At the risk of degrading this weekly research commentary into a gossip column: Ouch. Burn.

We’ll be providing a much deeper dive into this continued factor-timing debate (as well as our own thoughts) in next week’s commentary.

In the meantime, at least there is one thing we can all agree on – including Cliff and Rob – factor portfolios are better diversified than not.

Except, as an industry, we cannot even agree how to diversify them.

Diversifying Multi-Factor Portfolios: Composite vs. Integrated

When it comes to building multi-factor portfolios, there are two camps of thought.

The first camp believes in a two-step approach. First, portfolios are built for each factor. To do this, securities are often given a score for each factor, and when a factor sleeve is built, securities with higher scores receive an overweight position while those with lower scores receive an underweight. After those portfolios are built, they are blended together to create a combined portfolio. As an example, a value / momentum multi-factor portfolio would be built by first constructing value and momentum portfolios, and then blending these two portfolios together. This approach is known as “mixed,” “composite,” or “portfolio blend.”

Source: Ghayur, Heaney, and Platt (2016)

The second camp uses a single-step approach. Securities are still given a score for each factor, but those scores are blended into a single aggregate value representing the overall strength of that security. A single portfolio is then built, guided by this blended value, overweighting securities with higher scores and underweighting securities with lower scores. This approach is known as “integrated” or “signal blend.”

Source: Ghayur, Heaney, and Platt (2016)

To re-hash the general debate:

Portfolio blend advocates tend to prefer the simplicity, transparency, and control of the approach. Furthermore, there is a preponderance of evidence supporting single-factor portfolios, but research exploring the potential interaction effects of a signal blend approach is limited and therefore potentially introduces unknown risks.
Signal blend advocates argue that a portfolio blend approach introduces inefficiencies: that by constructing each sleeve independently, securities with canceling factor scores can be introduced and dilute overall factor exposure. The general argument goes along the line of, “we want the decathlon athlete, not a team full of individual sport athletes.”

Long-time readers of our commentary may, at this point, be groaning; how is this topic not dead yet? After all, we’ve written about it numerous times in the past.

In Beware Bad Multi-Factor Portfolios we argued that the integrated approach was fundamentally flawed due to the different decay rates of factor alpha (which is equivalent to saying that factor portfolios turnover at different rates). By combining a slow-moving signal with a fast-moving signal, variance in the composite signal becomes dominated by the fast-moving signal.In retrospect, our choice of wording here was probably a bit too concrete. We believe our point still stands that care must be taken in integrated approaches because of relative turnover speed differences in different factors, but it is not an insurmountable hurdle in construction.
In Multi-Factor: Mix or Integrate? we explored an AQR paper that advocated for an integrated approach. We found it ironic that this was published shortly after Cliff Asness had published an article discussing the turnover issues that make applying value-based timing difficult for factors like momentum – an argument similar to our past blog post.In this post, we continued to find evidence that integrated approaches ran the risk of being governed by high turnover factors.
In Is That Leverage in my Multi-Factor ETF? we explored an argument made by FTSE Russell that an integrated approach offered implicit leverage effects, allowing you to use the same dollar to access multiple factors simultaneously.This is probably the best argument we have heard for multi-factor portfolios to date.Unfortunately, empirical evidence suggested that existing integrated multi-factor ETF portfolios did not offer significantly more factor exposure than composite peers.
It is worth noting, however, that the data we were able to explore was limited as multi-factor portfolios are largely new. We were not even able to evaluate, for example, a FTSE Russell product despite the fact it was FTSE Russell making the argument.

Feeling that our empirical test did not necessarily do justice to FTSE Russell’s argument, we wrote Capital Efficiency in Multi-Factor Portfolios. If we were to make an argument for our most underrated article of 2016, this would be it – but that is probably because it was filled with obtuse mathematics.The point of the piece was to try to reconcile FTSE Russell’s argument from a theoretical basis. What we found, under some broad assumptions, was that under all cases, an integrated approach should provide at least as much, and generally much more, factor exposure than a mixed approach due to the implied leverage effect.

So, honestly, how much more can we say on this topic?

New Evidence of Interaction Effects in Multi-Factor Portfolios

Well the ActiveBeta Equity Strategies team at Goldman Sachs Asset Management published a paper late last year comparing the two approaches using Russell 1000 securities from January 1979 to June 2016.

Unlike our work, in which we compared composite and integrated portfolios built to match the percentage of stocks selected, Ghayur, Heaney, and Platt (2016) built portfolios to match factor exposure. Whereas we matched an integrated approach that picked the top 25% of securities with a composite approach where each sleeve picked the top 25%, Ghayur, Heaney, and Platt (2016) accounted for expected factor dilution by having the sleeves in the composite approach pick the top 12.5%.

Using this factor-exposure matching approach, their results are surprising. Rather than a definitive answer as to which approach is superior, they find that the portfolio blend approach offers a higher information ratio at lower levels of factor exposure (i.e. lower levels of active risk), while the signal blend approach offers a higher information ratio at higher levels of factor exposure (i.e. higher levels of active risk).

How can this be the case?

The answer comes down to interaction effects.

When a portfolio is built expecting more diluted overall factor exposure – e.g. to have lower tracking error to the index – the percentage overlap between securities in the composite and integrated approaches is higher. However, for more concentrated factor exposure, the overlap is lower.

Source: Ghayur, Heaney, and Platt (2016)

Advocates for an integrated approach have historically argued that securities found in Area 3 in the figure above would be a drag on portfolio performance. These are the securities found in a composite approach but not an integrated approach. The argument is that while high in one factor score, these securities are also very low in another, and including them in a portfolio only dilutes overall factor exposure via a canceling effect.

On the other hand, securities in Area 2, found only in the integrated approach, should increase factor exposure because you are getting securities with higher loadings on both factors simultaneously.

As it turns out, evidence suggests this is not the case.

In fact, for lower concentration factor portfolios, Ghayur, Heaney, and Platt (2016) find just the opposite.

Source: Ghayur, Heaney, and Platt (2016)

As it turns out, interaction effects give Area 3 positive active returns while Area 2 ends up delivering negative active returns. To quote,

“The securities held in the portfolio blend and the signal blend can be mapped to the 4×4 quartile matrix (Table 5). The portfolio blend holds securities in the top row (Q4 value) and second-to-last column (Q4 momentum). All buckets provide positive contributions to active return. The mapping is more complicated for the signal blend but is roughly consistent with the diagram in Figure 1 (i.e., holdings will be anything to the right of the diagonal line drawn from the top left to the bottom right of the 4×4 matrix). Examining contributions to active return and risk (not reported), we find that the signal blend suffers from not holding enough of the high value/low momentum (Q4/Q1) stocks and low value/high momentum (Q1/Q4) stocks. The signal blend also incurs significant risk from holding Q3 value/Q3 momentum stocks, which have a negative active return (-0.4%). High momentum/high value (Q4/Q4) stocks earn the highest active return. These stocks offer a greater benefit to the portfolio blend as they are double-weighted.
In terms of active risk contributions, we note that low momentum/high value (Q1/Q4) stocks have a net positive exposure to value, while high momentum/low value (Q4/Q1) stocks have a net positive exposure to momentum. These two groups exhibit a high negative active return correlation and are diversifying (i.e., reduce active risk), while delivering positive active returns. As such, the assertion that avoiding securities with offsetting factor exposures improves portfolio performance is not entirely correct. If factor payoffs depict strong interaction effects, then holding such securities may actually be beneficial, and the portfolio blend benefits from investing in such securities. These contextual relationships are also present to varying degrees in other factor pairings.”

When factor concentration is higher, however, the increased degree of idiosyncratic risk found in Area 1 of the composite approach outweighs the interaction benefits found in Area 3. This effect can be seen in the table below. We see that Shared Securities under Portfolio Blend have an increased Active Return Contribution in comparison to the Signal Blend but also significantly higher Active Risk Contribution. This is due to the fact that Shared Securities represent only 45% of the active weight in the High Factor Exposure example for the Signal Blend approach, but 72% of the weight in the Portfolio Blend. The large portfolio concentration on just a few securities ultimately introduces too much idiosyncratic risk.

Source: Ghayur, Heaney, and Platt (2016)

Furthermore, while Area 3 (Securities Held Only in Portfolio Blend) remains a positive contributor to Active Return, it does not have the negative Active Risk contribution as it did in the prior, low factor concentration example.

The broad result that Ghayur, Heaney, and Platt (2016) propose is simple: for low-to-moderate levels of factor exposures, a portfolio blend exhibits higher information ratios and for higher levels of factor exposure, a signal blend approach works better. That being said, we would be remiss if we didn’t point out that these types of conclusions are very dependent on the exact portfolio construction methodology used. There are varying qualities of approaches to building both portfolio blend and signal blend multi-factor portfolios, which brings us back full circle to…

Re-Addressing FTSE Russell’s Tilt-Tilt Method

In our initial empirical analysis of FTSE Russell’s leverage argument, we were unable to actually test the theory on FTSE Russell’s multi-factor approach itself due to a lack of data. In our analytical analysis, we used a standard integrated approach of averaging factor scores. FTSE Russell takes the integrated method a step further by introducing a “tilt-tilt” approach, where instead of averaging factor signals to create an integrated signal, they use a multiplicative approach.

This multiplicative approach, however, is not run on normally distributed variables (i.e. factor z-scores) as was the case in our own analysis (and GSAM paper discussed above), but rather on uniformly distributed scores between [0, 1].

This makes things analytically gnarly (e.g. instead of working with normal and chi-squared distributions, we’re working with Irwin-Hall and product of uniform distributions). Fortunately, we can employ a numerical approach to get an idea of what is going on. Below we simulate scores for two factors (assumed to be independent; let’s call them A and B) for 500 stocks and then plot the distribution of resulting integrated and tilt-tilt scoring methods using those scores.

Source: Newfound Research. Simulation-based methodology.

What we can see is that while the integrated approach looks somewhat normal (in fact, the Irwin-Hall distribution approaches normal as more uniform distributions are added; e.g. we incorporate more factors), the tilt-tilt distribution is single-tailed.

A standard next step in constructing an index would be to multiply these scores by benchmark weights and then normalize to come up with new, tilted weights. We can get a sense for how weights are scaled by taking each distribution above and dividing it by the distribution average and then plotting scores against each other.

Source: Newfound Research. Simulation-based methodology.

The grey dotted line provides guidance as to how the two methods differ. If a point is above the line, it means the integrated approach has a larger tilt; points below the line indicate that the tilt-tilt method has a larger tilt.

What we can see is that for scores below average, tilt-tilt is more aggressive at reducing exposure; similarly for scores above average, tilt-tilt is more aggressive at increasing exposure. In other words, the tilt-tilt approach works to aggressively increase the intensity of factor exposure.

Using index data for FTSE Russell factor indices, we can empirically test whether this approach actually captures the capital efficiency that integrated approaches should benefit from. Specifically, we can compare the FTSE Russell Comprehensive Factor Index (the tilt-tilt integrated multi-factor approach) versus an equal-weight composite of FTSE Russell single-factor indices. The FTSE Russell multi-factor approach includes value, size, momentum, quality, and low-volatility tilts, so our composite portfolio will be an equal-weight portfolio of long-only indices representing these factors.

To test for factor exposure, we regress both portfolios against long/short factors from AQR’s data library. Data covers the period of 9/30/2001 through 1/31/2017.

We find that factor loadings for the tilt-tilt method exceed those for the equal-weight composite.

Source: FTSE Russell; AQR; calculations by Newfound Research.

We also find they do an admirable job at capturing a significant share of factor exposure available that would be available in long-only single-factor indices. In other words, if instead of taking a composite approach – which we expect to be diluted – we decide to only purchase a long-only momentum portfolio, how much of that long-only momentum exposure can be re-captured by using this tilt-tilt integrated, multi-factor approach?

We find that for most factors, it is a significant proportion.

Source: FTSE Russell; AQR; calculations by Newfound Research.

(Note: The Bet-Against-Beta factor (“BAB”) is removed from this chart because the amount of the factor available in the FTSE Russell Volatility Factor Index was deemed to be insignificant, and so resulting relative proportions exceed 18x).

Conclusion

While the jury is still out on factor timing itself, diversifying across factors is broadly considered to be a prudent decision. How to implement that diversification remains in debate.

What makes the diversification concept in multi-factor investing unique, as compared to standard asset class diversification, is that through an integrated approach, implicit leverage can be accessed. The same dollar can be used to introduce multiple factor exposures simultaneously.

While this implicit leverage should lead to portfolios that empirically have more factor exposure, evidence suggests that is not always the case. A new paper by the ActiveBeta team at Goldman Sachs suggests that for low-to-moderate levels of factor exposure, a composite approach may be just as, if not more, effective as an integrated approach. More surprisingly is that this effectiveness comes from beneficial interaction effects exactly in the area of the portfolio that integrated advocates have claimed there to be a drag.

At higher concentration levels of factor exposure, however, the integrated approach is more efficient, as the composite approach appears to introduce too much idiosyncratic risk.

We bring the conversation full circle in this piece by going back to some original research we detailed last fall, testing FTSE Russell’s unique tilt-tilt methodology to integrated mutli-factor investing. In theory, the tilt-tilt method should increase the intensity of factor exposure compared to traditional integrated approaches. While we previously found little empirical evidence supporting the capital efficiency argument for integrated multi-factor ETFs versus composite peers, a test of FTSE Russell index data finds that the tilt-tilt method may provide a significant boost to factor exposure.

Anatomy of a Bull Market: Follow-Up

By Justin Sibears

On February 13, 2017

In Equity, Risk & Style Premia, Weekly Commentary

Based on our post from earlier today (“Anatomy of a Bull Market“), we received a request to decompose U.S. equity returns over rolling 10-year periods.

The graph presenting this data is below. To perform these calculations, we calculate the annualized return generated by each source (inflation, dividends, earnings growth, and valuation changes), take the absolute value, and then normalize so that the total sums to one.

Data Source: Robert Shiller’s data library. Calculations by Newfound Research. Monthly data is used to make these calculations. Past performance does not guarantee future results.

On average over all rolling 10-year periods, each source contributed the following percentage to total return (ordered from biggest to smallest contributor):

Dividends: 31%
Valuation Changes: 28%
Inflation: 25%
Earnings Growth: 16%

We also performed the analysis for shorter (3-year) and longer (30-year) rolling periods.

Data Source: Robert Shiller’s data library. Calculations by Newfound Research. Monthly data is used to make these calculations. Past performance does not guarantee future results.

Over shorter time horizons, valuation changes start to dominate returns:

Valuation Changes (40%)
Dividends (25%)
Inflation (21%)
Earnings Growth (15%)

Data Source: Robert Shiller’s data library. Calculations by Newfound Research. Monthly data is used to make these calculations. Past performance does not guarantee future results.

But over longer periods, the impact of valuations starts to approach zero as shorter-term fluctuations offset each other. Inflation and dividend yield together drive 70%+ of 30-year returns on average:

Dividends (44%)
Inflation (28%)
Earnings Growth (15%)
Valuation Changes (13%)

[Note: An earlier version of this post used total return data. We amended the analysis to use annualized returns.]

Category: Risk & Style Premia Page 14 of 16

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

Navigating Municipal Bonds With Factors

Summary

Constructing Long/Short Factor Portfolios

Moving From Single Factor to Multi-Factor Portfolios

Moving From Long/Short to Long Only

Conclusion

Did Declining Rates Actually Matter?

Summary­­

Rates Down, Bonds Up

Just How Much More Valuable?

The Impact of Time

The Impact of Choice

Turnover in a Bond Index

Conclusion: Were Declining Rates Important?

Diversification in Multi-Factor Portfolios

Summary­­

Diversifying Multi-Factor Portfolios: Composite vs. Integrated

New Evidence of Interaction Effects in Multi-Factor Portfolios

Re-Addressing FTSE Russell’s Tilt-Tilt Method

Conclusion

Anatomy of a Bull Market: Follow-Up

Summary

Summary

Summary