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.

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.

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).

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.

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.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.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.

Only 14 of the 33 funds in the universe have statistically significant exposure to the value factor with an average beta of -0.03.

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.

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.

## Factor Investing & The Bets You Didn’t Mean to Make

By Corey Hoffstein

On January 16, 2018

In Craftsmanship, Portfolio Construction, Risk & Style Premia, Risk Management, Weekly Commentary

This post is available as a PDF download here.SummaryIn quantitative investing, we seek a balance between generality and specificity. When a model is too specific – designed to have meaning on too few securities or in too few scenarios – we lose our ability to diversify. When a model is too generic, it loses meaning and forecasting power.

The big quant factors – value, momentum, defensive, carry, and trend – all appear to find this balance: generic enough to be applied broadly, but specific enough to maintain a meaningful signal.

As we argued in our past commentary

A Case Against Overweighting International Equity, the imprecision of the factors is a feature, not a bug. A characteristic like price-to-earnings may never fully capture the specific nuances of each firm, but it can provide a directionally accurate roadmap to relative firm valuations. We can then leverage diversification to average out the noise.Without diversification, we are highly subject to the imperfections of the model. This is why, in the same piece, we argued that making a large regional tilt – e.g. away from U.S. towards foreign developed – may not be prudent: it is a single bet that can take decades to resolve. If we are to sacrifice diversification in our portfolio, we’ll require a much more accurate model to justify the decision.

Diversification, however, is not just measured by the

quantityof bets we take. If diversification is too naively interpreted, the same imprecision that allows factors to be broadly applied can leave our portfolios subject to the returns of unintended bets.Value Investing with CountriesIf taking a single, large regional tilt is not prudent, perhaps value investing at a country level may better diversify our risks.

One popular way of measuring value is with the Shiller CAPE: a cyclically-smoothed price-to-earnings measure. In the table below, we list the current CAPE and historical average CAPE for major developed countries.

CAPEMean CAPEEffective WeightSource: StarCapital.de. Effective weight is market-capitalization weight of each country, normalized to sum to 100%.Mean CAPE figures use data post-1979 to leverage a common dataset.While evidence[1] suggests that valuation levels themselves are enough to determine relative valuation among countries, we will first normalize the CAPE ratio by its long-term average to try to account for structural differences in CAPE ratios (e.g. a high growth country may have a higher P/E, a high-risk country may have a lower P/E, et cetera). Specifically, we will look at the log-difference between the mean CAPE and the current CAPE scores.

Note that we recognize there is plenty to criticize and improve upon here. Using a normalized valuation metric will mean a country like Japan, which experienced a significant asset bubble, will necessarily look under-valued. Please do not interpret our use of this model as our advocacy for it: we’re simply using it as an example.Using this value score, we can compare how over and undervalued each country is relative to each other. This allows us to focus on the

relativecheapness of each investment. We can then use these relative scores to tilt our market capitalization weights to arrive at a final portfolio.Value ScoreRelative Z-ScoreScaled Z-ScoreScaled WeightsSource: StarCapital.de. Calculations by Newfound Research. “Value Score” is the log-difference between the country’s Mean CAPE and its Current CAPE. Relative Z-Score is the normalized value score of each country relative to peers. Scaled Z-Score applies the following function to the Relative Z-Score: (1+x) if x > 0 and 1 / (1+x) if x < 0. Scaled weights multiply the Scaled Z-Score against the Effective Weights of each country and normalize such that the total weights sum to 100%.While the Scaled Weights represent a long-only portfolio, what they really capture is the Market Portfolio plus a dollar-neutral long/short factor tilt.

Market Weight+ Long / Short= Scaled WeightsTo understand the characteristics of the

tiltwe are taking – i.e. the differences we have created from the market portfolio – we need only look at the long/short portfolio.Unfortunately, this is where our model loses a bit of interpretability. Since each country is being compared against its own long-term average, looking at the increase or decrease to the aggregate CAPE score is meaningless. Indeed, it is possible to imagine a scenario whereby this process actually

increasesthe top-level CAPE score of the portfolio, despite taking value tilts (if value, for example, is found in countries that have higher structural CAPE values). We can, on the other hand, look at the weighted average change to value score: but knowing that we increased our value score by 0.21 has little interpretation.One way of looking at this data, however, is by trying to translate value scores into return expectations. For example, Research Affiliates expects CAPE levels to mean-revert to the average level over a 20-year period.[2] We can use this model to translate our value scores into an annualized return term due to revaluation. For example, with a current CAPE of 30.5 and a long-term average of 20.3, we would expect a -2.01% annualized drag from revaluation.

By multiplying these return expectations against our long/short portfolio weights, we find that our long/short tilt is expected to create an annualized revaluation premium of +1.05%.

The Unintended BetUnfortunately, re-valuation is not the only bet the long/short portfolio is taking. The CAPE re-valuation is, after all, in

local currencyterms. If we look at our long/short portfolio, we can see a very large weight towards Japan. Not only will we be subject to the local currency returns of Japanese equities, but we will also be subject to fluctuations in the Yen / US Dollar exchange rate.Therefore, to achieve the re-valuation premium of our long/short portfolio, we will either need to bear the currency risk or hedge it away.

In either case, we can use

uncovered interest rate parityto develop an expected return for currency. The notion behind uncovered interest rate parity is that investors should be indifferent to sovereign interest rates. In theory, for example, we should expect the same return from investing in a 1-year U.S. Treasury bond that we expect from converting $1 to 1 euro, investing in the 1-year German Bund, and converting back after a year’s time.Under uncovered interest rate parity, our expectation is that currency change should offset the differential in interest rates. If a foreign country has a higher interest rate, we should expect that the U.S. dollar should appreciate against the foreign currency.

As a side note, please be aware that this is a highly, highly simplistic model for currency returns. The historical efficacy of the carry trade clearly demonstrates the weakness of this model. More complex models will take into account other factors such as relative purchasing power reversion and productivity differentials.Using this simple model, we can forecast currency returns for each country we are investing in.

FX Rate1-Year RateExpected FX RateCurrency ReturnSource: Investing.com, XE.com. Euro area yield curve employed for Eurozone countries on the Euro.Multiplying our long/short weights against the expected currency returns, we find that we have created an expected annualized currency return of -0.45%.

In other words, we should expect that almost 50% of the value premium we intended to generate will be eroded by a currency bet we never intended to make.

One way of dealing with this problem is through portfolio optimization. Instead of blindly value tilting, we could seek to maximize our value characteristics subject to currency exposure constraints. With such constraints, what we would likely find is that more tilts would be made within the Eurozone since they share a currency. Increasing weight to one Eurozone country while simultaneously reducing weight to another can capture their relative value spread while remaining currency neutral.

Of course, currency is not the only unintended bet we might be making. Blindly tilting with value can lead to time varying betas, sector bets, growth bets, yield bets, and a variety of other factor exposures that we may not actually intend. The assumption we make by looking at value alone is that these other factors will be independent from value, and that by diversifying both across assets and over time, we can average out their impact.

Left entirely unchecked, however, these unintended bets can lead to unexpected portfolio volatility, and perhaps even ruin.

ConclusionIn past commentaries, we’ve argued that investors should focus on achieving capital efficiency by employing active managers that provide more pure exposure to active views. It would seem constraints, as we discussed at the end of the last section, might contradict this notion.

Why not simply blend a completely unconstrained, deep value manager with market beta exposure such that the overall deviations are constrained by position limits?

One answer why this might be less efficient is that not all bets are necessarily compensated. Active risk for the sake of active risk is not the goal: we want to maximize

compensatedactive risk. As we showed above, a completely unconstrained value manager may introduce a significant amount of unintended tracking error. While we are forced to bear this risk, we do not expect the manager’s process to actually create benefit from it.Thus, a more constrained approach may actually provide more efficient exposure.

That is all not to say that unconstrained approaches do not have efficacy: there is plenty of evidence that the blind application of value at the country index level has historically worked. Rather, the application of value at a global scale might be further enhanced with the management of unintended bets.

[1] For example,

Predicting Stock Market Returns Using the Shiller CAPE(StarCapital Research, January 2016) andValue and Momentum Everywhere(Asness, Moskowitz, and Pedersen, June 2013)[2] See Research Affiliate’s Equity Methodology for their Asset Allocation tool.