We continue our exploration of quantitative signals in fixed income.

We use a measure of credit curve steepness as a valuation signal for timing exposure between corporate bonds and U.S. Treasuries.

The value signal generates a 0.84% annualized return from 1950 to 2019 but is highly regime dependent with meaningful drawdowns.

Introducing a naïve momentum strategy significantly improves the realized Sharpe ratio and drawdown profile, but does not reduce the regime-based nature of the returns.

With a combined return of just 1.0% annualized, this strategy may not prove effective after appropriate discounting for hindsight bias, costs, and manager fees. The signal itself, however, may be useful in other contexts.

In the last several weeks, we have been exploring the application of quantitative signals to fixed income.

In Tactical Credit we explored trend-following strategies with high yield bonds.

Value (measured as deviation from real yield), momentum (prior 12-month returns), and carry (yield-to-worst) were all profitable factors in cross-section municipal bond sector long/short portfolios.

Value (measured as deviation from real yield), trend (measured as prior return), and carry (measured as term spread + roll yield) have historically been effective timing signals for U.S. duration exposure.

Prior short-term equity returns proved to be an effective signal for near-term returns in U.S. Treasuries (related to the “flight-to-safety premium”).

Short-term trend proved effective for high yield bond timing, but the results were vastly determined by performance in 2000-2003 and 2008-2009. While the strategy appeared to still be able to harvest relative carry between high-yield bonds and core fixed income in other environments, a significant proportion of returns came from avoiding large drawdowns in high yield.

Short-term cross-section momentum (prior total returns), value (z-score of loss-adjusted yield-to-worst), carry (loss-adjusted yield-to-worst), and 3-year reversals all appeared to offer robust signals for relative selection in fixed income sectors. The time period covered in the study, however, was limited and mostly within a low-inflation regime.

Application of momentum, value, carry, and reversal as timing signals proved largely ineffective for generating excess returns.

In this week’s commentary, we want to further contribute to research by introducing a value timing signal for credit.

Finding Value in Credit

Identifying a value signal requires some measure or proxy of an asset’s “fair” value. What can make identifying value in credit so difficult is that there are a number of moving pieces.

Conceptually, credit spreads should be proportional to default rates, recovery rates, and aggregate risk appetite, making determining whether spreads are cheap or expensive rather complicated. Prior literature typically tackles the problem with one of three major categories of models:

Econometric: “Fair value” of credit spreads is modeled through a regression that typically explicitly accounts for default and recovery rates. Inputs are often related to economic and market variables, such as equity market returns, 10-year minus 2-year spreads, corporate leverage, and corporate profitability. Bottom-up analysis may use metrics such as credit quality, maturity, supply, and liquidity.

Merton Model: Based upon the idea the bond holders have sold a put on a company’s asset value. Therefore, options pricing models can be used to calculate a credit spread. Inputs include the total asset value, asset volatility, and leverage of the firm under analysis.

Spread Signal: A simple statistical model derived from credit spread themselves. For example, a rolling z-score of option-adjusted spreads or deviations from real yield. Other models (e.g. Haghani and Dewey (2016)) have used spread plus real yield versus a long-run constant (e.g. “150 basis points”).

The first method requires a significant amount of economic modeling. The second approach requires a significant amount of extrapolation from market data. The third method, while computationally (and intellectually) less intensive, requires a meaningful historical sample that realistically needs to cover at least one full market cycle.

While attractive for its simplicity, there are a number of factors that complicate the third approach.

First, if spreads are measured against U.S. Treasuries, the metric may be polluted by information related to Treasuries due to their idiosyncratic behavior (e.g. scarcity effects and flight-to-safety premiums). Structural shifts in default rates, recovery rates, and risk appetites may also cause a problem, as spreads may appear unduly thin or wide compared to past regimes.

In light of this, in this piece we will explore a similarly simple-to-calculate spread signal, but one that hopefully addresses some of these short-comings.

Baa vs. Aaa Yields

In order to adjust for these problems, we propose looking at the steepness of the credit curve itself by comparing prime / high-grade yield versus lower-medium grade yields. For example, we could compare Moody’s Season Aaa Corporate Bond Yield and Moody’s Season Baa Corporate Bond Yield. In fact, we will use these yields for the remainder of this study.

We may be initially inclined to measure the steepness of the credit curve by taking the difference in yield spreads, which we plot below.

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

We can find a stronger mean-reverting signal, however, if we calculate the log-difference in yields.

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

We believe this transformation is appropriate for two reasons. First, the log transformation helps control for the highly heteroskedastic and skewed nature of credit spreads.

Second, it helps capture both the steepness andthe level of the credit curve simultaneously. For example, a 50-basis-point premium when Aaa yield is 1,000 basis points is very different than when Aaa yield is 100 basis points. In the former case, investors may not feel any pressure to bear excess risk to achieve their return objectives, and therefore a 50-basis-point spread may be quite thin. In the latter case, 50 basis points may represent a significant step-up in relative return level in an environment where investors have either low default expectations, high recovery expectations, high risk appetite, or some combination thereof.

Another way of interpreting our signal is that it informs us about the relative decisions investors must make about their expected dispersion in terminal wealth.

Constructing the Value Strategy

With our signal in hand, we can now attempt to time credit exposure. When our measure signals that the credit curve is historically steep, we will take credit risk. When our signal indicates that the curve is historically flat we will avoid it.

Specifically, we will construct a dollar-neutral long/short portfolio using the Dow Jones Corporate Bond Index (“DJCORP”) and a constant maturity 5-year U.S. Treasury index (“FV”). We will calculate a rolling z-score of our steepness measure and go long DJCORP and short FV when the z-score is positive and place the opposite trade when the z-score is negative.

In line with prior studies, we will apply an ensemble approach. Portfolios are reformed monthly using formation ranging from 3-to-6 years with holding periods ranging from 1-to-6 months. Portfolio weights for the resulting strategy are plotted below.

Source: Federal Reserve of St. Louis and Global Financial Data. Calculations by Newfound Research.

We should address the fact that while both corporate bond yield and index data is available back to the 1930s, we have truncated our study to ignore dates prior to 12/1949 to normalize for a post-war period. It should be further acknowledged that the Dow Jones Corporate Bond index used in this study did not technically exist until 2002. Prior to that date, the index return tracks a Dow Jones Bond Aggregate, which was based upon four sub-indices: high-grade rails, second-grade rails, public utilities, and industries. This average existed from 1915 to 1976, when it was replaced with a new average at that point when the number of railway bonds was no longer sufficient to maintain the average.

Below we plot the returns of our long/short strategy.

Source: Federal Reserve of St. Louis and Global Financial Data. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.

The strategy has an annualized return of 0.84% with a volatility of 3.89%, generating a Sharpe ratio of 0.22. Of course, long-term return statistics belie investor and manager experience, with this strategy exhibiting at least two periods of decade-plus-long drawdowns. In fact, the strategy really has just four major return regimes: 1950 to 1970 (-0.24% annualized), 1970 to 1987 (2.59% annualized), 1987 to 2002 (-0.33%), and 2002 to 2019 (1.49% annualized).

Try the strategy out in the wrong environment and we might be in for a lot of pain.

Momentum to the Rescue?

It is no secret that value and momentum go together like peanut butter and jelly. Instead of tweaking our strategy to death in order to improve it, we may just find opportunity in combining it with a negatively correlated signal.

Using an ensemble model, we construct a dollar-neutral long/short momentum strategy that compares prior total returns of DJCORP and FV. Rebalanced monthly, the portfolios use formation periods ranging from 9-to-15 months and holding periods ranging from 1-to-6 months.

Below we plot the growth of $1 in our value strategy, our momentum strategy, and a 50/50 combination of the two strategies that is rebalanced monthly.

Source: Federal Reserve of St. Louis and Global Financial Data. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.

The first thing we note is – even without calculating any statistics – the meaningful negative correlation we see in the equity curves of the value and momentum strategies. This should give us confidence that there is the potential for significant improvement through diversification.

The momentum strategy returns 1.11% annualized with a volatility of 3.92%, generating a Sharpe ratio of 0.29. The 50/50 combination strategy, however, returns 1.03% annualized with a volatility of just 2.16% annualized, resulting in a Sharpe ratio of 0.48.

While we still see significant regime-driven behavior, the negative regimes now come at a far lower cost.

Conclusion

In this study we introduce a simple value strategy based upon the steepness of the credit curve. Specifically, we calculated a rolling z-score on the log-difference between Moody’s Seasoned Baa and Aaa yields. We interpreted a positive z-score as a historically steep credit curve and therefore likely one that would revert. Similarly, when z-scores were negative, we interpreted the signal as a flat credit curve, and therefore a period during which taking credit risk is not well compensated.

Employing an ensemble approach, we generated a long/short strategy that would buy the Dow Jones Corporate Bond Index and short 5-year U.S. Treasuries when credit appeared cheap and place the opposite trade when credit appeared expensive. We found that this strategy returned 0.84% annualized with a volatility of 3.89% from 1950 to 2019.

Unfortunately, our value signal generated significantly regime-dependent behavior with decade-long drawdowns. This not only causes us to question the statistical validity of the signal, but also the practicality of implementing it.

Fortunately, a naively constructed momentum signal provides ample diversification. While a combination strategy is still highly regime-driven, the drawdowns are significantly reduced. Not only do returns meaningfully improve compared to the stand-alone value signal, but the Sharpe ratio more-than-doubles.

Unfortunately, our study leveraged a long/short construction methodology. While this isolates the impact of active returns, long-only investors must cut return expectations of the strategy in half, as a tactical timing model can only half-implement this trade without leverage. A long-only switching strategy, then, would only be expected to generate approximately 0.5% annualized excess return above a 50% Dow Jones Corporate Bond Index / 50% 5-Year U.S. Treasury index portfolio.

And that’s before adjustments for hindsight bias, trading costs, and manager fees.

Nevertheless, more precise implementation may lead to better results. For example, our indices neither perfectly matched the credit spreads we evaluated, nor did they match each other’s durations. Furthermore, while this particular implementation may not survive costs, this signal may still provide meaningful information for other credit-based strategies.

## Value and the Credit Spread

By Corey Hoffstein

On July 1, 2019

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

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

In the last several weeks, we have been exploring the application of quantitative signals to fixed income.

Tactical Creditwe explored trend-following strategies with high yield bonds.Quantitative Styles and Multi-Sector Bondswe built off a prior piece (Navigating Municipal Bonds with Factors)and explored the cross-sectional application of momentum, value, carry, reversal, and volatility signals in a broad fixed income universe.Time Series Signals and Multi-Sector Bondswe explored the same momentum, value, carry, and reversal signals as market timing signals.Recent cross-sectional studies also build off of further research we’ve done in the past on applying trend, value, carry, and explicit measures of the bond risk premium as duration timing mechanisms (see

Duration Timing with Style Premia;Timing Bonds with Value, Momentum, and Carry; andA Carry-Trend-Hedge Approach to Duration Timing).Broadly, our studies have found:

In this week’s commentary, we want to further contribute to research by introducing a value timing signal for credit.

Finding Value in CreditIdentifying a value signal requires some measure or proxy of an asset’s “fair” value. What can make identifying value in credit so difficult is that there are a number of moving pieces.

Conceptually, credit spreads should be proportional to default rates, recovery rates, and aggregate risk appetite, making determining whether spreads are cheap or expensive rather complicated. Prior literature typically tackles the problem with one of three major categories of models:

Econometric: “Fair value” of credit spreads is modeled through a regression that typically explicitly accounts for default and recovery rates. Inputs are often related to economic and market variables, such as equity market returns, 10-year minus 2-year spreads, corporate leverage, and corporate profitability. Bottom-up analysis may use metrics such as credit quality, maturity, supply, and liquidity.Merton Model: Based upon the idea the bond holders have sold a put on a company’s asset value. Therefore, options pricing models can be used to calculate a credit spread. Inputs include the total asset value, asset volatility, and leverage of the firm under analysis.Spread Signal: A simple statistical model derived from credit spread themselves. For example, a rolling z-score of option-adjusted spreads or deviations from real yield. Other models (e.g. Haghani and Dewey (2016)) have used spread plus real yield versus a long-run constant (e.g. “150 basis points”).The first method requires a significant amount of economic modeling. The second approach requires a significant amount of extrapolation from market data. The third method, while computationally (and intellectually) less intensive, requires a meaningful historical sample that realistically needs to cover at least one full market cycle.

While attractive for its simplicity, there are a number of factors that complicate the third approach.

First, if spreads are measured against U.S. Treasuries, the metric may be polluted by information related to Treasuries due to their idiosyncratic behavior (e.g. scarcity effects and flight-to-safety premiums). Structural shifts in default rates, recovery rates, and risk appetites may also cause a problem, as spreads may appear unduly thin or wide compared to past regimes.

In light of this, in this piece we will explore a similarly simple-to-calculate spread signal, but one that hopefully addresses some of these short-comings.

Baa vs. Aaa YieldsIn order to adjust for these problems, we propose looking at the steepness of the credit curve itself by comparing prime / high-grade yield versus lower-medium grade yields. For example, we could compare Moody’s Season Aaa Corporate Bond Yield and Moody’s Season Baa Corporate Bond Yield. In fact, we will use these yields for the remainder of this study.

We may be initially inclined to measure the steepness of the credit curve by taking the difference in yield spreads, which we plot below.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.We can find a stronger mean-reverting signal, however, if we calculate the log-difference in yields.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.We believe this transformation is appropriate for two reasons. First, the log transformation helps control for the highly heteroskedastic and skewed nature of credit spreads.

Second, it helps capture both the steepness

andthe level of the credit curve simultaneously. For example, a 50-basis-point premium when Aaa yield is 1,000 basis points is very different than when Aaa yield is 100 basis points. In the former case, investors may not feel any pressure to bear excess risk to achieve their return objectives, and therefore a 50-basis-point spread may be quite thin. In the latter case, 50 basis points may represent a significant step-up in relative return level in an environment where investors have either low default expectations, high recovery expectations, high risk appetite, or some combination thereof.Another way of interpreting our signal is that it informs us about the relative decisions investors must make about their expected dispersion in terminal wealth.

Constructing the Value StrategyWith our signal in hand, we can now attempt to time credit exposure. When our measure signals that the credit curve is historically steep, we will take credit risk. When our signal indicates that the curve is historically flat we will avoid it.

Specifically, we will construct a dollar-neutral long/short portfolio using the Dow Jones Corporate Bond Index (“DJCORP”) and a constant maturity 5-year U.S. Treasury index (“FV”). We will calculate a rolling z-score of our steepness measure and go long DJCORP and short FV when the z-score is positive and place the opposite trade when the z-score is negative.

In line with prior studies, we will apply an ensemble approach. Portfolios are reformed monthly using formation ranging from 3-to-6 years with holding periods ranging from 1-to-6 months. Portfolio weights for the resulting strategy are plotted below.

Source: Federal Reserve of St. Louis and Global Financial Data. Calculations by Newfound Research.We should address the fact that while both corporate bond yield and index data is available back to the 1930s, we have truncated our study to ignore dates prior to 12/1949 to normalize for a post-war period. It should be further acknowledged that the Dow Jones Corporate Bond index used in this study did not technically exist until 2002. Prior to that date, the index return tracks a Dow Jones Bond Aggregate, which was based upon four sub-indices: high-grade rails, second-grade rails, public utilities, and industries. This average existed from 1915 to 1976, when it was replaced with a new average at that point when the number of railway bonds was no longer sufficient to maintain the average.

Below we plot the returns of our long/short strategy.

Source: Federal Reserve of St. Louis and Global Financial Data. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.The strategy has an annualized return of 0.84% with a volatility of 3.89%, generating a Sharpe ratio of 0.22. Of course, long-term return statistics belie investor and manager experience, with this strategy exhibiting at least two periods of decade-plus-long drawdowns. In fact, the strategy really has just four major return regimes: 1950 to 1970 (-0.24% annualized), 1970 to 1987 (2.59% annualized), 1987 to 2002 (-0.33%), and 2002 to 2019 (1.49% annualized).

Try the strategy out in the wrong environment and we might be in for a lot of pain.

Momentum to the Rescue?It is no secret that value and momentum go together like peanut butter and jelly. Instead of tweaking our strategy to death in order to improve it, we may just find opportunity in combining it with a negatively correlated signal.

Using an ensemble model, we construct a dollar-neutral long/short momentum strategy that compares prior total returns of DJCORP and FV. Rebalanced monthly, the portfolios use formation periods ranging from 9-to-15 months and holding periods ranging from 1-to-6 months.

Below we plot the growth of $1 in our value strategy, our momentum strategy, and a 50/50 combination of the two strategies that is rebalanced monthly.

Source: Federal Reserve of St. Louis and Global Financial Data. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.The first thing we note is – even without calculating any statistics – the meaningful negative correlation we see in the equity curves of the value and momentum strategies. This should give us confidence that there is the potential for significant improvement through diversification.

The momentum strategy returns 1.11% annualized with a volatility of 3.92%, generating a Sharpe ratio of 0.29. The 50/50 combination strategy, however, returns 1.03% annualized with a volatility of just 2.16% annualized, resulting in a Sharpe ratio of 0.48.

While we still see significant regime-driven behavior, the negative regimes now come at a far lower cost.

ConclusionIn this study we introduce a simple value strategy based upon the steepness of the credit curve. Specifically, we calculated a rolling z-score on the log-difference between Moody’s Seasoned Baa and Aaa yields. We interpreted a positive z-score as a historically steep credit curve and therefore likely one that would revert. Similarly, when z-scores were negative, we interpreted the signal as a flat credit curve, and therefore a period during which taking credit risk is not well compensated.

Employing an ensemble approach, we generated a long/short strategy that would buy the Dow Jones Corporate Bond Index and short 5-year U.S. Treasuries when credit appeared cheap and place the opposite trade when credit appeared expensive. We found that this strategy returned 0.84% annualized with a volatility of 3.89% from 1950 to 2019.

Unfortunately, our value signal generated significantly regime-dependent behavior with decade-long drawdowns. This not only causes us to question the statistical validity of the signal, but also the practicality of implementing it.

Fortunately, a naively constructed momentum signal provides ample diversification. While a combination strategy is still highly regime-driven, the drawdowns are significantly reduced. Not only do returns meaningfully improve compared to the stand-alone value signal, but the Sharpe ratio more-than-doubles.

Unfortunately, our study leveraged a long/short construction methodology. While this isolates the impact of active returns, long-only investors must cut return expectations of the strategy in half, as a tactical timing model can only half-implement this trade without leverage. A long-only switching strategy, then, would only be expected to generate approximately 0.5% annualized excess return above a 50% Dow Jones Corporate Bond Index / 50% 5-Year U.S. Treasury index portfolio.

And that’s before adjustments for hindsight bias, trading costs, and manager fees.

Nevertheless, more precise implementation may lead to better results. For example, our indices neither perfectly matched the credit spreads we evaluated, nor did they match each other’s durations. Furthermore, while this particular implementation may not survive costs, this signal may still provide meaningful information for other credit-based strategies.