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Tag: bond timing

Tactical Credit

This post is available as a PDF download here.

Summary­

  • In this commentary we explore tactical credit strategies that switch between high yield bonds and core fixed income exposures.
  • We find that short-term momentum signals generate statistically significant annualized excess returns.
  • We use a cross-section of statistically significant strategy parameterizations to generate an ensemble strategy.Consistent with past research, we find that this ensemble approach helps reduce idiosyncratic specification risk and dramatically increases the strategy’s information ratio above the median underlying strategy information ratio.
  • To gain a better understanding of the strategy, we attempt to determine the source of strategy returns. We find that a significant proportion of returns are generated as price returns occurring during periods when credit spreads are above their median value and are expanding.
  • Excluding the 2000-2003 and 2008-2009 sub-periods reduces gross-of-cost strategy returns from 2.9% to 1.5%, bringing into question how effective post-of-cost implementation can be if we do not necessarily expect another crisis period to unfold.

There is a certain class of strategies we get asked about quite frequently but have never written much on: tactical credit.

The signals driving these strategies can vary significantly (including momentum, valuation, carry, macro-economic, et cetera) and implementation can range from individual bonds to broad index exposure to credit default swaps.  The simplest approach we see, however, are high yield switching strategies.  The strategies typically allocate between high yield corporate bonds and core fixed income (or short-to-medium-term U.S. Treasuries) predominately based upon some sort of momentum-driven signal.

It is easy to see why this seemingly naïve approach has been attractive.  Implementing a simple rotation between –high-yield corporates– and –core U.S. fixed income– with a 3-month lookback with 1-month hold creates a fairly attractive looking –tactical credit– strategy.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  HY Corporates represents the Vanguard High-Yield Corporate Fund (VWEHX).  Core Bonds is represented by the Vanguard Total. Bond Market Index Fund (VBMFX).  Returns assume the reinvestment of all distributions.

Visualizing the ratio of the equity curves over time, we see a return profile that is reminiscent of past writings on tactical and trend equity strategies. The tactical credit strategy tends to outperform core bonds during most periods, with the exception of periods of economic stress (e.g. 2000-2002 or 2008).  On the other hand, the tactical credit strategy tends to underperform high yield corporates in most environments, but has historically added significant value in those same periods of economic stress.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  HY Corporates represents the Vanguard High-Yield Corporate Fund (VWEHX).  Core Bonds is represented by the Vanguard Total. Bond Market Index Fund (VBMFX).  Returns assume the reinvestment of all distributions.

This is akin to tactical equity strategies, which have historically out-performed the safety asset (e.g. cash) during periods of equity market tailwinds, but under-performed buy-and-hold equity during those periods due to switching costs and whipsaw. As the most aggressive stance the tactical credit strategy can take is a 100% position in high yield corporates, it would be unrealistic for us to expect such a strategy to out-perform in an environment that is conducive to strong high yield performance.

What makes this strategy different than tactical equity, however, is that the vast majority of total return in these asset classes comes from income rather than growth.  In fact, since the 1990s, the price return of high yield bonds has annualized at -0.8%.  This loss reflects defaults occurring within the portfolio offset by recovery rates.1

This is potentially problematic for a tactical strategy as it implies a significant potential opportunity cost of switching out of high yield.  However, we can also see that the price return is volatile.  In years like 2008, the price return was -27%, more than offsetting the 7%+ yield you would have achieved just holding the fund.

Source: Tiingo.  Calculations by Newfound Research.   Returns gross of all management fees and taxes, but net of underlying fund fees.

Like trend equity, we can think of this tactical credit strategy as being a combination of two portfolios:

  • A fixed-mix of 50% high yield corporates and 50% core bonds; and
  • 50% exposure to a dollar-neutral long/short portfolio that captures the tactical bet.

For example, when the tactical credit portfolio is 100% in high yield corporates, we can think of this as being a 50/50 strategy portfolio with a 50% overlay that is 100% long high yield corporates and 100% short core bonds, leading to a net exposure that is 100% long high yield corporates.

Thinking in this manner allows us to isolate the active returns of the portfolio actually being generated by the tactical signals and determine value-add beyond a diversified buy-and-hold core.  Thus, for the remainder of this commentary we will focus our exploration on the long/short component.

Before we go any further, we do want to address that a naïve comparison between high yield corporates and core fixed income may be plagued by changing composition in the underlying portfolios as well as unintended bets.  For example, without specifically duration matching the legs of the portfolio, it is likely that a dollar-neutral long/short portfolio will have residual interest rate exposure and will not represent an isolated credit bet.  Thus, naïve total return comparisons will capture both interest rate and credit-driven effects.

This is further complicated by the fact that sensitivity to these factors will change over time due both to the math of fixed income (e.g. interest rate sensitivity changing over time due to higher order effects like convexity) as well as changes in the underlying portfolio composition.  If we are not going to specifically measure and hedge out these unintended bets, we will likely want to rely on faster signals such that the bet our portfolio was attempting to capture is no longer reflected by the holdings.

We will begin by first evaluating the stability of our momentum signals.  We do this by varying formation period (i.e. lookback) and holding period of our momentum rotation strategy and calculating the corresponding t-statistic of the equity curve’s returns.  We plot the t-statistics below and specifically highlight those regions were t-statistics exceed 2, a common threshold for significance.

Source: Tiingo.  Calculations by Newfound Research.

It should be noted that data for this study only goes back to 1990, so achieving statistical significance is more difficult as the sample size is significantly reduced. Nevertheless, unlike trend equity which tends to exhibit strong significance across formation periods ranging 6-to-18 months, we see a much more limited region with tactical credit. Only formation periods from 3-to-5 months appear significant, and only with holding periods where the total period (formation plus holding period) is less than 6-months.

Note that our original choice of 63-day (approximately 3 months) formation and 21-day (approximately 1 month) hold falls within this region.

We can also see that very short formation and holding period combinations (e.g. less than one month) also appear significant.  This may be due to the design of our test.  To achieve the longest history for this study, we employed mutual funds.  However, mutual funds holding less liquid underlying securities tend to exhibit positive autocorrelation. While we adjusted realized volatility levels for this autocorrelation effect in an effort to create more realistic t-statistics, it is likely that positive results in this hyper short-term region emerge from this effect.

Finally, we can see another rather robust region representing the same formation period of 3-to-5 months, but a much longer holding length of 10-to-12 months.  For the remainder of this commentary, we’ll ignore this region, though it warrants further study.

Assuming formation and holding periods going to a daily granularity, the left-most region represents over 1,800 possible strategy combinations.  Without any particular reason for choosing one over another, we will embrace an ensemble approach, calculating the target weights for all possible combinations and averaging them together in a virtual portfolio-of-portfolios configuration.

Below we plot the long/short allocations as well as the equity curve for the ensemble long/short tactical credit strategy.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Returns assume the reinvestment of all distributions.

Note that each leg of the long/short portfolio does not necessarily equal 100% notional.  This reflects conflicting signals in the underlying portfolios, causing the ensemble strategy to reduce its gross allocation as a reflection of uncertainty.

As a quick aside, we do want to highlight how the performance of the ensemble compares to the performance of the underlying strategies.

Below we plot the annualized return, annualized volatility, maximum drawdown, and information ratio of all the underlying equity curves of the strategies that make up the ensemble.  We also identify the –ensemble approach–.  While we can see that the ensemble approach brings the annualized return in-line with the median annualized return, its annualized volatility is in the 14thpercentile and its maximum drawdown is in the 8thpercentile.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Returns assume the reinvestment of all distributions.

By maintaining the median annualized return and significantly reducing annualized volatility, the ensemble has an information ratio in the 78thpercentile.  As we’ve demonstrated in prior commentaries, by diversifying idiosyncratic specification risk, the ensemble approach is able to generate an information ratio significantly higher than the median without having to explicitly choose which specification we believe will necessarily outperform.

Given this ensemble implementation, we can now ask, “what is the driving force of strategy returns?”  In other words, does the strategy create returns by harvesting price return differences or through carry (yield) differences?

One simple way of evaluating this question is by evaluating the strategy’s sensitivity to changes in credit spreads.  Specifically, we can calculate daily changes in the ICE BofAML US High Yield Master II Option-Adjusted Spread and multiply it against the strategy’s exposure to high yield bonds on the prior day.

By accumulating these weighted changes over time, we can determine how much spread change the strategy has captured.  We can break this down further by isolating positive and negative change days and trying to figure out whether the strategy has benefited from avoiding spread expansion or from harvesting spread contraction.

In the graph below, we can see that the strategy harvested approximately 35,000 basis points (“bps”) from 12/1996 to present (the period for which credit spread data was available). Point-to-point, credit spreads actually widened by 100bps over the period, indicating that tactical changes were able to harvest significant changes in spreads.

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

We can see that over the full period, the strategy predominately benefited from harvesting contracting spreads, as exposure to expanding spreads had a cumulative net zero impact.  This analysis is incredibly regime dependent, however, and we can see that periods like 2000-2003 and 2008 saw a large benefit from short-exposure in high yield during a period when spreads were expanding.

We can even see that in the case of post-2008, switching to long high yield exposure allowed the strategy to benefit from subsequent credit spread declines.

While this analysis provides some indication that the strategy benefits from harvesting credit spread changes, we can dig deeper by taking a regime-dependent view of performance. Specifically, we can look at strategy returns conditional upon whether spreads are above or below their long-term median, as well as whether they expand or contract in a given month.

Source: St. Louis Federal Reserve.  Calculations by Newfound Research.  Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Returns assume the reinvestment of all distributions.

Most of the strategy return appears to occur during times when spreads are above their long-term median. Calculating regime-conditional annualized returns confirms this view.

Above

Below

Expanding

10.88%

-2.79%

Contracting

1.59%

4.22%

 

The strategy appears to perform best during periods when credit spreads are expanding above their long-term median level (e.g. crisis periods like 2008).  The strategy appears to do its worst when spreads are below their median and begin to expand, likely representing periods when the strategy is generally long high yield but has not had a chance to make a tactical switch.

This all points to the fact that the strategy harvests almost all of its returns in crisis periods.  In fact, if we remove 2000-2003 and 2008-2009, we can see that the captured credit spread declines dramatically.

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

Capturing price returns due to changes in credit spreads are not responsible for all of the strategy’s returns, however.

Below we explicitly calculate the yield generated by the long/short strategy over time.  As high yield corporates tend to offer higher yields, when the strategy is net long high yield, the strategy’s yield is positive.  On the other hand, when the strategy is net short high yield, the strategy’s yield is negative.

This is consistent with our initial view about why these sorts of tactical strategies can be so difficult.  During the latter stages of the 2008 crisis, the long/short strategy had a net negative yield of close to -0.5% per month.2   Thus, the cost of carrying this tactical position is rather expensive and places a larger burden on the strategy accurately timing price return.

Source: Tiingo.  Calculations by Newfound Research.  Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.

From this graph, we believe there are two interesting things worth calling out:

  • The long-run average yield is positive, representing the strategy’s ability to capture carry differences between high yield and core bonds.
  • In the post-crisis environments, the strategy generates yields in excess of one standard deviation of the full-period sample, indicating that the strategy may have benefited from allocating to high yield when yields were abnormally large.

To better determine whether capturing changes in credit spreads or carry differences had a larger impact on strategy returns, we can explicitly calculate the –price– and –total return– indices of the ensemble strategy.

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

The –price return– and –total return– series return 2.1% and 2.9% annualized respectively, implying that capturing price return effects account for approximately 75% of the strategy’s total return.

This is potentially concerning, because we have seen that the majority of the price return comes from a single regime: when credit spreads are above their long-term median and expanding.  As we further saw, simply removing the 2000-2003 and 2008-2009 periods significantly reduced the strategy’s ability to harvest these credit spread changes.

While the strategy may appear to be supported by nearly 30-years of empirical evidence, in reality we have a situation where the vast majority of the strategy’s returns were generated in just two regimes.

If we remove 2000-2003 and 2008-2009 from the return series, however, we can see that the total return of the strategy only falls to 0.7% and. 1.6% annualized for –price return– and –total return– respectively.  While this may appear to be a precipitous decline, it indicates that there may be potential to capture both changes in credit spread and net carry differences even in normal market environments so long as implementation costs are kept low enough.

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

Conclusion

In this commentary, we explored a tactical credit strategy that switched between high yield corporate bonds and core fixed income.  We decompose these strategies into a 50% high yield / 50% core fixed income portfolio that is overlaid with 50% exposure to a dollar-neutral long/short strategy that captures the tactical tilts.  We focus our exploration on the dollar-neutral long/short portfolio, as it isolates the active bets of the strategy.

Using cross-sectional momentum, we found that short-term signals with formation periods ranging from 3-to-5 months were statistically significant, so long as the holding period was sufficiently short.

We used this information to construct an ensemble strategy made out of more than 1,800 underlying strategy specifications.  Consistent with past research, we found that the ensemble closely tracked the median annualized return of the underlying strategies, but had significantly lower volatility and maximum drawdown, leading to a higher information ratio.

We then attempted to deconstruct where the strategy generated its returns from.  We found that a significant proportion of total returns were achieved during periods when credit spreads were above their long-term median and expanding.  This is consistent with periods of economic volatility such as 2000-2003 and 2008-2009.

The strategy also benefited from harvesting net carry differences between high yield and core fixed income.  Explicitly calculating strategy price and total return, we find that this carry component accounts for approximately 25% of strategy returns.

The impact of the 2000-2003 and 2008-2009 periods on strategy returns should not be understated.   Removing these time periods reduced strategy returns from 2.9% to 1.6% annualized. Interestingly, however, the proportion of total return explained by net carry only increased from 25% to 50%, potentially indicating that the strategy was still able to harvest some opportunities in changing credit spreads.

For investors evaluating these types of strategies, cost will be an important component.  While environments like 2008 may lead to opportunities for significant out-performance, without them the strategy may offer anemic returns.  This is especially true when we recall that a long-only implementation only has 50% implicit exposure to the long/short strategy we evaluated in this piece.

Thus, the 2.9% annualized return is really closer to a 1.5% annualized excess return above the 50/50 portfolio.  For the ex-crisis periods, the number is closer to 0.8% annualized.  When we consider that this analysis was done without explicit consideration for management costs or trading costs and we have yet to apply an appropriate expectation haircut given the fact that this analysis was all backtested, there may not be sufficient juice to squeeze.

That said, we only evaluated a single signal in this piece.  Combining momentum with valuation, carry, or even macro-economic signals may lead to significantly better performance.  Further, high yield corporates is a space where empirical evidence suggests that security selection can make a large difference.  Careful selection of funds may lead to meaningfully better performance than just broad asset class exposure.

 


 

Timing Bonds with Value, Momentum, and Carry

This post is available as a PDF download here.

Summary­­

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

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

Historically Speaking, This is a Bad Idea

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

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

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

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

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

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

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

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

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

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

This Might Now be a Good Idea

Yet this idea might have legs.

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

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

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

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

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

Timing Bonds with Value

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We plot the results of the strategy below.

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

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

Timing Bonds with Momentum

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Timing Bonds with Carry

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

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

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

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

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

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

Building a Portfolio of Strategies

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

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

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

StrategyAnnualized ReturnAnnualized VolatilityInformation
Ratio
Max
Drawdown
10-Year Index Excess Return2.0%7.3%0.2736.2%
Value L/S2.0%5.0%0.4119.8%
Momentum L/S1.9%6.9%0.2720.9%
Carry L/S2.5%6.6%0.3820.1%
Equal Weight2.3%4.0%0.5710.2%

Source: Federal Reserve of St. Louis.  Philadelphia Federal Reserve.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not a guarantee of future results.  Returns are gross of all fees (including management fees, transaction costs, and taxes).  Returns assume the reinvestment of all income and distributions.  Performance measured from 6/1974 to 1/2018, representing the full overlapping investment period of the strategies.

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

Value L/SMomentum L/SCarry L/S
Value L/S1.0-0.2-0.1
Momentum L/S-0.21.00.6
Carry L/S-0.10.61.0

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

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

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

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

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

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

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

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

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

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

Conclusion

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

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

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

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

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

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

 


 

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

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

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

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

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