*This post is available as a PDF download here.*

# Summary

- We expand last week’s commentary to explore momentum, carry, value, and long-term reversal signals in a time-series context.
- Using these signals, we generate long/short portfolios for each asset class. We use a sub-sampling methodology to bootstrap and annualized return distribution.
- We find that the signals are only selectively significant, and rarely consistent.
- We believe this initial study supports the idea that the application of these signals for the purpose of generating excess returns may not be supported. It is still possible, however, that these signals can meaningfully manipulate return distributions in other ways (e.g. reduce drawdowns) that investors may value.

This week’s commentary aims to extend last week’s commentary (*Quantitative Styles and Multi-Sector Bonds*) by evaluating the same quantitative signals in a time-series, rather than cross-sectional, context.

With cross-sectional signals, we are making a relative comparison and asking, “which of these securities do we prefer?” With time-series signals, we are making an absolute comparison and are asking a different question, “do I want to hold this security at all?”

For example, consider a simple momentum signal. In last week’s commentary, we used prior returns to rank securities in quintiles and compared the performance of those quintiles, attempting to determine if we could find an edge by selecting securities that had recently outperformed their peers.

This week, we will employ the same total return calculation, but simply measure whether it is positive or negative. When it is positive, we will invest and when it is negative, we will go short.

In contrast to last week’s analysis where we built portfolios, this week we will evaluate each security individually. Specifically, we will construct dollar-neutral long/short portfolios for each security, going long the asset and short a 1-3 Year U.S. Treasuries index when signals are positive and short the asset and long a 1-3 Year U.S. Treasury index when signals are negative.

Here we should pause and address the fact that the assets in this universe can have significant borrowing costs. For example, going short a high yield bond ETF such as HYG could cost you well in excess of 0.5% annualized in borrowing costs. Thus, this analysis may not be sufficient for investors actually considering explicitly shorting. However, this analysis may still be highly relevant for investors looking to construct long/flat portfolios, where short positions are implicitly achieved through the reduction of position size.

In an effort to perform more robust analysis, we employ a sub-sampling approach. For each asset, we calculate long/short portfolio returns and then randomly drop 25% of periods, using the remaining 75% to estimate the annualized return. We repeat this 1,000 times to generate a distribution of annualized returns. Our goal in taking this approach is to attempt to determine if the results are highly regime dependent or due to an outlier time-period. If either of these are the case, we would expect to see a wide dispersion in annualized returns.

For each asset, we plot the intra-quartile range of the data as well as whiskers that cover approximately 99% of the data.

In the remainder of this rather brief commentary, we will review four separate sigals: momentum, carry, value, and reversal.

**Momentum**

We generate momentum signals by computing 12-, 6- and 3- month prior total returns to reflect slow, intermediate, and fast momentum signals. Portfolios are long when prior returns are positive and short when prior returns are negative. The portfolios assume a 1-month holding period for momentum signals. To avoid timing luck, four sub-indexes are used, each rebalancing on a different week of the month.

A few interesting data-points stand out:

- Results are highly inconsistent across 3-, 6-, and 12-month measures.
- Only three of the assets are significant for the 3- and 6-month momentum signals at the 1% level: hedged international bonds, U.S. credit, and short-term high yield.
- The significant dispersion in returns is reminiscent of the highly regime-driven results we identified when attempting to apply trend following to high yield in our commentary Tactical Credit.

*Source: Bloomberg; Tiingo. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.*

**Carry**

Carry is the expected excess return of an asset assuming price does not change. For our fixed income universe, we proxy carry using yield-to-worst minus the risk-free rate. For non-Treasury holdings, we adjust this figure for expected defaults and recovery.

Strategies are long when carry is positive and short when it is negative. The portfolios assume a 12-month holding period for carry signals. To avoid timing luck, 52 sub-indexes are used, each rebalancing on a different week of the year.

- Carry generates statistically positive results for 11 of the assets at a 5% level, and 9 of the assets at a 1% level.
- Two stand-outs are unhedged international government bonds and local currency emerging market debt, whose returns are highly influenced by currency fluctuations.
- It is worth acknowledging that carry was largely positive for most assets over the period, and this graph may largely represent just a buy-and-hold result.

*Source: Bloomberg; Tiingo. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.*

**Value**

In past commentaries, we have used real yield as our value proxy in fixed income. In this commentary, we deviate from that methodology slightly and use a time-series z-score of carry as our value of measure. Historically high carry levels are considered to be cheap while historically low carry levels are considered to be expensive.

Strategies are long when z-scores are positive and short when they are negative. The portfolios assume a 12-month holding period for value signals. To avoid timing luck, 52 sub-indexes are used, each rebalancing on a different week of the year.

- 7-10 year U.S. Treasuries, mortgage-backed securities, and TIPS are all significant at a 1% level. Hedged international bonds and US credit are significant at a 5% level.

*Source: Bloomberg; Tiingo. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions.** *

**Reversal**

Reversal signals are the opposite of momentum: we expect past losers to outperform and past winners to underperform. Empirically, reversals tend to occur over very short time horizons (e.g. 1 month) and longer-term time horizons (e.g. 3- to 5-years). In many ways, long-term reversals can be thought of as a naive proxy for value, though there may be other behavioral and structural reasons for the historical efficacy of reversal signals.

As we did in our prior commentary, we employ a z-score on prior rolling returns. Strategies short when z-scores are positive (return dynamics above average) and go long when z-scores are negative (return dynamics below average). The portfolios assume a 12-month holding period for value signals. To avoid timing luck, 52 sub-indexes are used, each rebalancing on a different week of the year.

We can see that reversal signals are largely unsuccessful, telling us that simply buying something because it has done poorly in the past, or selling it because it has done well, has not been a successful approach.

* *

**Conclusion**

In this study, we extend last week’s commentary and use the same quantitative signals – momentum, carry, value, and reversals – in a time-series manner.

In almost all cases, we find little statistical significance.

Time-series momentum – i.e. trend following – is not robust across formation periods or asset classes. In fact, it only appears to work for a small subset of asset classes (hedged international bonds, broad credit, and short-term high yield) in short-term formation periods.

Carry signals appear more significant, but likely only due to the fact that they remained largely positive over the entire testing period, leading to largely buy-and-hold portfolios.

The design of our value signals partially addresses the carry signal’s flaws through z-scoring. Unfortunately, we see – as with many other contexts – that value timing on its own rarely works.

Finally, we see that reversal signals offer almost no potential.

Taken together, we see little evidence herein supporting an *excess-return*driven motive for pursuing these signals in a time-series fashion. It is entirely possible, however, that these signals may manipulate return distributions in other meaningful ways (e.g. cut drawdown risk) and are still worth further exploration.

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