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

# Summary

- We explore “top N” sector rotation strategies based upon momentum signals.
- We find that too much concentration (i.e. N is too small) leads to poor performance, whereas performance does not appear to materially degrade for larger N.
- We find that short- to long-term signals all appear to generate higher total returns than the S&P 500 and there may be room to benefit from diversification by using multiple signals.
- However, in attempting to use momentum information in an optimization, we struggle to generate any value.
- We find that the majority of “top N” returns actually come from the tilt towards an equal-weight sector approach, with momentum adding little-to-no beneficial information.
- Of 1,000 randomly generated “top 4” sector strategies, 97% out-performed the S&P 500 from 2000-2012, highlighting the importance of decomposing strategy returns into the contribution of each step of the portfolio’s construction. In this case, by more appropriately measuring the impact of momentum information after accounting for the return generated by equal-weight tilts, we find no benefit since the turn of the century.

In last week’s commentary (“Es-CAPE Velocity: Value-Driven Sector Rotation,” August 26^{th}, 2019) we explored value-based sector rotation in the 20^{th}century. Specifically, we deconstructed the Shiller CAPE US Sector Rotation strategy and ultimately found that the largest driver of performance was *not *value, but a momentum-based filter.

Given the success of the momentum-based filter and the fact that momentum often exhibits negative correlation to value, in this week’s research note we wanted to explore the application of momentum-based signals in US sector rotation.

To perform this analysis, we will apply momentum-based signals to portfolios build from the SSgA Sector Select ETFs. After REITs were spun out of the Financial sector in 2016, a Vanguard REIT ETF was included in the investible universe. With the introduction of the Communication Services sector and a significant re-classification of Consumer Discretionary and Technology companies in September 2018, we utilized hypothetical indices that more accurately reflect the re-categorization (when historically applied) to generate momentum signals.

**How Many Sectors?**

To begin our analysis, we will start with a very traditional sector rotation model: a “top N” system. In this system, sectors are ranked on a quantitative signal and then the top N sectors with the strongest signals are equally weighted.

For example, in a top 4 12-month momentum system, sectors would be ranked based upon their prior 12-month total return and the strategy would allocate 25% of the portfolio to the top 4 ranking sectors for the next month.

The choice of N largely depends upon our expectations of signal strength, accuracy, and relative performance between ranks. For example, if the signal demonstrates a monotonic improvement in return (i.e. higher ranks imply higher returns) with a strong degree of accuracy, we might choose a small N to maximize our returns. The stronger the improvement, the more concentration risk we may be willing to bear.

On the other hand, if the signal is largely flat, with a drop-off in performance for lower ranking sectors, than we might treat it more as a screen, equally weighting a large number of sectors and avoiding just a few.

Below we plot the equity curves for different 12-month top N momentum strategies, where N is varied from 1 to 9. We have shaded the graph from darker-to-lighter blues in an effort to determine if there are any parameterization-based patterns that emerge visually.

We can quickly see that the more concentrated strategies – for example, Top 1 and Top 3 – have the lowest total returns. However, among more diversified strategies, there appears to be a large degree of consistency in their terminal wealth. This might suggest that momentum, when applied in the last century, served better in avoiding the worst sectors rather than picking the best.

*Source: CSI Data; S&P Dow Jones; Calculations by Newfound Research. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

**Long- versus Short-Term Momentum**

Below we plot all the top 4 systems with momentum lookbacks ranging from 1 to 18 months. Again, we vary the shades from darker-to-lighter blues in an effort to determine if any visual patterns emerge.

Interestingly, we can see that both short- (1-to-3 months) and long-term (16-to-18 months) momentum appear to perform the worst on a total return basis, while more intermediate-term measures (10- and 11-month momentum) appear to perform the best.

Of course, in the short-term, results can vary dramatically and even a 20-year period is not sufficient to determine if a cluster of parameterizations is superior. If we plot rolling 1-year returns, we can see dramatic dispersion in results versus the average return of the different parameterizations. For example, fromJune 2007 to June 2008, the 1M variation under-performed the average result by over 1100 basis points, but from February 2009 to February 2010, it out-performed by over 2000 basis points.

With no statistical difference in Sharpe ratios over the period, we would suggest that – once again – different parameterizations represent an opportunity for diversification.

*Source: CSI Data; S&P Dow Jones; Calculations by Newfound Research. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

**Tracking-Error Based**

The above analysis suggests that sector-based momentum may be most effective if we simply try to avoid the worst sectors and apply an ensemble of parameterizations. One potential way of improving our model, then, is via optimization. Specifically, we can seek to maximize our momentum exposure subject to tracking-error constraints with respect to the S&P 500.

To implement this idea, we:

- Generate N-month returns for each sector
- Calculate a covariance matrix from sector returns (exponentially weighted over the prior 252 days).
- Given current S&P 500 sector weights, select portfolio that maximizes weighted N-month returns subject to a given tracking error constraint.

The goal of this process is for the optimization process – despite the added computational complexity and embedded estimation risk – to more intelligently apply our active risk budget.

We also construct a variation where instead of maximizing the weighted N-month returns, we will transform the N-month returns to ranks and maximize the weighted rank. This can be thought of as a regularization step, sacrificing potential non-linear information but reducing the impact of outlier returns.

*Source: CSI Data; S&P Dow Jones; Calculations by Newfound Research. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

The results here are a bit of a head scratcher, as we have almost completely lost any out-performance generated in the top N models.

Which suggests that, perhaps, the out-performance had nothing to do with momentum-based information, but rather something else entirely.

**It Was Always You, Equal Weight**

If we return to our foundational framework that any active strategy is really just the market-capitalization-weighted portfolio plus a dollar-neutral long/short portfolio overlaid on top, then we can really think of our top N portfolios in a two-step active process:

- Start with the S&P 500 and tilt to equal-weight sector implementation;
- Remove low-momentum sectors and re-allocate capital among the rest.

To more accurately demonstrate the impact of our momentum decisions, then, we really should be isolating the impact of each of these steps.

For example, plotting the weight differences over time, we can see that equal-weight sectors are typically overweight Utilities and Materials and underweight Technology. We would expect this to dramatically help in the dot-com fallout, but hurt us after 2008.

If we actually generate the performance of this long/short strategy, we can see the results almost perfectly line up with our expectations: it was a generally profitable trade in the new century through early 2012, at which point it began to reverse.

If we plot the S&P 500, an equal-sector portfolio, and a top 4 momentum strategy, we can see that there is actually very little performance differential between the equal-sector approach and the momentum strategy. In fact, the momentum strategy does not appear to add much value at all other than active noise.

Which very much confirms the results we saw in our tracking-error-based solution: in the last century, the edge has not been in momentum.

Rather, it would appear that a top N momentum strategy was merely able to back its way into harvesting the return benefits of the equal-weight portfolio. The question we must now ask is whether that represents skill in the signal or merely luck.

Given the abject failure of momentum to dislodge itself from the equal weight portfolio *after *2012, our initial guess is “luck.”

But to explore this idea further, we generate 1,000 randomly generated “top 4” strategies. At the end of each month, each strategy randomly selects four sectors and holds them in equal weight over the next month. Note that as the number of strategies increases, the average allocation across all strategies should approach an equally weighted sector portfolio.

We then plot the distribution of annualized excess returns (versus the S&P 500) of each randomly generated strategy from 7/2000 to 3/2012.

The grey bar highlights the zero excess return line and the orange bar highlights the annualized return of the top 4 momentum strategy.

Two things are immediately apparent:

- Simply throwing a dart to select sectors from 7/2000 to 3/2012 proved to be a very effective strategy. In fact,
*97%*of the randomly generated strategies exhibited positive excess returns over this period. - The ensemble top 4 momentum strategy finds itself almost exactly in the middle of the road of all the randomly generated portfolios.One positive interpretation is that the momentum strategy was likely not data mined, as it is not a significant positive outlier. A negative interpretation, however, is that momentum may not have provided much information to trade off of in the last twenty years.

It would appear that the real hero in our top N momentum strategy is not momentum, but rather the equal-weight sector tilt implied in the strategy.

**Conclusion**

As we have stressed in the past, we believe it is very important to evaluate the contribution of each step in a portfolio’s construction. By treating each step as the overlay of a dollar-neutral long/short portfolio, we can not only isolate the allocation changes implied by that step, but also track the performance over time.

In the case of a top N momentum sector rotation strategy, we believe there are two key transformations: (1) the tilt from market-capitalization-weights to equal sector weights, and (2) the removal of low-ranking sectors.

With respect to performance over the last two decades, we find that the first step accounts for the vast majority of returns, while the second step has merely added noise.

To explore this further, we randomly generate 1000 different top 4 sector strategies and find that from the 2000-2012 period, 97% of the randomly generated strategies would have outperformed the S&P 500.

This fact has important implications for anyone evaluating a “top N”-style sector rotation track record from that era. The evidence suggests that it does not matter whether the process was based upon market cycle analysis, momentum, value, or dart-throwing monkeys: it would have been hard to under-perform.

While some might say that “top N” momentum strategies stopped working after 2012, we would suggest that they never appeared to work in this century at all.

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