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

**Summary**

- Momentum-based sector rotation is a popular investment strategy.
- Recent academic studies have shown that alternative implementations of standard momentum – including risk-adjusted momentum, residual momentum, and “frog-in-the-pan” momentum – can significantly improve the risk-adjusted and total return potential of stock-based momentum systems.
- We explore whether these approaches create value for sector rotation systems.

Momentum is a system of investing that buys and sells securities based upon recent returns. Momentum investors buy outperforming securities and avoid – or sell short – underperforming ones.

In the traditional academic implementation of momentum, hundreds of individual securities must be bought and sold. One popular – albeit simplified – implementation of this approach is sector rotation, where investors implement a momentum strategy through industry groups or sectors.

In a past commentary[1], we demonstrated that sector rotation was entirely subsumed by the momentum factor (i.e. does not represent its own unique risk factor) and dampens total return potential. We also found, however, that as the number of sectors utilized decreased, so did the risk of momentum crashes. Risk-averse investors, therefore, still may find traditional sector rotation a valuable approach.

Since the momentum factor was identified and published by Jegadeesh and Titman in 1993, several other approaches have been explored and documented. Most prominently have been risk-adjusted momentum, idiosyncratic momentum, and frog-in-the-pan momentum.

In this study, we explore whether these approaches are value-add in a traditional sector rotation approach.

**Risk-Adjusted Momentum**

Whereas traditional momentum looks at trading 12-1 month returns, *risk-adjusted *momentum scales this return figure by trailing realized volatility.

One argument for this approach is that it is secretly a multi-factor approach. Here, we can think of 12-1 returns as our “momentum score” and inverse realized volatility as our “low volatility score.” By multiplying them together to create a risk-adjusted momentum score, we are invoking a multi-factor scoring process somewhat similar to the “tilt-tilt” process advocated for by FTSE Russell.

Another potential argument for this approach is that by scaling by volatility, we overweight those sectors whose return has been more continuous in nature and less discrete (e.g. the return is driven by a large jump). The rational inattention theory posits that since time is a scarce resource, investors may selectively ignore information or only obtain news on a limited frequency or with limited accuracy. Chen and Yu (2014) found that portfolios constructed for stocks “more likely to grab attention” based on visual patterns induces investor overreaction.[2] Indeed, momentum continuation could be induced by visually-based psychological biases.

Several studies have demonstrated the benefits of risk-adjusted momentum, including Shaik (2011) [3] and Soe (2016)[4], who find that risk-adjusted momentum creates excess risk-adjusted and total returns in large-cap U.S. equities, small-cap U.S. equities, and global equities.

Similarly, Ahti (2012)[5] finds that beta-adjusted momentum (where the anti-beta and low-volatility anomalies are close cousins) enhances global equity momentum by increasing total return and lowering volatility.

To test risk-adjusted momentum in a sector rotation context, we sort sectors based on their trailing 12-1 month risk-adjusted return. We build an equal-weight portfolio of the top three sectors with the highest scores. Similarly, for our short leg, we build an equal-weight portfolio of the bottom three sectors with the lowest scores. Portfolios are rebalanced monthly (using overlapping portfolios).

*Data from Kenneth French data library. Calculations by Newfound Research. All returns are hypothetical and are gross of all costs.*

We can see that risk-adjusted momentum ends up being a drag on our sector rotation approach. And without a commensurate reduction in volatility, we end up with a worse Sharpe ratio.

Annualized Return | Annualized Volatility | Sharpe Ratio | |

Momentum | 3.90% | 12.65% | 0.30 |

Risk-Adjusted Momentum | 2.75% | 11.30% | 0.24 |

Of course, most investors implementing a sector rotation approach do so in a long-only capacity, so we believe it is important to distinguish between returns originating from the long and short legs of this analysis. Specifically, we can plot the long-only legs to determine whether the short-leg was a drag on performance and we can still harvest some benefit in a long-only model.

*Data from Kenneth French data library. Calculations by Newfound Research. All returns are purely hypothetical and are gross of all costs.*

Again, we find no evidence that a risk-adjusted momentum approach is advantageous in a long-only sector rotation system.

** **

**Residual (Idiosyncratic) Momentum**

One argument against the traditional approach to momentum is that the portfolios constructed have time-varying exposures to return factors such as market beta, value, and size.

In an effort to control for this effect, residual (or idiosyncratic) momentum first regresses a stock’s returns against these common risk factors and extracts only the residual, unexplained return stream. The traditional 12-1 momentum approach is then applied to this idiosyncratic component.

Blitz, Huij, and Martens (2009) found that controlling for market beta, value, and size, risk-adjusted profits of their residual momentum process were about twice as large as those associated with total return momentum, with greater consistency.[6]

By correcting stocks for market returns, Chaves (2012) finds that momentum applied to idiosyncratic returns works better than traditional momentum in a sample of 21 developed countries. Perhaps most importantly, the approach was successful in Japan, where traditional momentum has historically failed.[7]

More recently, Blitz, Hanauer, and Vidojevic (2017) found that residual momentum could not be subsumed by the conventional momentum factor and that traditional arguments of investor over-confidence and overreaction fail to explain the anomaly.[8]

In our sector rotation framework, we can explore this approach by employing the CAPM model, regressing sector returns against the market and extracting the idiosyncratic component. Specifically, we will use rolling three year periods for calculating our residuals. After residuals are calculated for each sector, we run a traditional 12-1 momentum approach.

*Data from Kenneth French data library. Calculations by Newfound Research. All returns are purely hypothetical and are gross of all costs.*

Annualized Return | Annualized Volatility | Sharpe Ratio | |

Momentum | 3.90% | 12.65% | 0.30 |

Idiosyncratic Momentum | 3.38% | 10.79% | 0.31 |

Unlike risk-adjusted momentum, idiosyncratic momentum *does *improve risk-adjusted returns for the long/short implementation – though just narrowly. Again, however, we find the long-only implementation lacking. In fact, the long-only momentum strategy has a Sharpe ratio of 0.47 while the idiosyncratic approach has a Sharpe ratio of just 0.44.

*Data from Kenneth French data library. Calculations by Newfound Research. All returns are purely hypothetical and are gross of all costs.*

**Frog-in-the-Pan Momentum**

Da, Gurun, and Warachka (2014) introduced a new concept in momentum: “frog in the pan” (FIP)[9]. The hypothesis behind FIP is that “investors are inattentive to information arriving continuously in small amounts. […] [A] series of frequent gradual changes attracts less attention than infrequent dramatic changes.”

To test this hypothesis, the authors double-sort stock returns, first on trailing 12-1 month total returns and then on an information discreteness (ID) score. This ID score is calculated as the sign of the trailing 12-month return multiplied by the difference between the percentage of negative days and the percentage of positive days. By construction, this figure will range from -1 to +1, with a lower score corresponding to greater return continuity.

The authors find that, consistent with their hypothesis, stocks exhibiting continuous information exhibit stronger momentum returns than those that exhibit information discreteness.

Unfortunately, with only 10 sectors, a double-sort approach is not possible. To incorporate the concept of information discreteness, we create a new score: ID = (sign(PRET)[%pos - %neg] + 1) / 2. Our information discreteness measure is bound between 0 and 1, with 0 being more discrete returns and 1 being more continuous. We then multiply our traditional momentum score by this ID score, highly continuous returns retain their magnitude while discrete returns are pulled towards zero.

Annualized Return | Annualized Volatility | Sharpe Ratio | |

Momentum | 3.90% | 12.65% | 0.30 |

Frog-in-the-Pan | 3.69% | 12.63% | 0.29 |

Like the approaches before, FIP seems to fall short for sector rotation. We see the same holds true for the long-only side as well.

What’s going on here? Why is FIP so close to momentum for sector rotation? Quite simply, it is likely that with only ten sectors, there is not enough differential in the information discreteness score to significantly change the momentum score magnitude and cause relative ranks to shift.

**Conclusion**

It may seem, at the end of the day, all was for naught. While we did not test every extension of momentum or combinations thereof (e.g. residual momentum using the Fama-French 3-factor model, risk-adjusted idiosyncratic momentum, etc), these initial tests were not promising for creating value-add in a sector rotation system.

To this, we would say two things.

First, we would argue that these adjustments to momentum general try to capture the concept of “consistency” and “smoothness.” These tweaks may be relevant when dealing with individual securities that can exhibit a significant amount of jump risk in their returns. However, much of this risk is diluted at the sector level, where we already benefit from a significant amount of diversification. Therefore, the added steps to try to address this risk may not be necessary, and perhaps only harmful to returns.

Second, the mere fact that none of these variations *broke *sector rotation says something about momentum’s robustness. These are not just minor variations either: idiosyncratic momentum, for example, is a significant change in methodology. Nevertheless, evaluated in isolation, it would appear to be a statistically significant anomaly. In other words, regardless of its form, momentum seems to persist.

The nature of research is that you are going to often find yourself at dead ends. We believe, however, learning what *doesn’t *work, and why it doesn’t work, is just as, if not more important, than identifying what does.

[1] https://blog.thinknewfound.com/2017/03/sector-rotation-momentum-factor/

[2] Chen, Li-Wen and Yu, Hsin-Yi, Investor Attention, Visual Price Pattern, and Momentum Investing (August 12, 2014). 27th Australasian Finance and Banking Conference 2014 Paper. Available at SSRN: http://ssrn.com/abstract=2292895 or http://dx.doi.org/10.2139/ssrn.2292895

[3] Shaik, Rasool. 2011. “Risk-Adjusted Momentum: A Superior Approach to Momentum Investing.” Bridgeway Capital Management.

[4] Soe, Aye. 2016. “Momentum: Does Adjusting By Risk Matter?” S&P Dow Jones Indices.

[5] Ahti, Valterri. 2012. “BAMM: MSCI World.” Evli Bank.

[6] Blitz, David and Huij, Joop and Martens, Martin, Residual Momentum (August 1, 2009). Available at SSRN: https://ssrn.com/abstract=2319861 or http://dx.doi.org/10.2139/ssrn.2319861

[7] Chaves, Denis. 2012. “Eureka! A Momentum Strategy that Also Works in Japan.” Research Affiliates Working Paper (January 9).

[8] Blitz, David and Hanauer, Matthias X. and Vidojevic, Milan, The Idiosyncratic Momentum Anomaly (April 5, 2017). Available at SSRN: https://ssrn.com/abstract=2947044

[9] Da, Zhi and Gurun, Umit G. and Warachka, Mitch, Frog in the Pan: Continuous Information and Momentum (December 21, 2013). Available at SSRN: https://ssrn.com/abstract=2370931 or http://dx.doi.org/10.2139/ssrn.2370931

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