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

# Summary

- After the Great Financial Crisis, the Momentum factor has exhibited positive returns, but those returns have been largely driven by the short side of the portfolio.
- One research note suggests that this is driven by increased risk aversion among investors, using the correlation of high volatility and low momentum baskets as evidence.
- In contradiction to this point, the iShares Momentum ETF (MTUM) has generated positive excess annualized returns against its benchmark since inception. The same note suggests that this is due to the use of risk-adjusted momentum measures.
- We explore whether risk-adjusting momentum scores introduces a meaningful and structural tilt towards low-volatility equities.
- For the examples tested, we find that it does not, and risk-adjusted momentum portfolios behave very similarly to momentum portfolios.

A research note recently crossed my desk that aimed to undress the post-Global Financial Crisis (GFC) performance of the momentum factor in U.S. equities. Not only have we witnessed a significant reduction in the factor’s return, but the majority of the return has been generated by the short side of the strategy, which can be more difficult for long-only investors to access.

*Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. The Long (Alpha) strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum and shorts an equal-weight S&P 500 portfolio. The Short (Alpha) strategy is a monthly rebalanced portfolio that goes long an equal-weight S&P 500 portfolio and shorts, in equal weight, the bottom 50 securities in the S&P 500 ranked on 12-1 month momentum.*

The note makes the narratively-appealing argument that the back-to-back recessions of the dot-com bubble and the Great Financial Crisis amplified investor risk aversion to downside losses. The proposed evidence of this fact is the correlation of the cumulative alpha generated from shorting low momentum stocks and the cumulative alpha generated from shorting high volatility stocks.

While correlation does not imply causation, one argument might be that in a heightened period of risk aversion, investors may consistently punish higher risk stocks, causing them to become persistent losers. Or, conversely, losers may be rapidly sold, creating both persistence and high levels of volatility. We can arguably see this in the convergence of holdings in low momentum and high volatility stocks during “risk off” regimes.

*Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. The HI VOL (Alpha) strategy is a monthly rebalanced portfolio that goes long an equal-weight S&P 500 portfolio and shorts, in equal weight, the bottom 50 securities in the S&P 500 ranked on trailing 252-day realized volatility. The LO MOM (Alpha) strategy is a monthly rebalanced portfolio that goes long an equal-weight S&P 500 portfolio and shorts, in equal weight, the bottom 50 securities in the S&P 500 ranked on 12-1 month momentum.*

Given these facts, we would expect long-only momentum investors to have harvested little out-performance in recent years. Yet we find that the popular iShares Momentum ETF (MTUM) has out-performed the S&P 500 by 290 basis points per year since its inception in 2013.

The answer to this conundrum, as proposed by the research note, is that MTUM’s use of *risk-adjusted* momentum is the key.

If we think of risk-adjusted momentum as simply momentum divided by volatility (which is how MTUM defines it), we might interpret it as an integrated signal of both the momentum and low-volatility factors. Therefore, risk-adjusting creates a multi-factor portfolio that tilts away from high volatility stocks.

And hence the out-performance.

Except if we actually create a risk-adjusted momentum portfolio, that does not appear to really be the case at all.

*Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. The alpha of the risk-adjusted momentum strategy is defined as the return of a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility) and shorts an equal-weight S&P 500 portfolio.*

To be fair, MTUM’s construction methodology differs quite a bit from that employed herein. We are simply equally-weighting the top 50 stocks in the S&P 500 when ranked by risk-adjusted momentum, whereas MTUM uses a blend of 6- and 12-month risk-adjusted momentum scores and then tilts market-capitalization weights based upon those scores.

Nevertheless, if we look at actual holdings overlap over time of our Risk-Adjusted Momentum portfolio versus Momentum and Low Volatility portfolios, not only do we see persistently higher overlap with the Momentum portfolio, but we see fairly low average overlap with the Low Volatility portfolio.

For the latter point, it is worth first anchoring ourselves to the standard overlap between Momentum and Low Volatility (green line below). While we can see that the Risk-Adjusted Momentum portfolio does indeed have a higher average overlap with Low Volatility than does the Momentum portfolio, the *excess *tilt to Low Volatility due to the use of risk-adjusted momentum (i.e. the orange line minus the green line) appears rather small. In fact, on average, it is just 10%.

*Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. The risk-adjusted momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility). The momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum. The low volatility strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on trailing 252-day realized volatility.*

This is further evident by looking at the actual returns of the strategies themselves:

*Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. The risk-adjusted momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility). The momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum. The low volatility strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on trailing 252-day realized volatility.*

The Risk-Adjusted Momentum portfolio performance tracks that of the Momentum portfolio very closely.

As it turns out, the step of adjusting for risk creates far less of a low volatility factor tilt in our top-decile portfolio than one might initially suspect. (Or, at least, I’ll speak for myself: it created far less of a tilt than *I *expected.)

To understand this point, we will first re-write our risk-adjusted momentum signal as:

While trivial algebra, re-writing risk-adjusted momentum as the product of momentum and inverse volatility is informative to understanding why risk-adjusted momentum appears to load much more heavily on momentum than low volatility.

At a given point in time, it would appear as if Momentum and Low Volatility should have an equal influence on the rank of a given security. However, we need to dig a level deeper and consider how changes in these variables impact change in risk-adjusted momentum.

Fortunately, the product makes this a trivial exercise: holding INVVOL constant, changes in MOM are scaled by INVVOL and vice versa. This scaling effect can cause large changes in risk-adjusted momentum – and therefore ordinal ranking – particularly as MOM crosses the zero level.

Consider a trivial example where INVVOL is a very large number (e.g. 20) due to a security having a very low volatility profile (e.g. 5%). This would appear, at first glance, to give a security a structural advantage and hence create a low volatility tilt in the portfolio. However, a move from positive prior returns to negative prior returns would shift the security from ranking among the best to ranking among the worst in risk-adjusted momentum.^{1}

A first order estimate of change in risk-adjusted momentum is:

So which term ultimately has more influence on the change in scores over time?

To get a sense of relative scale, we plot the cross-sectional mean absolute difference between the two terms over time. This should, at least partially, capture interaction effects between the two terms.

*Source: Sharadar. Calculations by Newfound Research.*

We can see that the term including the change in MOM has a much more significant influence on changes in risk-adjusted momentum than changes in INVVOL do. Thus, we might expect a portfolio driven entirely by changes in momentum to share more in common with our risk-adjusted momentum portfolio than one driven entirely by changes in volatility.

This is somewhat evident when we plot the return of MTUM versus our top 50 style portfolios. The correlation of daily returns between MTUM and our Momentum, Low Volatility, and Risk-Adjusted Momentum portfolios is 0.93, 0.72, and 0.93 respectively, further suggesting that MTUM is driven more by momentum than volatility.

*Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. The risk-adjusted momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility). The momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum. The low volatility strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on trailing 252-day realized volatility.*

This is only one part of the equation, however, as it is possible that changes to the risk-adjusted momentum score are so small – despite being largely driven by momentum – that relative rankings never actually change. Or, because we have constructed our portfolios by choosing only the top 50 ranked securities, that momentum does drive the majority of change across the entire universe, but the top 50 are always structurally advantaged by the non-linear scaling of low volatility.

To create a more accurate picture, we can rank-weight the entire S&P 500 and evaluate the holdings overlap over time.

*Source: Sharadar. Calculations by Newfound Research.*

Note that by now including all securities, and not just selecting the top 50, the overlap with both the Momentum and Low Volatility portfolios naturally appears higher on average. Nonetheless, we can see that the overlap with the Momentum portfolio is consistently higher than that of the Low Volatility portfolio, again suggesting that momentum has a larger influence on the overall portfolio composition than volatility does.

**Conclusion**

Without much deep thought, it would be easy to assume that a risk-adjusted momentum measure – i.e. prior returns divided by realized volatility – would tilt a portfolio towards both prior winners and low-volatility securities, resulting in a momentum / low-volatility barbell.

Upon deeper consideration, however, the picture complicates quickly. For example, momentum can be both positive and negative; dividing by volatility creates a non-linear impact; and momentum tends to change more rapidly than volatility.

We do not attempt to derive a precise, analytical equation that determines which of the two variables ultimately drives portfolio composition, but we do construct long-only example portfolios for empirical study. We find that a high-concentration risk-adjusted momentum portfolio has significantly more overlap in holdings with a traditional momentum portfolio than a low-volatility portfolio, resulting in a more highly correlated return stream.

The most important takeaway from this note is that intuition can be deceiving: it is important to empirically test our assumptions to ensure we truly understand the impact of our strategy construction choices.

## Factor Orphans

By Corey Hoffstein

On October 28, 2019

In Risk & Style Premia, Weekly Commentary

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

Contrarian investing is nothing new. Holding a variant perception to the market is often cited as a critical component to generating differentiated performance. The question in the details is, however, “contrarian to what?”

In the last decade, we’ve witnessed a dramatic rise in the popularity of systematically managed active strategies. These so-called “smart beta” portfolios seek to harvest documented risk premia and market anomalies and implement them with ruthless discipline.

But when massively adopted, do these strategies become the commonly-held view and therefore more efficiently priced into the market? Would this mean that the variant perception would actually be buying those securities totally ignored by these strategies?

This is by no means a new idea. Morningstar has long maintained its Unloved strategy that purchases the three equity categories that have witnessed the largest outflows at the end of the year. A few years ago, Vincent Deluard constructed a “DUMB” beta portfolio that included all the stocks shunned by popular factor ETFs. In the short out-of-sample period the performance of the strategy was tested, it largely kept pace with an equal-factor portfolio. More recently, a Bank of America research note claimed that a basket of most-hated securities – as defined by companies neglected by mutual funds and shorted by hedge funds hedge funds – had tripled the S&P 500’s return over the past year.

The approach certainly has an appealing narrative: as the crowd zigs to adopt smart beta, we zag. But has it worked?

To test this concept, we wanted to identify what we call “factor orphans”: those securities not held by any factor portfolio. Once identified, we can build a portfolio holding these stocks and track its performance over time.

As a quant, this idea strikes us as a little crazy. A stock

notheld in a value, momentum, low volatility, or quality index is likely one that is expensive, highly volatile, with poor fundamentals and declining performance. Precisely the type of stock factor investing would tell us not to own.But perhaps the fact that these securities are orphaned means that there are no more sellers: the major cross-section of market strategies have already abandoned the stock. Thus, stepping in to buy them may allow us to offload them later when they are picked back up by these systematic approaches.

Perhaps this idea is crazy enough it just might work…

To test this idea, we first sought to replicate four common factor benchmarks: the S&P 500 Enhanced Value index, the S&P 500 Momentum index, the S&P 500 Low Volatility index and the S&P 500 Quality index. Once replicated, we can use the underlying baskets as being representative of the holdings for factor portfolios is general.

Results of our replication efforts are plotted below. We can see that our models fit the shape of most of the indices closely, with very close fits for the Momentum and Low Volatility portfolios.

Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.The Quality replication represents the largest deviation from the underlying index, but still approximates the shape of the total return profile rather closely. This gives us confidence that the portfolio we constructed is a quality portfolio (which should come as no surprise, as securities were selected based upon common quality metrics), but the failure to more closely replicate this index may represent a thorn in our ability to identify truly orphaned stocks.

At the end of each month, we identify the set of all securities held by any of the four portfolios. The securities in the S&P 500 (at that point in time) but not in the factor basket are the orphaned stocks. Somewhat surprisingly, we find that approximately 200 names are orphaned at any given time, with the number reaching as high as 300 during periods when underlying factors converge.

Also interesting is that the actual overlap in holdings in the factor portfolios is quite low, rarely exceeding 30%. This is likely due to the rather concentrated nature of the indices selected, which hold only 100 stocks at a given time.

Source: Sharadar. Calculations by Newfound Research.Once our orphaned stocks are identified, we construct a portfolio that holds them in equal weight. We rebalance our portfolio monthly to sell those stocks that have been acquired by a factor portfolio and roll into those securities that have been abandoned.

We plot the results of our exercise below as well as an equally weighted S&P 500 benchmark.

Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.While the total return is modestly less (but certainly not statistically significantly so), what is most striking is how little deviation there is in the orphaned stock portfolio versus the equal-weight benchmark.

However, as we have demonstrated in the past, the construction choices in a portfolio can have a significant impact upon the realized results. As we look at the factor portfolios themselves, we must acknowledge that they represent

relativetilts to the benchmark, and that the absence of one security might actually represent a significantly smaller relative underweight to the benchmark than the absence of another. Or the absence of one security may actually represent a smaller relative underweight than another that is actually included.Therefore, as an alternative test we construct an equal-weight factor portfolio and subtract the S&P 500 market-capitalization weights. The result is the implied over- and under-weights of the combined factor portfolios. We then rank securities to select the 100 most under-weight securities each month and hold them in equal weight.

Source: Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.Of course, we didn’t actually have to perform this exercise had we stepped back to think for a moment. We generally know that these (backtested) factors have out-performed the benchmark. Therefore, selecting stocks that they are underweight means we’re taking the opposite side of the factor trade, which we know has not worked.

Which does draw an important distinction between

most underweightandorphaned.It would appear that factor orphans do not necessarily create the strong anti-factor tilt the way that the most underweight portfolio does.For the sake of completion, we can also evaluate the portfolios containing securities held in just one of the factor portfolios, two of the factor portfolios, three of the factor portfolios, or all of the factor portfolios at a given time.

Below we plot the count of securities in such portfolios over time. We can see that it is very uncommon to identify securities that are simultaneously held by all the factors, or even three of the factors, at once.

Source: Sharadar. Calculations by Newfound Research.We can see that the portfolio built from stocks held in just one factor (“In One”) closely mimics the portfolio built from stocks held in no factor (“In Zero”), which in turn mimics the S&P 500 Equal Weight portfolio. This is likely because the portfolios include so many securities that they effectively bring you back to the index.

On the other end of the spectrum, we see the considerable risks of concentration manifest in the portfolios built from stocks held in three or four of the factors. The portfolio comprised of stocks held in all four factors simultaneously (“In Four”) not only goes long stretches of holding nothing at all, but is also subject to large bouts of volatility due to the extreme concentration.

We also see this for the portfolio that holds stocks held by three of the factors simultaneously (“In Three”). While this portfolio has modestly more diversification – and even appears to out-perform the equal-weight benchmark – the concentration risk finally materializes in 2018-2019, causing a dramatic drawdown.

The portfolio holding stocks held in just two of the factors (“In Two”), though, appears to offer some out-performance opportunity. Perhaps by forcing just two factors to agree, we strike a balance between confirmation among signals and portfolio diversification.

Unfortunately, our enthusiasm quickly wanes when we realize that this portfolio closely matches the results achieved just by naively equally-weighting exposure among the four factor portfolios themselves, which is far more easily implemented.

ConclusionTo achieve differentiated results, we must take a differentiated stance from the market. As systematic factor portfolios are more broadly adopted, we should consider asking ourselves if taking an anti-factor stance might lead to contrarian-based profits.

In this study, we explore the idea of factor orphans: stocks not held by any factor portfolio at a given time. Our hypothesis is that these orphaned securities may be systematically over-sold, leading to an opportunity for future out-performance if they are re-acquired by the factor portfolios at a later date.

We begin by replicating four factor indices: the S&P 500 Enhanced Value index, the S&P 500 Momentum index, the S&P 500 Low Volatility index, and the S&P 500 Quality index. Replicating these processes allows us to identify historical portfolio holdings, which in turn allows us to identify stocks

notheld by the factors.We are able to closely replicate the S&P 500 Momentum and Low Volatility portfolios, create meaningful overlap with the S&P 500 Enhanced Value method, and generally capture the S&P 500 Quality index. The failure to more closely replicate the S&P 500 Quality index may have a meaningful impact on the results herein, though we believe our methodology still captures the generic return of a quality strategy.

We find that, on average, there are over 200 factor orphans at a given time. Constructing an equal-weight portfolio of these orphans, however, only seems to lead us back to an S&P 500 Equal Weight benchmark. While there does not appear to be an edge in this strategy, it is interesting that there does not appear to be a

negativeedge either.Recognizing that long-only factor portfolios represent active bets expressed as over- and underweights relative to the S&P 500, we also construct a portfolio of the most underweight stocks. Not surprisingly, as this portfolio actively captures a negative factor tilt, the strategy meaningfully underperforms the S&P 500 Equal Weight benchmark. Though the relative underperformance meaningfully dissipates in recent years.

Finally, we develop portfolios to capture stocks held in just one, two, three, or all four of the factors simultaneously. We find the portfolios comprised stocks held in either three or four of the factors at once exhibit significant concentration risk. As with the orphan portfolio, the portfolio of stocks held by just one of the factors closely tracks the S&P 500 Equal Weight benchmark, suggesting that it might be

over-diversified.The portfolio holding stocks held by just two factors at a time appears to be the Goldilocks portfolio, with enough concentration to be differentiated from the benchmark but not so much as to create significant concentration risk.

Unfortunately, this portfolio also almost perfectly replicates a naïve equal-weight portfolio among the four factors, suggesting that the approach is likely a wasted effort.

In conclusion, we find no evidence that factor orphans have historically offered a meaningful excess return opportunity. Nor, however, do they appear to have been a drag on portfolio returns either. We should acknowledge, however, that the adoption of factor portfolios accelerated rapidly after the Great Financial Crisis, and that backtests may not capture current market dynamics. More recent event studies of orphaned stocks being added to factor portfolios may provide more insight into the current environment.