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

# Summary

- To generate returns that are different than the market, we must adopt a positioning that is different than the market.
- With the increasing adoption of systematic factor portfolios, we explore whether an anti-factor stance can generate contrarian-based profits.
- Specifically, we explore the idea of factor orphans: stocks that are not included in any factor portfolio at a given time.
- To identify these stocks, we replicate four popular 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.
- On average, there are over 200 stocks in the S&P 500 that are orphaned at any given time.
- Generating an equal-weight portfolio of these stocks does not exhibit meaningfully different performance than a naïve equal-weight S&P 500 portfolio.

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 *not *held 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.

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.

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 *relative *tilts 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.

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 underweight *and *orphaned.* 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.

**Conclusion**

To 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 *not *held 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 *negative *edge 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.

## Pursuing Factor Purity

By Corey Hoffstein

On January 6, 2020

In Risk & Style Premia, Weekly Commentary

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

Several years ago, we penned a note titled

Separating Ingredients and Recipe in Factor Investing(May 21, 2018). In the note we discussed why we believe it is important for investors and allocators to consider not just what ingredients are going into their portfolios – i.e. securities, styles, asset classes, et cetera – but the recipe by which those ingredients are combined. Far too often the ingredients are given all the attention, but mistake salt for sugar and I can guarantee that you’re not going to enjoy your cake, regardless of the quality of the salt.As an example, the note focused on constructing momentum portfolios. By varying the momentum measure, lookback period, rebalance frequency, portfolio construction, weighting scheme, and sector constraints we constructed over 1,000 momentum strategies. The resulting dispersion between the momentum strategies was more-often-than-not larger than the dispersion between generic value (top 30% price-to-book) and momentum (top 30% by 12-1 prior returns).

Yet having some constant definition for factor portfolios is desirable for a number of reasons, including both alpha signal generation and return attribution.

One potential problem for naïve factor construction – e.g. a simple characteristic rank-sort – is that it can lead to time-varying correlations between factors.

For example, below we plot the correlation between momentum and value, size, growth, and low volatility factors. We can see significant time-varying behavior; for example, in 2018 momentum and low volatility exhibited moderate negative correlation, while in 2019 they exhibited significant positive correlation.

The risk of time-varying correlations is that they can potentially leading to the introduction of unintended bets within single- or multi-factor portfolios or make it more difficult to determine with accuracy a portfolio’s sensitivity to different factors.

More broadly, low and stable correlations are preferable – assuming they can be achieved without meaningfully sacrificing expected returns – because they should allow investors to develop portfolios with lower volatility and higher information ratios.

Naively constructed equity styles can also exhibit time-varying correlations to traditional economic factors (e.g. interest rate risk), risk premia (e.g. market beta) or risk factors (e.g. sector or country exposure).

But equity styles can even exhibit time-varying sensitivities to

themselves.For example, below we multiply the weights of naively constructed long/short style portfolios against the characteristic z-scores for the underlying holdings. As the characteristics of the underlying securities change, so does the actual weighted characteristic score of the portfolio. While some signals stay quite steady (e.g. size), others can vary substantially; sometimes value is just more value-y.Source: Sharadar. Calculations by Newfound Research. Factor portfolios self-financing long/short portfolios that are long the top quintile and short the bottom quintile of securities, equally weighted and rebalanced monthly, ranked based upon their specific characteristics (see below).In the remainder of this note, we will explore two approaches to constructing “pure” factor portfolios that can be used to generate a factor portfolio that neutralizes exposure to risk factors and other style premia.

Using the S&P 500 as our parent universe, we will construct five different factors defined by the security characteristics below:

^{1}, negative accruals ratio, negative leverage ratio^{2}.All characteristics are first cross-sectionally winsorized at the 5

^{th}and 95^{th}percentiles, then cross-sectionally z-scored, and finally averaged (if a style is represented by multiple scores) to create a single score for each security.Naively constructed style benchmarks are 100% long the top-ranked quintile of securities and 100% short the bottom-ranked quintile, with securities receiving equal weights.

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.Factor Mimicry with Fama-MacBethOur first approach to designing “pure” factor portfolios is inspired by Fama-MacBeth (1973)

^{3}. Fama-MacBeth regression is a two-step approach:Similarly, we will assume a factor model where the return for a given security can be defined as:

Where R

_{m}is the return of the market and RF_{j}is the return for some risk factor. In this equation, the betas define a security’s sensitivity to a given risk factor. However, instead of using the Fama-MacBeth two-step approach to solve for the factor betas, we can replace the betas with factor characteristic z-scores.Using these known scores, we can both estimate the factor returns using standard regression

^{4}and extract the weights of the factor mimicking portfolios. The upside to this approach is that each factor mimicking portfolios will, by design, have constant unit exposure to its specific factor characteristic and zero exposure to the others.Here we should note that unless an intercept is added to the regression equation, the factor mimicking portfolios will be

beta-neutral but notdollar-neutral. This can have a substantial impact on factors like low volatility (VOL), where we expect our characteristics to be informative about risk-adjusted returns but not absolute returns. We can see the impact of this choice in the factor return graphs plotted below.^{5}Furthermore, by utilizing factor z-scores, this approach will neutralize

characteristicexposure, but not necessarily return exposure. In other words, correlations between factor returns may not be zero. A further underlying assumption of this construction is that anequal-weightportfolio of all securities is style neutral. Given that equal-weight portfolios are generally considered to embed positive size and value tilts, this is an assumption we should be cognizant of.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.Attempting to compare these mimic portfolios versus our original naïve construction is difficult as they target a constant unit of factor exposure, varying their total notional exposure to do so. Therefore, to create an apples-to-apples comparison, we adjust both sets of factors to target a constant volatility of 5%.

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.We can see that neutralizing market beta and other style factors leads to an increase in annualized return for value, size, momentum, and quality factors, leading to a corresponding increase in information ratio. Unfortunately, none of these results are statistically significant at a 5% threshold.

Nevertheless, it may still be informative to take a peek under the hood to see how the weights shook out. Below we plot the average weight by security characteristic percentile (at each rebalance, securities are sorted into percentile score bins and their weights are summed together; weights in each bin are then averaged over time).

Before reviewing the weights, however, it is important to recall that each portfolio is designed to capture a constant unit exposure to a style and therefore total notional exposure will vary over time. To create a fairer comparison across factors, then, we scale the weights such that each leg has constant 100% notional exposure.

As we would generally expect, all the factors are over-weight high scoring securities and underweight low scoring securities. What is interesting to note, however, is that the shapes by which they achieve their exposure are different. Value, for example leans strongly into top decile securities whereas quality leans heavily away (i.e. shorts) the bottom decile. Unlike the other factors which are largely positively sloped in their weights, low volatility exhibits fairly constant positive exposure above the 50

^{th}percentile.What may come as a surprise to many is how diversified the portfolios appear to be across securities. This is because the regression result is equivalent to minimizing the sum of squared weights subject to target exposure constraints.

Source: Sharadar. Calculations by Newfound Research.While we focused specifically on neutralizing style exposure, this approach can be extended to also neutralize industry / sector exposure (e.g. with dummy variables), region exposure, and even economic factor exposure. Special care must be taken, however, to address potential issues of multi-collinearity.

Pure Quintile Portfolios with OptimizationLiu (2016)

^{6}proposes an alternative means for constructing pure factor portfolios using an optimization-based approach. Specifically, long-only quintile portfolios are constructed such that:While the regression-based approach was fast due to its closed-form solution, an optimization-based approach can potentially allow for greater flexibility in objectives and constraints.

Below we replicate the approach proposed in Liu (2016) and then create dollar-neutral long/short factor portfolios by going long the top quintile portfolio and short the bottom quintile portfolio. Portfolios are re-optimized and rebalanced monthly. Unlike the regression-based approach, however, these portfolios do not seek to be beta-neutral.

We can see that the general shapes of the factor equity curves remain largely similar to the naïve implementations. Unlike the results reported in Liu (2016), however, we measure a decline in return among several factors (e.g. value and size). We also find that annualized volatility is meaningfully reduced for all the optimized portfolios; taken together, information ratio differences are statistically indistinguishable from zero.

As with the regression-based approach, we can also look at the average portfolio exposures over time to characteristic ranks. Below we plot these results for both the naïve and optimized Value quintiles. We can see that the top and bottom quintiles lean heavily into top- and bottom-decile securities, while 2

^{nd}, 3^{rd}, and 4^{th}quintiles had more diversified security exposure on average. Similar weighting profiles are displayed by the other factors.Source: Sharadar. Calculations by Newfound Research.ConclusionFactors are easy to define in general but difficult to define explicitly. Commonly accepted academic definitions are easy to construct and track, but often at the cost of inconsistent style exposure and the risk of latent, unintended bets. Such impure construction may lead to time-varying correlations between factors, making it more difficult for managers to manage risk as well as disentangle the true source of returns.

In this research note we explored two approaches that attempt to correct for these issues: a regression-based approach and an optimization-based approach. With each approach, we sought to eliminate non-target style exposure, resulting in a pure factor implementation.

Despite a seemingly well-defined objective, we still find that how “purity” is defined can lead to different results. For example, in our regression-based approach we targeted unit style exposure and beta-neutrality, allowing total notional exposure to vary. In our optimization-based approach, we constructed long-only quintiles independently, targeting the same weighted-average characteristic exposure as a naïve, equal-weight factor portfolio. We then built a long/short implementation from the top and bottom quintiles. The results between the regression-based and optimization-based approaches were markedly different.

And, statistically, not any better than the naïve approaches.

This is to say nothing of other potential choices we could make about defining “purity.” For example, what assumptions should we make about industry, sector, or regional exposures?

More broadly, is “purity” even desirable?

In

Do Factors Market Time?(June 5, 2017)we demonstrated that beta timing was an unintentional byproduct of naïve value, size, and momentum portfolios and had actually been a meaningful tailwind for value from 1927-1957. Some factors might actually be priced across industries rather than just within them (Vyas and van Baren (2019)^{7}). Is the chameleon-like nature of momentum to rapidly tilt towards whatever style, sector, or theme has been recently outperforming a feature or a bug?And this is all to say nothing of the actual factor definitions we selected.

While impurity may be a latent risk for factor portfolios, we believe this research suggests that purity is in the eye of the beholder.