Flirting with Models

The Research Library of Newfound Research

Can Managed Futures Offset Equity Losses?

This post is available as a PDF download here.

Summary

  • Managed futures strategies have historically provided meaningful positive returns during left-tail equity events. Yet as a trading strategy, this outcome is by no means guaranteed.
  • While trend following is “mechanically convex,” the diverse nature of managed futures programs may actually prevent the strategy from offsetting equity market losses.
  • We generate a large number of random managed futures strategies by varying the asset classes included. We find that more diverse strategies have, historically, provided a larger offset to negative equity events.
  • This curious outcome appears to be caused by two effects: (1) diversification allows for increased total notional exposure; and (2) past crises saw coincidental trends across multiple markets simultaneously.
  • Therefore, for investors trying to offset equity market losses, an allocation to managed futures requires believing that future crises will be marked by a large number of simultaneous trends across multiple assets.
  • Less diversified strategies – such as just trading S&P 500 futures contracts – appear to work if the volatility target is removed.

Shortly after the 2008 crisis, the appetite for risk management strategies exploded.  At the forefront of this trend was managed futures, which had already proven itself in the dot-com fallout.  With the Societe Generale Trend Index1 returning 20.9% in 2008, the evidence for CTAs to provide “crisis alpha”2 seemed un-debatable.  AUM in these strategies sky-rocketed, growing from $200 billion in 2007 to approximately $325 billion by 2012.

Source: http://managedfuturesinvesting.com

Subsequent performance has, unfortunately, been lack-luster.  Since 12/31/2011, the SG Trend Index has returned just 14.2% compared to the S&P 500’s 200.8% total return.  While this is an unfair, apples-to-oranges comparison, it does capture the dispersion the strategy has exhibited to the benchmark most investors measure performance against during a bull market.

Furthermore, the allocation to managed futures had to come from somewhere.  If investors reduced exposure to equities to introduce managed futures, the spread in performance captures the opportunity cost of that decision.  There is hope yet: if the S&P 500 fell 50% over the next year, managed futures would have to return just 32% for their full-period performance (2011-2020) to equalize.

Yet how certain are we that managed futures would necessarily generate a positive return in an S&P 500 left-tail environment?  Hurst, Ooi, and Pedersen (2017)3 find that managed futures have generated anything from flat to meaningfully positive results during the top 10 largest drawdowns of a 60/40 portfolio since the late 1800s.  This evidence makes a strong empirical case, but we should acknowledge the N=10 nature of the data.

Perhaps we can lean into the mechanically convex nature of trend following.  Trend following is a close cousin to the trading strategy that delta-hedges a strangle, generating the pay-off profile of a straddle (long an at-the-money put and call).  Even without an anomalous premium generated by autocorrelation in the underlying security, the trading strategy itself should – barring trading frictions – generate a convex payoff.

Yet while mechanical convexity may be true on a contract-by-contract basis, it is entirely possible that the convexity we want to see emerge is diluted by trades across other contracts.  Consider the scenario where the S&P 500 enters a prolonged and significant drawdown and our managed futures strategy goes short S&P 500 futures contract.  While this trade may generate the hedge we were looking for, it’s possible that it is diluted by trades on other contracts such as wheat, the Japanese Yen, or the German Bund.

When we consider that many investors have portfolios dominated by equity risk (recall that equities have historically contributed 90% of the realized volatility for a 60/40 portfolio), it is possible that too much breadth within a managed futures portfolio could actually prevent it from providing negative beta during left-tail equity events.

 

Replicating Managed Futures

We begin our study by first replicating a generic trend-following CTA index.  We adopt an ensemble approach, which is effectively equivalent to holding a basket of managers who each implement a trend-following strategy with a different model and parameterization.

Specifically, we assume each manager implements using the same 47 contracts that represent a diversified basket of equities, rates, commodities, and currencies.4

We implement with three different models (total return, price-minus-moving-average, and dual-moving-average-cross) and five potential lookback specifications (21, 42, 84, 168, and 336 days) for a total of 15 different implementations.

Each implementation begins by calculating an equal-risk contribution (“risk parity”) portfolio.  Weights for each contract are then multiplied by their trend signal (which is simply either +1 or -1).

The weights for all 15 implementations are then averaged together to generate our index weights.  Notional exposure of the aggregate weights is then scaled to target a 10% annualized volatility level.  We assume that the index is fully collateralized using the S&P U.S. Treasury Bill Index.

Below we plot our index versus the SG Trend Index.  The correlation of monthly returns between these two indices is 75% suggesting that our simple implementation does a reasonable job approximating the broad trend-following style of CTAs.  We can also see that it captures the salient features of the SG Trend Index, including strong performance from 2001-2003, Q4 2008 and Q1 2009, and the 2014-2015 period.  We can also see it closely tracks the shape the SG Trend Index equity curve from 2015 onward in all its meandering glory.

Source: Stevens Analytics.  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.  These results do not reflect the returns of any strategy managed by Newfound Research.

Convexity versus Diversification

To explore the impact of diversification in managed futures versus convexity exhibited against the S&P 500, we will create a number of managed futures strategies and vary the number of contracts included.  As we are attempting to create a convex payoff against the S&P 500, the S&P 500 futures contract will always be selected.

For example, a 2-contract strategy will always include S&P 500 futures, but the second contract could be 10-year U.S. Treasuries, the Nikkei, the Australian Dollar, Oil, or any of the other 42 futures contracts.  Once selected, however, that pair defines the strategy.

For 2-, 4-, 8-, 16-, and 32- contract systems, we generate the performance of 25 randomly selected strategies.  We then generate scatter plots with non-overlapping 6-month returns for the S&P 500 on the x-axis and non-overlapping 6-month returns for the managed futures strategies on the y-axis.5 We then fit a 2nd-degree polynomial line to visualize the realized convexity.

(Note that for the single contract case – i.e. just the S&P 500 futures contract – we plot overlapping 6-month returns.)

Source: Stevens Analytics and 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.  These results do not reflect the returns of any strategy managed by Newfound Research.

There are two particularly interesting artifacts to note.

First, as the number of contracts goes up, the best-fit model turns from a “smile” to a “smirk,” suggesting that diversification dilutes positive convexity relationships with the S&P 500.  This outcome should have been expected, as we generally know how managed futures has done over the 20-year period we’re examining.  Namely, managed futures did quite well offsetting losses in 2000-2003 and 2008-2009, but has failed to participate in the 2010s.

Perhaps more interestingly, however, is the increase in left-tail performance of managed futures, climbing from 20% when just trading the S&P 500 futures contract to 150% in the 32-contract case.  The subtle reason here is diversification’s impact on total notional exposure.

Consider this trivial example: Asset A and Asset B have constant 10% volatility and are uncorrelated with one another.  As they are uncorrelated, any combination of these assets will have a volatility that is less than 10%.  Therefore, if we want to achieve 10%, we need to apply leverage.  In fact, a 50-50 mix of these assets requires us to apply 1.41x leverage to achieve our volatility target, resulting in 70.7% exposure to each asset.

As a more concrete example, when trading just the S&P 500 futures contract, achieving 10% volatility position in 2008 requires diluting gross notional exposure to just 16%.  For the full, 47-contract model, gross notional exposure during 2008 dipped to 90% at its lowest point.

Now consider that trend following tends to transform the underlying distributions of assets to generate positive skewness.  Increasing leverage can help push those positive trades even further out in the tails.

But here’s the trade-off: the actual exposure to S&P 500 futures contracts, specifically, still remains much, much higher in the case where we’re trading it alone.  In practice, the reason the diversified approach was able to generate increased returns during left-tail equity events – such as 2008 – is due to the fact correlations crashed to extremes (both positive and negative) between global equity indices, rates, commodities, and currencies.  This allowed the total notional exposure of directionally similar trades (e.g. short equities, long bonds, and short commodities in 2008) to far exceed the total notional exposure achieved if we were just trading the S&P 500 futures contract alone.

Source: Stevens Analytics.  Calculations by Newfound Research. 

Our confidence in achieving negative convexity versus equity left-tail events, therefore, is inherently tied to our belief that we will see simultaneously trends across a large number of assets during such environments.

Another interpretation of this data is that because negative trends in the S&P 500 have historically coincided with higher volatility, a strategy that seeks to trade just the S&P 500 futures with constant volatility will lose convexity in those tail events.  An alternative choice is to vary the volatility of the system to target the volatility of the S&P 500, whose convexity profile we plot below.

Source: Stevens Analytics and 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.  These results do not reflect the returns of any strategy managed by Newfound Research.

This analysis highlights a variety of trade-offs to consider:

  1. What, specifically, are we trying to create convexity against?
  2. Can diversification allow us to increase our notional exposure?
  3. Will diversification be dilutive to our potential convexity?

Perhaps, then, we should consider approaching the problem from another angle: given exposure to managed futures, what would be a better core portfolio to hold?  Given that most managed futures portfolios start from a risk parity core, the simplest answer is likely risk parity.

As an example, we construct a 10% target volatility risk parity index using equity, rate, and commodity contracts.  Below we plot the convexity profile of our managed futures strategy against this risk parity index and see the traditional “smile” emerge.  We also plot the equity curves for the risk parity index, the managed futures index, and a 50/50 blend.  Both the risk parity and managed futures indices have a realized volatility of level of 10.8%; the blended combination drops this volatility to just 7.6%, achieving a maximum drawdown of just -10.1%.

Source: Stevens Analytics and 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.  These results do not reflect the returns of any strategy managed by Newfound Research.

Conclusion

Managed futures have historically generated significant gains during left-tail equity events.  These returns, however, are by no means guaranteed.  While trend following is a mechanically convex strategy, the diversified nature of most managed futures programs can potentially dilute equity-crisis-specific returns.

In this research note, we sought to explore this concept by generating a large number of managed futures strategies that varied in the number of contracts traded.  We found that increasing the number of contracts had two primary effects: (1) it reduced realized convexity from a “smile” to a “smirk” (i.e. exhibited less up-side participation with equity markets); and (2) meaningfully increased returns during negative equity markets.

The latter is particularly curious but ultimately the byproduct of two facts.  First, increasing diversification allows for increased notional exposure in the portfolio to achieve the same target volatility level.  Second, during past crises we witnessed a large number of assets trending simultaneously.  Therefore, while increasing the number of contracts reduced notional exposure to S&P 500 futures specifically, the total notional exposure to trades generating positive gains during past crisis events was materially higher.

While the first fact is evergreen, the second may not always be the case.  Therefore, employing managed futures specifically as a strategy to provide offsetting returns during an equity market crisis requires the belief that a sufficient number of other exposures (i.e. equity indices, rates, commodities, and currencies) will be exhibiting meaningful trends at the same time.

Given its diversified nature, it should come as no surprise that managed futures appear to be a natural complement to a risk parity portfolio.

Investors acutely sensitive to significant equity losses – e.g. those in more traditional strategic allocation portfolios – might therefore consider strategies designed more specifically with such environments in mind.  At Newfound, we believe that trend equity strategies are one such solution, as they overlay trend-following techniques directly on equity exposure, seeking to generate the convexity mechanically and not through correlated assets.  When overlaid with U.S. Treasury futures – which have historically provided a “flight-to-safety” premium during equity crises – we believe it is a particularly strong solution.

 


Should I Stay or Should I Growth Now?

This post is available as a PDF download here.

Summary

  • Naïve value factor portfolios have been in a drawdown since 2007.
  • More thoughtful implementations performed well after 2008, with many continuing to generate excess returns versus the market through 2016.
  • Since 2017, however, most value portfolios have experienced a steep drawdown in their relative performance, significantly underperforming glamour stocks and the market as a whole.
  • Many investors are beginning to point to the relative fundamental attractiveness of value versus growth, arguing that value is well poised to out-perform going forward.
  • In this research note, we aim to provide further data for the debate, constructing two different value indices (a style-box driven approach and a factor-driven approach) and measuring the relative attractiveness of fundamental measures versus both the market and growth stocks.

 

“Should I stay or should I go now?
If I go, there will be trouble
And if I stay it will be double”

— The Clash

 

It is no secret that quantitative value strategies have struggled as of late.  Naïve sorts – like the Fama-French HML factor – peaked around 2007, but most quants would stick their noses up and say, “See? Craftsmanship matters.”  Composite metrics, industry-specific scoring, sector-neutral constraints, factor-neutral constraints, and quality screens all helped quantitative value investors stay in the game.

Even a basket of long-only value ETFs didn’t peak against the S&P 500 until mid-2014.

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 Value ETF basket is an equal-weight portfolio of FVAL, IWD, JVAL, OVLU, QVAL, RPV, VLU, and VLUE, with each ETF being included when it is first available.  Performance of the long/short portfolio is calculated as the monthly return of the Value ETF Basket minus the monthly return of the S&P 500 (“SPY”).

Many strategies were able to keep the mojo going until 2016 or so.  But at that point, the wheels came off for just about everyone.

A decade of under-performance for the most naïve approaches and three-plus years of under-performance for some of the most thoughtful has many people asking, “is quantitative value an outdated idea?  Should we throw in the towel and just buy growth?”

Of course, it should come as no surprise that many quantitative value managers are now clamoring that this is potentially the best time to invest in value since the dot-com bubble.  “No pain, no premium,” as we like to say.

Nevertheless, the question of value’s attractiveness itself is muddied for a variety of reasons:

  • How are we defining value?
  • Are we talking about long/short factors or long-only implementations?
  • Are we talking about the style-box definition or the factor definition of value?

By no means will this commentary be a comprehensive evaluation as to the attractiveness of Value, but we do hope to provide some more data for the debate.

Replicating Style-Box Growth and Value

If you want the details of how we are defining Growth and Value, read on.  Otherwise, you can skip ahead to the next section.

Morningstar invented the style box back in the early 1990s.  Originally, value was simply defined based upon price-to-book and price-to-earnings.  But somewhere along the line, things changed.  Not only was the definition of value expanded to include more metrics, but growth was given an explicit set of metrics to quantify it, as well.

The subtle difference here is rather than measuring cheap versus expensive, the new model more explicitly attempted to capture value versus growth.  The problem – at least in my opinion – is that the model makes it such that the growth-iest fund is now the one that simultaneously ranks the highest on growth metrics and the lowest on value metrics.  Similarly, the value-iest fund is the one that ranks the highest on value metrics and the lowest on growth metrics.  So growth is growing but expensive and value is cheap but contracting.

The index providers took the same path Morningstar did.  For example, while MSCI originally defined value and growth based only upon price-to-book, they later amended it to include not only other value metrics, but growth metrics as well.  S&P Dow Jones and FTSE Russell follow this same general scheme.  Which is all a bit asinine if you ask me.1

Nevertheless, it is relevant to the discussion as to whether value is attractive or not, as value defined by a style-box methodology can differ from value as defined by a factor methodology.  Therefore, to dive under the hood, we created our own “Frankenstein’s style-box” by piecing together different components of S&P Dow Jones’, FTSE Russell’s, and MSCI’s methodologies.

  • The parent universe is the S&P 500.
  • Growth metrics are 3-year earnings-per-share growth, 3-year revenue-per-share growth, internal growth rate2, and 12-month price momentum.3
  • Value metrics are book-to-price4, earnings-to-price5, free-cash-flow-to-price, and sales-to-enterprise-value6.
  • Metrics are all winsorized at the 90th percentile.
  • Z-scores for each Growth and Value metric are calculated using market-capitalization weighted means and standard deviations.
  • An aggregate Growth and Value score is calculated for each security as the sum of the underlying style z-scores.

From this point, we basically follow MSCI’s methodology.  Each security is plotted onto a “style space” (see image below) and assigned value and growth inclusion factors based upon the region it falls into.  These inclusion factors represent the proportion of a security’s market cap that can be allocated to the Value or Growth index.

Securities are then sorted by their distance from the origin point.  Starting with the securities that are furthest from the origin (i.e. those with more extreme style scores), market capitalizations are proportionally allocated to Value and Growth based upon their inclusion factors.  Once one style hits 50%, the remaining securities are allocated to the other style regardless of inclusion factors.

Source: MSCI.

The result of this process is that each style represents approximately 50% of the total market capitalization of the S&P 500.  The market capitalization for each security will be fully represented in the combination of growth and value and may even be represented in both Value and Growth as a partial weight (though never double counted).

Portfolios are rebalanced semi-annually using six overlapping portfolios.

How Attractive is Value?

To evaluate the relative attractiveness of Growth versus Value, we will evaluate two approaches.

In the first approach, we will make the assumption that fundamentals will not change but prices will revert.  In this approach, we will plot the ratio of price-to-fundamental measures (e.g. price-to-earnings of Growth over price-to-earnings of Value) minus 1.  This can be thought of as how far price would have to revert between the two indices before valuations are equal.

As an example, consider the following two cases.  First, Value has an earnings yield of 2% and Growth has an earnings yield of 1%.  In this case, both are expensive (Value has a P/E of 50 and Growth has a P/E of 100), but the price of Value would have to double (or the price of Growth would have to get cut in half) for their valuations to meet.  As a second case, Value has an earnings yield of 100% and Growth has an earnings yield of 50%.  Both are very cheap, but we would still have to see the same price moves for their fundamentals to meet.

For our second approach, we will assume prices and fundamentals remain constant and ask the question, “how much carry do I earn for this trade?”  Specifically, we will measure shareholder yield (dividend yield plus buyback yield) for each index and evaluate the spread.

In both cases, we will decompose our analysis into Growth versus the Market and the Market versus Value to gain a better perspective as to how each leg of the trade is influencing results.

Below we plot the relative ratio for price-to-book, price-to-earnings, price-to-free-cash-flow, and price-to-sales.

Source: Sharadar.  Calculations by Newfound Research.

A few things stand out:

  • The ratio of Growth’s price-to-book versus the S&P 500’s price-to-book appears to be at 2000-level highs. Even the ratio of the S&P 500’s price-to-book versus Value’s price-to-book appears extreme.  However, the interpretation of this data is heavily reliant upon whether we believe price-to-book is still a relevant valuation metric.  If not, this result may simply be a byproduct of naïve value construction loading up on financials and ignoring technology companies, leading to an artificially high spread.  The fact that Growth versus the S&P 500 has far out-stripped the S&P 500 versus Value in this metric might suggest that this result might just be caused Growth loading up on industries where the market feels book value is no longer relevant.
  • The ratio of price-to-earnings has certainly increased in the past year for both Growth versus the S&P 500 and the S&P 500 versus Value, suggesting an even larger spread for Growth versus Value. We can see, however, that we are still a far way off from 2000 highs.
  • Ratios for free cash flows actually look to be near 20-year lows.
  • Finally, we can see that ratios in price-to-sales have meaningfully increased in the last few years. Interestingly, Growth versus the S&P 500 has climbed much faster than the S&P 500 versus Value, suggesting that moving from Growth to the S&P 500 may be sufficient for de-risking against reversion.  Again, while these numbers sit at decade highs, they are still well below 2000-era levels.

Below we plot our estimate of carry (i.e. our return expectation given no change in prices): shareholder yield.  Again, we see recent-era highs, but levels still well below 2000 and 2008 extremes.

Source: Sharadar.  Calculations by Newfound Research.

Taken all together, value certainly appears cheaper – and a trade we likely would be paid more to sit on than we had previously – but a 2000s-era opportunity seems a stretch.

Growth is not Glamour

One potential flaw in the above analysis is that we are evaluating “Value 1.0” indices.  More modern factor indices drop the “not Growth” aspect of defining value, preferring to focus only on valuation metrics.  Therefore, to acknowledge that investors today may be evaluating the choice of a Growth 1.0 index versus a modern Value factor index, we repeat the above analysis using a Value strategy more consistent with current smart-beta products.

Specifically, we winsorize earnings yield, free-cash-flow yield, and sales yield and then compute market-cap-weighted z-scores.  A security’s Value score is then equal to its average z-score across all three metrics with no mention of growth scores.  The strategy selects the securities in the top quintile of Value scores and weights them in proportion to their value-score-scaled market capitalization.  The strategy is rebalanced semi-annually using six overlapping portfolios.

Source: Sharadar.  Calculations by Newfound Research.

We can see:

  • In the Value 1.0 approach, moving from Growth appeared much more expensive versus the S&P 500 than the S&P 500 did versus Value. With a more concentrated approach, the S&P 500 now appears far more expensive versus Value than Growth does versus the S&P 500.
  • Relative price-to-book (despite price-to-book no longer being a focus metric) still appears historically high. While it peaked in Q3 2019, meaningful reversion could still occur.  All the same caveats as before apply, however.
  • Relative price-to-earnings did appear to hit multi-decade highs (excluding the dot-com era) in early 2019. If the prior 6/2016-to-2/2018 reversion is the playbook, then we appear to be halfway home.
  • Relative price-to-free-cash-flow and price-to-sales are both near recent highs, but both below 2008 and dot-com era levels.

Plotting our carry for this trade, we do see a more meaningful divergence between Value and Growth.  Furthermore, the carry for bearing Value risk does appear to be at decade highs; however it is certainly not at extreme levels and it has actually reverted from Q3 2019 highs.

Source: Sharadar.  Calculations by Newfound Research.

Conclusion

In this research note, we sought to explore the current value-of-value.  Unfortunately, it proves to be an elusive question, as the very definition of value is difficult to pin down.

For our first approach, we build a style-box driven definition of Value.  We then plot the relative ratio of four fundamental measures – price-to-book, price-to-earnings, price-to-sales, and price-to-free-cash-flow – of Growth versus the S&P 500 and the S&P 500 versus Value.  We find that both Growth and the S&P 500 look historically expensive on price-to-book and price-to-earnings metrics (implying that Value is very, very cheap), whereas just Growth looks particularly expensive for price-to-sales (implying that Value may not be cheap relative to the Market).  However, none of the metrics look particularly cheap compared to the dot-com era.

We also evaluate Shareholder Yield as a measure of carry, finding that Value minus Growth reached a 20-year high in 2019 if the dot-com and 2008 periods are excluded.

Recognizing that many investors may prefer a more factor-based definition of value, we run the same analysis for a more concentrated value portfolio.  Whereas the first analysis generally pointed to Growth versus the S&P 500 being more expensive than the S&P 500 versus Value trade, the factor-based approach finds the opposite conclusion. Similar to the prior results, Value appears historically cheap for price-to-book, price-to-earnings, and price-to-sales metrics, though it appears to have peaked in Q3 2019.

Finally, the Shareholder Yield spread for the factor approach also appears to be at multi-decade highs ignoring the dot-com and 2008 extremes.

Directionally, this analysis suggests that Value may indeed be cheaper-than-usual.  Whether that cheapness is rational or not, however, is only something we’ll know with the benefit of hindsight.

For further reading on style timing, we highly recommend Style Timing: Value vs Growth (AQR).  For more modern interpretations: Value vs. Growth: The New Bubble (QMA), It’s Time for a Venial Value-Timing (AQR), and Reports of Value’s Death May Be Greatly Exaggerated (Research Affiliates).

 


 

Pursuing Factor Purity

This post is available as a PDF download here.

Summary

  • Factors play an important role for quantitative portfolio construction.
  • How a factor is defined and how a factor portfolio is constructed play important roles in the results achieved.
  • Naively constructed portfolios – such as most “academic” factors – can lead to latent style exposures and potentially large unintended bets.
  • Through numerical techniques, we can seek to develop pure factors that provide targeted exposure to one style while neutralizing exposure to the rest.
  • In this research note, we implement a regression-based and optimized-based approach to achieving pure factor portfolios and report the results achieved.

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:

  • Value (VAL): Earnings yield, free cash flow yield, and revenue yield.
  • Size (SIZE): Negative log market capitalization.
  • Momentum (MOM): 12-1 month total return.
  • Quality (QUAL): Return on equity1, negative accruals ratio, negative leverage ratio2.
  • Low Volatility (VOL): Negative 12-month realized volatility.

All characteristics are first cross-sectionally winsorized at the 5th and 95th 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-MacBeth

Our first approach to designing “pure” factor portfolios is inspired by Fama-MacBeth (1973)3.  Fama-MacBeth regression is a two-step approach:

  1. Regress each security against proposed risk factors to determine the security’s beta for that risk factor;
  2. Regress all security returns for a fixed time period against the betas to determine the risk premium for each factor.

Similarly, we will assume a factor model where the return for a given security can be defined as:

Where Rm is the return of the market and RFj 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 regression4 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 not dollar-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 characteristic exposure, 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 an equal-weight portfolio 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 50th 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 Optimization

Liu (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:

  • They minimize the squared sum of weights;
  • Their weighted characteristic exposure for the target style is equal to the weighted characteristic exposure of a naïve, equally-weighted, matching quintile portfolio; and
  • Weighted characteristic exposure for non-targeted styles equals zero.

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.

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 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.

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. 

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 2nd, 3rd, and 4th quintiles had more diversified security exposure on average.  Similar weighting profiles are displayed by the other factors.

Source: Sharadar.  Calculations by Newfound Research.

Conclusion

Factors 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.

 


 

 

Timing Trend Model Specification with Momentum

A PDF version of this post is available here.

Summary

  • Over the last several years, we have written several research notes demonstrating the potential benefits of diversifying “specification risk.”
  • Specification risk occurs when an investment strategy is overly sensitive to the outcome of a single investment process or parameter choice.
  • Adopting an ensemble approach is akin to creating a virtual fund-of-funds of stylistically similar managers, exhibiting many of the same advantages of traditional multi-manager diversification.
  • In this piece, we briefly explore whether model specification choices can be timed using momentum within the context of a naïve trend strategy.
  • We find little evidence that momentum-based parameter specification leads to meaningful or consistent improvements beyond a naively diversified approach.

Over the last several years, we’ve advocated on numerous occasions for a more holistic view of diversification: one that goes beyond just what we invest in, but also considers how those decisions are made and when they are made.

We believe that this style of thinking can be applied “all the way down” our process.  For example, how-based diversification would advocate for the inclusion of both value and momentum processes, as well as for different approaches to capturing value and momentum.

Unlike correlation-based what diversification, how-based diversification often does little for traditional portfolio risk metrics.  For example, in Is Multi-Manager Diversification Worth It? we demonstrated that within most equity categories, allocating across multiple managers does almost nothing to reduce  portfolio volatility.  It does, however, have a profound impact on the dispersion of terminal wealth that is achieved, often by avoiding manager-specific tail-risks.  In other words, our certainty of achieving a given outcome may be dramatically improved by taking a multi-manager approach.

Ensemble techniques to portfolio construction can be thought of as adopting this same multi-manager approach by creating a set of virtual managers to allocate across.

In late 2018, we wrote two notes that touched upon this:  When Simplicity Met Fragility and What Do Portfolios and Teacups Have in Common?  In both studies we injected a bit of randomness into asset returns to measure the stability of trend-following strategies.  We found that highly simplistic models tended to exhibit significant deviations in results with just slightly modified inputs, suggesting that they are highly fragile.  Increasing diversification across what, how, and when axes led to a significant improvement in outcome stability.

As empirical evidence, we studied the real-time results of the popular Dual Momentum GEM strategy in our piece Fragility Case Study: Dual Momentum GEM, finding that slight deviations in model specification lead to significantly different allocation conclusions and therefore meaningfully different performance results.  This was particularly pronounced over short horizons.

Tying trend-following to option theory, we then demonstrated how an ensemble of trend following models and specifications could be used to increase outcome certainty in Tightening the Uncertain Payout of Trend-Following.

Yet while more diversification appears to make portfolios more consistent in the outcomes they achieve, empirical evidence also suggests that certain specifications can lead to superior results for prolonged periods of time.  For example, slower trend following signals appear to have performed much, much better than fast trend following signals over the last two decades.

One of the benefits of being a quant is that it is easy to create thousands of virtual managers, all of whom may follow the same style (e.g. “trend”) but implement with a different model (e.g. prior total return, price-minus-moving-average, etc) and specification (e.g. 10 month, 200 day, 13 week / 34 week cross, etc).  An ancillary benefit is that it is also easy to re-allocate capital among these virtual managers.

Given this ease, and knowing that certain specifications can go through prolonged periods of out-performance, we might ask: can we time specification choices with momentum?

Timing Trend Specification

In this research note, we will explore whether momentum signals can help us time out specification choices as it relates to a simple long/flat U.S. trend equity strategy.

Using data from the Kenneth French library, our strategy will hold broad U.S. equities when the trend signal is positive and shift to the risk-free asset when trends are negative.  We will develop 1023 different strategies by employing three different models – prior total return, price-minus-moving-average, and dual-moving-average-cross-over – with lookback choices spanning from 20-to-360 days in length.

After constructing the 1023 different strategies, we will then apply a momentum model that ranks the models based upon prior returns and equally-weights our portfolio across the top 10%.  These choices are made daily and implemented with 21 overlapping portfolios to reduce the impact of rebalance timing luck.

It should be noted that because the underlying strategies are only allocating between U.S. equities and a risk-free asset, they can go through prolonged periods where they have identical returns or where more than 10% of models share the highest prior return.  In these cases, we select all models that have returns equal-to-or-greater-than the model identified at the 10th percentile.

Before comparing performance results, we think it is worthwhile to take a quick look under the hood to see whether the momentum-based approach is actually creating meaningful tilts in specification selection.  Below we plot both aggregate model and lookback weights for the 126-day momentum strategy.

Source: Kenneth French Data Library. Calculations by Newfound Research.

We can see that while the model selection remains largely balanced, with the exception of a few periods, the lookback horizon selection is far more volatile.  On average, the strategy preferred intermediate-to-long-term signals (i.e. 181-to-360 day), but we can see intermittent periods where short-term models carried favor.

Did this extra effort generate value, though?  Below we plot the ratio of the momentum strategies’ equity curves versus the naïve diversified approach.

We see little consistency in relative performance and four of the five strategies end up flat-to-worse.  Only the 252-day momentum strategy out-performs by the end of the testing period and this is only due to a stretch of performance from 1950-1964.  In fact, since 1965 the relative performance of the 252-day momentum model has been negative versus the naively diversified approach.

Source: Kenneth French Data Library. 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.

This analysis suggests that naïve, momentum-based specification selection does not appear to have much merit against a diversified approach for our simple trend equity strategy.

The Potential Benefits of Virtual Rebalancing

One potential benefit of an ensemble approach is that rebalancing across virtual managers can generate growth under certain market conditions.  Similar to a strategically rebalanced portfolio, we find that when returns across virtual managers are expected to be similar, consistent rebalancing can harvest excess returns above a buy-and-hold approach.

The trade-off, of course, is that when there is autocorrelation in specification performance, rebalancing creates a drag.   However, given that the evidence above suggests that relative performance between specifications is not persistent, we might expect that continuously rebalancing across our ensemble of virtual managers may actually allow us to harvest returns above and beyond what might be possible with just selecting an individual manager.

Source: Kenneth French Data Library. 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.

Conclusion

In this study, we explored whether we could time model specification choices in a simple trend equity strategy using momentum signals.

Testing different lookback horizons of 21-through-378 days, we found little evidence of meaningful persistence in the returns of different model specifications.  In fact, four of the five momentum models we studied actually under-performed a naïve, diversified.  The one model that did out-perform only seemed to do so due to strong performance realized over the 1950-1964 period, actually relatively under-performing ever since.

While this evidence suggests that timing specification with momentum may not be a fruitful approach, it does suggest that the lack of return persistence may benefit diversification for a second reason: rebalancing.  Indeed, barring any belief that one specification would necessarily do better than another, consistently re-pooling and distributing resources through rebalancing may actually lead to the growth-optimal solution.1 This potentially implies an even higher hurdle rate for specification-timers to overcome.

 


 

Re-specifying the Fama French 3-Factor Model

This post is available as a PDF download here.

Summary­

  • The Fama French three-factor model provides a powerful tool for assessing exposures to equity risk premia in investment strategies.
  • In this note, we explore alternative specifications of the value (HML) and size (SMB) factors using price-to-earnings, price-to-cash flow, and dividend yield.
  • Running factor regressions using these alternate specifications on a suite of value ETFs and Newfound’s Systematic Value strategy, lead to a wide array of results, both numerically and directionally.
  • While many investors consider the uncertainty of the parameter estimates from the regression using the three-factor model, most do not consider the uncertainty that comes from the assumption of how you construct the equity factors in the first place.
  • Understanding the additional uncertainty is crucial for manager and investors who must consider what risks they are trying to measure and control by using tools like factor regression and make sure their assumptions align with their goals.

In their 1992 paper, The Cross-Section of Expected Stock Returns, Eugene Fama and Kenneth French outlined their three-factor model to explain stock returns.

While the Capital Asset Pricing Model (CAPM) only describes asset returns in relation to their exposure to the market’s excess return through the stock’s beta and identifies any return beyond that as alpha, Fama and French’s three-factor model reattributed some of that supposed alpha to exposures to a value factor (High-minus-low or HML) based on returns stratified by price-to-book ratios and a size factor (small-minus-big or SMB) based on returns stratified by market capitalization.

This gave investors a tool to judge investment strategies based on the loadings to these risk factors. A manager with a seemingly high alpha may have simply been investing in value and small-cap stocks historically.

The notion of compensated risk premia has also opened the floodgate of many additional factors from other researchers (such as momentum, quality, low beta, etc.) and even two more factors from Fama and French (investment and profitability).

A richer factor universe opens up a wide realm of possibilities for analysis and attribution. However, setting further developments aside and going back to the original three-factor model, we would be remiss if we didn’t dive a bit further into its specification.

At the highest level, we agree with treating “value” and “size” as risk factors, but there is more than one way to skin a factor.

What is “value”?

Fama and French define it using the price-to-book ratio of a stock. This seems legitimate for a broad swath of stocks, especially those that are very capital intensive – such as energy, manufacturing, and financial firms – but what about industries that have structurally lower book values and may have other potential price drivers? For example, a technology company might have significant intangible intellectual property and some utility companies might employ leverage, which decreases their book value substantially.

To determine value in these sectors, we might utilize ratios that account for sales, dividends, or earnings. But then if we analyzed these strategies using the Fama French three-factor model as it is specified, we might misjudge the loading on the value factor.

“Size” seems more straightforward. Companies with low market capitalizations are small. However, when we consider how the size factor is defined based on the value factor, there might even be some differences in SMB using different value metrics.

In this commentary, we will explore what happens when we alter the definition of value for the value factor (and hence the size factor) and see how this affects factor regressions of a sample of value ETFs along with our Systematic Value strategy.

HML Factor Definitions

In the standard version of the Fama French 3-factor model, HML is constructed as a self-financing long/short portfolio using a 2×3 sort on size and value. The investment universe is split in half based on market capitalization and in three parts (30%/40%/30%) based on valuation, in this base case, price-to-book ratio.

Using additional data from the Kenneth French Data Library and the same methodology, we will construct HML factors using sorts based on size and:

  • Price-to-earnings ratios
  • Price-to-cash flow ratios
  • Dividend yields

The common inception date for all the factors is June 1951.

The chart below shows the growth of each of the four value factor portfolios.

Source: Kenneth French Data Library. 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. 

Over the entire time period – and for many shorter time horizons – the standard HML factor using price-to-book does not even have the most attractive returns. Price-to-earnings and price-to-cash flow often beat it out.

On the other hand, the HML factor formed using dividend yields doesn’t look so hot.

One of the reasons behind this is that the small, low dividend yield companies performed much better than the small companies that were ranked poorly by the other value factors. We can see this effect borne out in the SMB chart for each factor, as the SMB factor for dividend yield performed the best.

(Recall that we mentioned previously how the Fama French way of defining the size factor is dependent on which value metric we use.)

Source: Kenneth French Data Library. 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.

Looking at the statistical significance of each factor through its t-statistic, we can see that Price-to-Earnings and Price-to-Cash Flow yielded higher significance for the HML factor than Price-to-Book. And those two along with Dividend Yield all eclipsed the Price-to-Book construction of the SMB factor.

T-Statistics for HML and SMB Using Various Value Metrics

 Price-to-BookDividend YieldPrice-to-EarningsPrice-to-Cash Flow
HML2.90.03.73.4
SMB1.02.41.61.9

Assuming that we do consider all metrics to be appropriate ways to assess the value of companies, even if possibly under different circumstances, how do different variants of the Fama French three-factor model change for each scenario with regression analysis?

The Impact on Factor Regressions

Using a sample of U.S. value ETFs and our Systematic Value strategy, we plot the loadings for the different versions of HML. The regressions are carried out using the trailing three years of monthly data ending on October 2019.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

For each different specification of HML, the differences in the loading between investments is generally directionally consistent. For instance, DVP has higher loadings than FTA for all forms of HML.

However, sometimes this is not the case.

VLUE looks more attractive than VTV based on price-to-cash flow but not dividend yield. FTA is roughly equivalent to QVAL in terms of loading when price-to-book is used for HML, but it varies wildly when other metrics are used.

The tightest range for the four models for any of the investments is 0.09 (PWV) and the widest is 0.52 (QVAL). When we factor in that these estimates each have their own uncertainty, distinguishing which investment has the better value characteristic is tough. Decisions are commonly made on much smaller differences.

We see similar dispersion in the SMB loadings for the various constructions.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

Many of these values are not statistically significant from zero, so someone who has a thorough understanding of uncertainty in regression would likely not draw a strict comparison between most of these investments.

However, one implication of this is that if a metric is chosen that does ascribe significant size exposure to one of these investments, an investor may make a decision based on not wanting to bear that risk in what they desire to be a large-cap investment.

Can We Blend Our Way Out?

One way we often mitigate model specification risk is by blending a number of models together into one.

By averaging all of our HML and SMB factors, respectively, we arrive at blended factors for the three-factor model.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

All of the investments now have HML loadings in the top of their range of the individual model loadings, and many (FTA, PWV, RPV, SPVU, VTV, and the Systematic Value strategy) have loadings to the blended HML factor that exceed the loadings for all of the individual models.

The opposite is the case for the blended SMB factor: the loadings are in the low-end of the range of the individual model loadings.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

So which is the correct method?

That’s a good question.

For some investments, it is situation-specific. If a strategy only uses price-to-earnings as its value metric, then putting it up against a three-factor model using the P/E ratio to construct the factors is appropriate for judging the efficacy of harvesting that factor.

However, if we are concerned more generally about the abstract concept of “value”, then the blended model may be the best way to go.

Conclusion

In this study, we have explored the impact of model specification for the value and size factor in the Fama French three-factor model.

We empirically tested this impact by designing a variety of HML and SMB factors based on three additional value metrics (price-to-earnings, price-to-cash flow, and dividend yield). These factors were constructed using the same rules as for the standard method using price-to-book ratios.

Each factor, with the possible exceptions of the dividend yield-based HML, has performance that could make it a legitimate specification for the three-factor model over the time that common data is available.

Running factor regressions using these alternate specifications on a suite of value ETFs and Newfound’s Systematic Value strategy, led to a wide array of results, both numerically and directionally.

While many investors consider the uncertainty of the parameter estimates from the regression using the three-factor model, most do not consider the uncertainty that comes from the assumption of how you construct the equity factors in the first place.

Understanding the additional uncertainty is crucial for decision-making. Managers and investors alike must consider what risks they are trying to measure and control by using tools like factor regression and make sure their assumptions align with their goals.

“Value” is in the eye of the beholder, and blind applications of two different value factors may lead to seeing double conclusions.

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