Flirting with Models

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Is Managed Futures Value-able?

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On June 19, 2023

In Craftsmanship, Inflation, Portfolio Construction, Trend, Value

In Return StackingTM: Strategies for Overcoming a Low Return Environment, we advocated for the addition of managed futures to traditionally allocated portfolios.  We argued that managed futures’ low empirical correlation to both equities and bonds and its historically positive average returns makes it an attractive diversifier. More specifically, we recommended implementing managed futures as an overlay to a portfolio to avoid sacrificing exposure to core stocks and bonds.

The luxury of writing research is that we work in a “clean slate” environment.  In the real world, however, investors and allocators must contemplate changes in the context of their existing portfolios.  Investors rarely just hold pure beta exposure, and we must consider, therefore, not only how a managed futures overlay might interact with stocks and bonds, but also how it might interact with existing active tilts.

The most common portfolio tilt we see is towards value stocks (and, often, quality-screened value).  With this in mind, we want to briefly explore whether stacking managed futures remains attractive in the presence of an existing value tilt.

Diversifying Value

If we are already allocated to value, one of our first concerns might be whether an allocation to managed futures actually provides a diversifying return stream.  One of our primary arguments for including managed futures into a traditional stock/bond portfolio is its potential to hedge against inflationary pressures.  However, there are arguments that value stocks do much of the same, acting as “low duration” stocks compared to their growth peers.  For example, in 2022, the Russell 1000 Value outperformed the broader Russell 1000 by 1,145 basis points, offering a significant buoy during the throes of the largest bout of inflation volatility in recent history.

However, broader empirical evidence does not actually support the narrative that value hedges inflation (see, e.g., Baltussen, et al. (2022), Investing in Deflation, Inflation, and Stagflation Regimes) and we can see in Figure 1 that the long-term empirical correlations between managed futures and value is near-zero.

(Note that when we measure value in this piece, we will look at the returns of long-only value strategies minus the returns of broad equities to isolate the impact of the value tilt.  As we recently wrote, a long-only value tilt can be effectively thought as long exposure to the market plus a portfolio that is long the over-weight positions and short the under-weight positions1.  By subtracting the market return from long-only value, we isolate the returns of the active bets the tilt is actually taking.)

Figure 1: Excess Return Correlation

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

Correlations, however, do not tell us about the tails.  Therefore, we might also ask, “how have managed futures performed historically conditional upon value being in a drawdown?” As the past decade has shown, underperformance of value-oriented strategies relative to the broad market can make sticking to the strategy equally difficult.

Figure 2 shows the performance of the various value tilts as well as managed futures during periods when the value tilts realized a 10% or greater drawdown2.

Figure 2: Value Relative Drawdowns Greater than 10%

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

We can see that while managed futures may not have explicitly hedged the drawdown in value, its performance remained largely independent and accretive to the portfolio as a whole.

To drive the point of independence home, we can calculate the univariate regression coefficients between value implementations and managed futures.  We find that the relationship between the strategies is statistically insignificant in almost all cases. Figure 3 shows the results of such a regression.

Figure 3: Univariate Regression Coefficients

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. *, **, and *** indicate statistical significance at the 0.05, 0.01, and 0.001 level. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

But How Much?

As our previous figures demonstrate, managed futures has historically provided a positively diversifying benefit in relation to value; but how can we thoughtfully integrate an overlay into an portfolio that wants to retain an existing value tilt?

To find a robust solution to this question, we can employ simulation techniques.  Specifically, we block bootstrap 100,000 ten-year simulated returns from three-month blocks to find the robust information ratios and MAR ratios (CAGR divided by maximum drawdown) of the value-tilt strategies when paired with managed futures.

Figure 4 shows the information ratio frontier of these portfolios, and Figure 5 shows the MAR ratio frontiers.

Figure 4: Information Ratio Frontier

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

Figure 5: MAR Ratio Frontier

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

Under both metrics it becomes clear that a 100% tilt to either value or managed futures is not prudent. In fact, the optimal mix, as measured by either the Information Ratio or MAR Ratio, appears to be consistently around the 40/60 mark. Figure 6 shows the blends of value and managed futures that maximizes both metrics.

Figure 6: Max Information and MAR Ratios

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

In Figure 7 we plot the backtest of a 40% value / 60% managed futures portfolio for the different value implementations.

Figure 7: 40/60 Portfolios of Long/Short Value and Managed Futures

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

These numbers suggest that an investor who currently tilts their equity exposure towards value may be better off by only tilting a portion of their equity towards value and introducing a managed futures overlay onto their portfolio.  For example, if an investor has a 60% stock and 40% bond portfolio and the 60% stock exposure is currently all value, they might consider moving 36% of it into passive equity exposure and introducing a 36% managed futures overlay.

Depending on how averse a client is to tracking error, we can plot how the tracking error changes depending on the degree of portfolio tilt. Figure 8 shows the estimated tracking error when introducing varying allocations to the 40/60 value/managed futures overlay.

Figure 8: Relationship between Value/Managed Futures Tilt and Tracking Error

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

For example, if we wanted to implement a tilt to a quality value strategy, but wanted a maximum tracking error of 3%, the portfolio might add an approximate allocation of 46% to the 40/60 value/managed futures overlay.  In other words, 18% of their equity should be put into quality-value stocks and a 28% overlay to managed futures should be introduced.

Using the same example of a 60% equity / 40% bond portfolio as before, the 3% tracking error portfolio would hold 42% in passive equities, 18% in quality-value, 40% in bonds, and 28% in a managed futures overlay.

What About Other Factors?

At this point, it should be of no surprise that these results extend to the other popular equity factors. Figures 8 and 9 show the efficient information ratio and MAR ratio frontiers when we view portfolios tilted towards the Profitability, Momentum, Size, and Investment factors.

Figure 9: Information Ratio Frontier for Profitability, Momentum, Size, and Investment Tilts

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions. 

Figure 10: MAR Ratio Frontier for Profitability, Momentum, Size, and Investment Tilts

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

Figure 11: Max Information and MAR Ratios for Profitability, Momentum, Size, and Investment Tilts

Source: Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Performance is backtested and hypothetical.  Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise.  Performance assumes the reinvestment of all dividends.  Past performance is not indicative of future results.  See Appendix A for index definitions.

Once again, a 40/60 split emerges as a surprisingly robust solution, suggesting that managed futures has historically offered a unique, diversifying return to all equity factors.

Conclusion

Our analysis highlights the considerations surrounding the use of managed futures as a complement to a traditional portfolio with a value tilt. While value investing remains justifiably popular in real-world portfolios, our findings indicate that managed futures can offer a diversifying return stream that complements such strategies. The potential for managed futures to act as a hedge against inflationary pressures, while also offering a diversifying exposure during relative value drawdowns, strengthens our advocacy for their inclusion through a return stackingTM framework.

Our examination of the correlation between managed futures and value reveals a near-zero relationship, suggesting that managed futures can provide distinct benefits beyond those offered by a value-oriented approach alone. Moreover, our analysis demonstrates that a more conservative tilt to value, coupled with managed futures, may be a prudent choice for inverse to tracking error. This combination offers the potential to navigate unfavorable market environments and potentially holds more of a portfolio benefit than a singular focus on value.

Appendix A: Index Definitions

Book to Market – Equal-Weighted HiBM Returns for U.S. Equities (Kenneth French Data Library)

Profitability – Equal-Weighted HiOP Returns for U.S. Equities (Kenneth French Data Library)

Momentum – Equal-Weighted Hi PRIOR Returns for U.S. Equities (Kenneth French Data Library)

Size – Equal-Weighted SIZE Lo 30 Returns for U.S. Equities (Kenneth French Data Library)

Investment – Equal-Weighted INV Lo 30 Returns for U.S. Equities (Kenneth French Data Library)

Earnings Yield – Equal-Weighted E/P Hi 10 Returns for U.S. Equities (Kenneth French Data Library)

Cash Flow Yield – Equal-Weighted CF/P Hi 10 Returns for U.S. Equities (Kenneth French Data Library)

Dividend Yield – Equal-Weighted D/P Hi 10 Returns for U.S. Equities (Kenneth French Data Library)

Quality Value – Equal-Weighted blend of BIG HiBM HiOP, ME2 BM4 OP3, ME2 BM3 OP3, and ME2 BM3 OP4 Returns for U.S. Equities (Kenneth French Data Library)

Value Blend – An equal-weighted Returns of Book to Market, Earnings Yield, Cash Flow Yield, and Dividend Yield returns for U.S. Equities (Kenneth French Data Library)

Passive Equities (Market, Mkt) – U.S. total equity market return data from Kenneth French Library.

Managed Futures – BTOP50 Index (BarclayHedge). The BTOP50 Index seeks to replicate the overall composition of the managed futures industry with regard to trading style and overall market exposure. The BTOP50 employs a top-down approach in selecting its constituents. The largest investable trading advisor programs, as measured by assets under management, are selected for inclusion in the BTOP50. In each calendar year the selected trading advisors represent, in aggregate, no less than 50% of the investable assets of the Barclay CTA Universe.

Index Funds Reimagined?

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On May 19, 2023

In Craftsmanship, Portfolio Construction, Value

I recently had the privilege to serve as a discussant at the Democratize Quant 2023 conference to review Research Affliates’s new paper, Reimagining Index Funds.  The post below is a summary of my presentation.

Introduction

In Reimagining Index Funds (Arnott, Brightman, Liu and Nguyen 2023), the authors propose a new methodology for forming an index fund, designed to avoid the “buy high, sell low” behavior that can emerge in traditional index funds while retaining the depth of liquidity and capacity.  Specifically, they propose selecting securities based upon the underlying “economic footprint” of the business.

By using fundamental measures of size, the authors argue that the index will not be subject to sentiment-driven turnover.  In other words, it will avoid those additions and deletions that have primarily been driven by changes in valuation rather than changes in fundamentals.  Furthermore, the index will not arbitrarily avoid securities due to committee bias.  The authors estimate that total turnover is reduced by 20%.

The added benefit to this approach, the authors further argue, is that index trading costs are actually quite large.  While well-telegraphed additions and deletions allow index fund managers to execute market-on-close orders and keep their tracking error low, it also allows other market participants to front run these changes.  The authors’ research suggests that these hidden costs could be upwards of 20 basis points per year, creating a meaningful source of negative alpha.

Methodology & Results

The proposed index construction methodology is fairly simple:

Footnote #3 in the paper further expands upon the four fundamental measures:

The results of this rather simple approach are impressive.

  • Tracking error to the S&P 500 comparable to that of the Russell 1000.
  • Lower turnover than the S&P 500 or the Russell 1000.
  • Statistically meaningful Fama-French-Carhart 4-Factor alpha.

But What Is It?

One of the most curious results of the paper is that despite having a stated value tilt, the realized value factor loading in the Fama-French-Carhart regression is almost non-existent.  This might suggest that the alpha emerges from avoiding the telegraphed front-running of index additions and deletions.

However, many equity quants may notice familiar patterns in the cumulative alpha streams of the strategies.  Specifically, the early years look similar to the results we would expect from a value tilt, whereas the latter years look similar to the results we might expect from a growth tilt.

With far less rigor, we can create a strategy that holds the Russell 1000 Value for the first half of the time period and switches to the Russell 1000 Growth for the second half.  Plotting that strategy versus the Russell 1000 results in a very familiar return pattern. Futhermore, such a strategy would load positively on the value factor for the first half of its life and negatively for the second half of its life, leading a full-period factor regression to conclude zero exposure.

But how could such a dynamic emerge from such a simple strategy?

“Economic Footprint” is a Multi-Factor Tilt

The Economic Footprint variable is described as being an equal-weight metric of four fundamental measures: book value, sales, cash flow, and dividends, all measured as a percentage of all publicly-traded U.S. listed companies.  With a little math (inspired by this presentation from Cliff Asness), we will show that Economic Footprint is actually a mutli-factor screen on both Value and Market-Capitalization.

Define the weight of a security in the market-capitalization weighted index as its market capitalization divided by the total market capitalization of the universe.

If we divide both sides of the Economic Footprint equation by the weight of the security, we find:Some subtle re-arrangements leave us with: The value tilt effectively looks at each security’s value metric (e.g. book-to-price) relative to the aggregate market’s value metric.  When the metric is cheaper, the value tilt will be above 1; when the metric is more expensive, the value tilt will be less than 1.  This value tilt then effectively scales the market capitalization weight.

Importantly, economic footprint does not break the link to market capitalization.

Breaking economic footprint into two constituent parts allows us to get a visual intuition as to how the strategy operates.

In the graphs below, I take the largest 1000 U.S. companies by market capitalization and plot them based upon their market capitalization weight (x-axis) and their value tilt (y-axis).

(To be clear, I have no doubt that my value tilt scores are precisely wrong if compared against Research Affiliates’s, but I have no doubt they are directionally correct.  Furthermore, the precision does not change the logic of the forthcoming argument.)

If we were constructing a capitalization weighted index of the top 500 companies, the dots would be bisected vertically.

As a multi-factor tilt, however, economic footprint leads to a diagonal bisection.

The difference between these two graphs tells us what we are buying and what we are selling in the strategy relative to the naive capitalization-weighted benchmark.

We can clearly see that the strategy sells larg(er) glamour stocks and buys small(er) value stocks.  In fact, by definition, all the stocks bought will be both (1) smaller and (2) “more value” and any of the stocks sold.

This is, definitionally, a size-value tilt.  Why, then, are the factor loadings for size and value so small?

The Crucial Third Step

Recall the third step of the investment methodology: after selecting the companies by economic footprint, they are re-weighted by their market capitalization.  Now consider an important fact we stated above: every company we screen out is, by definition, larger than any company we buy.

That means, in aggregate, the cohort we screen out will have a larger aggregate market cap than the cohort we buy.

Which further means that the cohort we don’t screen out will, definitionally, become proportionally larger.

For example, at the end of April 2023, I estimate that screening on economic footprint would lead to the sale of a cohort of securities with an aggregate market capitalization of $4 trillion and the purchase of a cohort of securities with an aggregate market capitalization of $1.3 trillion.

The cohort that remains – which was $39.5 trillion in aggregate market capitalization – would grow proportionally from being 91% of the underlying benchmark to 97% of our new index.  Mega-cap growth names like Amazon, Google, Microsfot, and Apple would actually get larger based upon this methodology, increasing their collective weights by 120 basis points.

Just as importantly, this overweight to mega-cap tech would be a persistent artifact throughout the 2010s, suggesting why the relative returns may have looked like a growth tilt.

Why Value in 1999?

How, then, does the strategy create value-like results in the dot-com bubble?  The answer appears to lie in two important variables:

  1. What percentage of the capitalization-weighted index is being replaced?
  2. How strongly do the remaining securities lean into a value tilt?

Consider the scatter graph below, which estimates how the strategy may have looked in 1999.  We can see that 40% of the capitalization-weighted benchmark is being screened out, and 64% of the securities that remain have a positive value tilt.  (Note that these figures are based upon numerical count; it would likely be more informative to measure these figures weighted by market capitalization.)

By comparison, in 2023 only 20% of the underlying benchmark names are replaced and of the securities that remain, just 30% have a tilt towards value. These graphics suggest that while a screen on economic footprint creates a definitive size/value tilt, the re-weighting based upon relative market capitalization can lead to dynamic style drift over time.

Conclusion

The authors propose a new approach to index construction that aims to maintain a low tracking error to traditional capitalization-weighted benchmarks, reduce turnover costs, and avoid “buy high, sell low” behavior.  By selecting securities based upon the economic footprint of their respective businesses, the authors find that they are able to produce meaningful Fama-French-Carhart four-factor alpha while reducing portfolio turnover by 20%.

In this post I find that economic footprint is, as defined by the authors, actually a multi-factor tilt based value and market capitalization.  By screening for companies with a high economic footprint, the proposed method introduces a value and size tilt relative to the underlying market capitalization weighted benchmark.

However, the third step of the proposed process, which then re-weights the selected securities based upon their relative market capitalization, will always increase the weight of the securities of the benchmark that were not screened out.  This step creates the potential for meaningful style drift within the strategy over time.

I would argue the reason the factor regression exhibited little-to-no loading on value is that the strategy exhibited a positive value tilt over the first half of its lifetime and a negative value tilt over the second half, effectively cancelling out when evaluated over the full period.  The alpha that emerges, then, may actually be style timing alpha.

While the authors argue that their construction methodology should lead to the avoidance of “buy high, sell low” behavior, I would argue that the third step of the investment process has the potential to lead to just that (or, at the very least, buy high).  We can clearly see that in certain environments, portfolio construction choices can actually swamp intended factor bets.

Whether this methodology actually provides a useful form of style timing, or whether it is an unintended bet in the process that lead to a fortunate, positive ex-post result is an exercise left to other researchers.

Rebalance Timing Luck: The (Dumb) Luck of Smart Beta

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On August 14, 2020

In Defensive, Momentum, News, Risk & Style Premia, Value

We are proud to announce the release of our newest paper, Rebalance Timing Luck: The (Dumb) Luck of Smart Beta.

Abstract

Prior research and empirical investment results have shown that portfolio construction choices related to rebalance schedules may have non-trivial impacts on realized performance. We construct long-only indices that provide exposures to popular U.S. equity factors (value, size, momentum, quality, and low volatility) and vary their rebalance schedules to isolate the effects of “rebalance timing luck.” Our constructed indices exhibit high levels of rebalance timing luck, often exceeding 100 basis points annualized, with total impact dependent upon the frequency of rebalancing, portfolio concentration, and the nature of the underlying strategy. As a case study, we replicate popular factor-based index funds and similarly find meaningful performance impacts due to rebalance timing luck. For example, a strategy replicating the S&P Enhanced Value index saw calendar year return differentials above 40% strictly due to the rebalance schedule implemented. Our results suggest substantial problems for analyzing any investment when the strategy, its peer group, or its benchmark is susceptible to performance impacts driven by the choice of rebalance schedule.

Should I Stay or Should I Growth Now?

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On January 21, 2020

In Value, Weekly Commentary

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).

 

 

Re-specifying the Fama French 3-Factor Model

By

On December 16, 2019

In Craftsmanship, Portfolio Construction, Risk & Style Premia, Risk Management, Value, Weekly Commentary

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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