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:
- What percentage of the capitalization-weighted index is being replaced?
- 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.
Diversification with Portable Beta
By Nathan Faber
On February 18, 2020
In Craftsmanship, Portfolio Construction, Risk & Style Premia, Risk Management, Weekly Commentary
This post is available as a PDF download here.
Summary
Portable beta strategies seek to enhance returns by overlaying an existing portfolio strategy with complementary exposure to diversifying asset classes and strategies. In overlaying exposure on an existing portfolio strategy, portable beta strategies seek to make every invested dollar work harder. This idea can create “capital efficiency” for investors, freeing up dollars in an investor’s portfolio to invest in other asset classes or investment opportunities.
At Newfound, we focus on managing risk. Trend following – or absolute momentum – is a key approach we employ do this, especially in equities. Trend equity strategies are a class of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following.
We wrote previously how a trend equity strategy can be decomposed into passive and active components in order to isolate different contributors to performance. There is more than one way to do this, but in the most symmetric formulation, a “long/flat” trend equity strategy (one that that either holds equities or cash; i.e. does not short equities) can be thought of as a 100% passive allocation to a 50/50 portfolio of stocks and cash plus a 50% overlay allocation to a long/short trend equity strategy that can move between fully short and fully long equities. This overlay component is portable beta.
We have also written previously about how a portable beta overlay of bonds can be beneficial to trend equity strategies – or even passive equity investments, for that matter. For example, 95% of a portfolio could be invested in a trend equity strategy, and the remaining 5% could be set aside as collateral to initiate a 60% overlay to 10-year U.S. Treasury futures. This approximates a 60/40 portfolio that is leveraged by 50%
Source: Newfound. Allocations are hypothetical and for illustrative purposes only.
Since this bond investment introduces interest rate risk, we have proposed ways to manage risk in this specific sleeve using factors such as value, carry, and momentum. By treating these factors as fully tactical long/short portfolios themselves, if we hold them in equal weight, we can also break down the tactical U.S. Treasury futures overlay into active and passive components, with a 30% passive position in U.S. Treasury futures and 10% in each of the factor-based strategies.
Source: Newfound. Allocations are hypothetical and for illustrative purposes only.
When each overlay is fully invested, the portfolio will hold 95% stocks, 5% cash, and 60% U.S. Treasury futures. When all the overlays are fully short, the strategy will be fully invested in cash with no bond overlay position.
While the strategy has not changed at all with this slicing and dicing, we now have a framework to explore the historical contributions of the active and passive components and the potential diversification benefits that they offer.
Diversification Among Components
For the passive portfolio 50/50 stock/cash, we will use a blend of the Vanguard Total U.S. stock market ETF (VTI) and the iShares Short-term Treasury Bond ETF (SHV) with Kenneth French data for market returns and the risk-free rate prior to ETF inception.
For the active L/S Trend Equity portfolio, we will use a long/short version of the Newfound U.S. Trend Equity Index.
The passive 10-year U.S. Treasury futures is the continuous futures contract with a proxy of the 10-year constant maturity Treasury index minus the cash index used before inception (January 2000). The active long/short bond factors can be found on the U.S. Treasuries section of our quantitative signals dashboard, which is updated frequently.
All data starts at the common inception point in May 1957.
As a technical side note, we must acknowledge that a constant maturity 10-year U.S. Treasury index minus a cash index will not precisely match the returns of 10-year U.S. Treasury futures. The specification of the futures contracts state that the seller of such a contract has the right to deliver any U.S. Treasury bond with maturity between 6.5 and 10 years. In other words, buyers of this contract are implicitly selling an option, knowing that the seller of the contract will likely choose the cheapest bond to deliver upon maturity (referred to as the “cheapest to deliver”). Based upon the specification and current interest rate levels, that current cheapest to deliver bond tends to have a maturity of 6.5 years.
This has a few implications. First, when you buy U.S. Treasury futures, you are selling optionality. Finance 101 will teach you that optionality has value, and therefore you would expect to earn some premium for selling it. Second, the duration profile between our proxy index and 10-year U.S. Treasury futures has meaningfully diverged in the recent decade. Finally, the roll yield harvested by the index and the futures will also diverge, which can have a non-trivial impact upon returns.
Nevertheless, we believe that for the purposes of this study, the proxy index is sufficient for broad, directional attribution and understanding.
Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
The 50/50 Stock/Cash portfolio is the only long-only holding. While the returns are lower for all the other strategies, we must keep in mind that they are all overlays that can add to the 50/50 portfolio rather than simply de-risk and cannibalize its return.
This is especially true since these overlay strategies have exhibited low correlation to the 50/50 portfolio.
The table below shows the full period correlation of monthly returns for all the portfolio components. The equity and bond sub-correlation matrices are outlined to highlight the internal diversification.
Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
Not only do all of the overlays have low correlation to the 50/50 portfolio, but they generally exhibit low cross-correlations. Of the overlays, the L/S bond carry and L/S bond momentum strategies have the highest correlation (0.57), and the L/S bond carry and passive bond overlay have the next highest correlation (0.47).
The bond strategies have also exhibited low correlation to the equity strategies. This results in good performance, both absolute and risk-adjusted, relative to a benchmark 60/40 portfolio and a benchmark passive 90/60 portfolio.
Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
Finding the Optimal Blend
Up to this point, we have only considered the fixed allocations to each of the active and passive strategies outlined at the beginning. But these may not be the optimal holdings.
Using a block-bootstrap method to simulate returns, we can utilize mean-variance optimization to determine the optimal portfolios for given volatility levels.1 This yields a resampled historical realized efficient frontier.
Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
Plotting the benchmark 60/40, benchmark 90/60, and the tactical 90/60 on this efficient frontier, we see that the tactical 90/60 lies very close to the frontier at about 11.5% volatility. The allocations for the frontier are shown below.
Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
As expected, the lower volatility portfolios hold more cash and the high volatility portfolios hold more equity. For the 9% volatility level, these two allocations match, leading to the full allocation to a 50/50 stock/cash blend as in the tactical 90/60.
The passive allocation to the Treasury futures peaks at about 60%, while the L/S bond factor allocations are generally between 5% and 20% with more emphasis on Value and typically equal emphasis on Carry and Momentum.
The allocations in the point along the efficient frontier that matches the tactical 90/60 portfolio’s volatility are shown below.
Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
In this portfolio, we see a higher allocation to passive equities, a smaller position in the tactical equity L/S, and a larger position in passive Treasury futures. However, given the resampled nature of the process, these allocations are not wildly far away from the tactical 90/60.
The differences in the allocations are borne out in the Ulcer Index risk metric, which quantifies the severity and duration of drawdowns.
Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
The efficient frontier portfolio has a lower Ulcer Index than that of the tactical 90/60 even though their returns and volatility are similar. However, the Ulcer index of the tactical 90/60 is very close to that of the benchmark 60/40.
These differences are likely due to the larger allocation to the tactical equity long/short which can experience whipsaws (e.g. in October 1987), the lower allocation to passive U.S. equities, and the lower allocation to the Treasury overlay.
In an uncertain future, there can be significant risk in relying too much on the past, but having this framework can be useful for gaining a deeper understanding of which market environments benefit or hurt each component within the portfolio and how they diversify each other when held together.
Conclusion
In this research note, we explored diversification in a long/flat tactical equity strategy with a portable beta bond overlay. By decomposing the strategy into its passive holdings (50/50 stock/bond portfolio and U.S. Treasury futures) and active long/short overlays (trend equity, bond carry, bond momentum, and bond value), we found that each of the overlays has historically exhibited low correlation to the passive portfolios and low cross-correlations to each other. Combining all of these strategies using a tactical 90/60 portfolio has led to strong performance on both an absolute and risk-adjusted basis.
Using these strategy components, we constructed an efficient frontier of portfolios and also found that the “intuitive” tactical 90/60 portfolio that we have used in much of our portable beta research is close to the optimal portfolio for its volatility level. While this does not guarantee that this portfolio will be optimal over any given time period, it does provide evidence for the robustness of the multi-factor risk-managed approach.
Utilizing portable beta strategies can be an effective way for investors to pursue capital efficiency and maximize portfolio returns while simultaneously managing risk. While leverage can introduce risks of its own, relying on diversification and robust risk-management methods (e.g. trend following) can mitigate the risk of large losses.
The fear of using leverage and derivatives may be an uphill battle for investors, and there are a few operational burdens to overcome, but when used appropriately, these tools can make portfolios work harder and lead to more flexibility for allocating to additional opportunities.
If you are interested in learning how Newfound applies the concepts of tactical portable beta to its mandates, please reach out (info@thinknewfound.com).