The Research Library of Newfound Research

Author: Corey Hoffstein Page 1 of 18

Corey is co-founder and Chief Investment Officer of Newfound Research.

Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University.

You can connect with Corey on LinkedIn or Twitter.

15 Ideas, Frameworks, and Lessons from 15 Years

Today, August 28th, 2023, my company Newfound Research turns 15.  It feels kind of absurd saying that.  I know I’ve told this story before, but I never actually expected this company to turn into anything.  I started the company while I was still in undergrad and I named it Newfound Research after a lake my family used to visit in New Hampshire.  I fully expected the company to be shut down within a year and just go on to a career on Wall Street.

But here we are, 15 years later.  I’m not sure why, but this milestone feels larger than any recent birthday I can remember.  I’m so incredibly grateful for what this company has given me.  I’m grateful to my business partner, Tom.  I’m grateful to employees – both past and present – who dedicated part of their lives and careers to work here.  I’m grateful to our clients who supported this business.  I’m grateful for all the friends in the industry that I’ve made.  And I’m grateful to people like you who have given me a bit of a platform to explore the ideas I’m passionate about.

Coming up on this anniversary, I reflected quite a bit on my career.  And one of the things I thought about was all the lessons I’ve learned over the years.  And I thought that a fun way to celebrate would be to take the time and write down some of those ideas and lessons that have come to influence my thinking.

So, without further ado, here are 15 lessons, ideas, and frameworks from 15 years.

1.     Risk cannot be destroyed, only transformed.

For graduate school, I pursued my MS in Computational Finance at Carnegie Mellon University.  This financial engineering program is a cross-disciplinary collaboration between the finance, mathematics, statistics, and computer-science departments.

In practice, it was a study on the theoretical and practical considerations of pricing financial derivatives.

I don’t recall quite when it struck me, but at some point I recognized a broader pattern at play in every assignment.  The instruments we were pricing were always about the transference of risk in some capacity.  Our goal was to identify that risk, figure out how to isolate and extract it, package it into the appropriate product type, and then price it for sale.

Risk was driving the entire equation.  Pricing was all about understanding distribution of the potential payoffs and trying to identify “fair compensation” for the variety of risks and assumptions we were making.

For every buyer, there is a seller and vice versa and, at the end of the day, sellers who did not want risk would have to compensate buyers to bear it.

Ultimately, when you build a portfolio of financial assets, or even strategies, you’re expressing a view as to the risks you’re willing to bear.

I’ve come to visualize portfolio risk like a ball of play-doh.  As you diversify your portfolio, the play-doh is getting smeared over risk space.  For example, if you move from an all equity to an equity/bond portfolio, you might reduce your exposure to economic contractions but increase your exposure to inflation risk.

The play-doh doesn’t disappear – it just gets spread out.  And in doing so, you become sensitive to more risks, but less sensitive to any single risk in particular.

I’ll add that the idea of the conservation of risk is by no means unique to me.  For example, Chris Cole has said, on a number of occasions, that “volatility is never created or destroyed, only transmuted.”  In 2008, James Saft wrote in Reuters that “economic volatility, a bit like energy, cannot be destroyed, only switched from one form to another.”  In 2007, Swasti Kartikaningtyas wrote on the role of central counterparties in Indonesian markets, stating, “a simple entropy law for finance is that risks cannot be destroyed, only shifted among parties.”  In his 2006 book “Precautionary Risk Management,” Mark Jablonowski stated, “risk cannot be destroyed, it can only be divided up.”  In 1999, Clarke and Varma, writing on long-run strategic planning for enterprises, said, “like matter, risk cannot be destroyed.”

My point here is only that this idea is not novel or unique to me by any means.  But that does not make it any less important.

2.     “No pain, no premium”

The philosophy of “no pain, no premium” is just a reminder that over the long run, we get paid to bear risk.  And, eventually, risk is likely going to manifest and create losses in our portfolio.  After all, if there were no risk of losses, then why would we expect to earn anything above the risk-free rate?

Modern finance is largely based upon the principal that the more risk you take, the higher your expected reward.  And most people seem to inherently understand this idea when they buy stocks and bonds.

But we can generally expect the same to be true for many investment strategies.  Value investors, for example, are arguably getting paid to bear increased bankruptcy risk in the stocks they buy.

What about strategies that are not necessarily risk-based?  What about strategies that have a more behavioral explanation, like momentum?

At a meta level, we need the strategy to be sufficiently difficult to stick with to prevent the premium from being arbed away.  If an investment approach is viewed as easy money, enough people will adopt it that the inflows will drive out the excess return.

So, almost by definition, certain strategies – especially low frequency ones – need to be difficult to stick with for any premium to exist.  The pain is, ultimately, what keeps the strategy from getting crowded and allows the premium to exist.

3.     Diversifying, cheap beta is worth just as much as equally diversifying, expensive alpha.

I’ll put this lesson in the category of, “things that are obvious but might need to be said anyway.”

Our industry is obsessed with finding alpha.  But, for the most part, a portfolio doesn’t actually care if something is actually alpha or beta.

If you have a portfolio and can introduce a novel source of diversifying beta, it’s not only likely to be cheaper than any alpha you can access, but you can probably ascribe a much higher degree of confidence to its risk premium.

For example, if you invest only in stocks, finding a way to thoughtfully introduce bonds may do much, much more for your portfolio over the long run, with a higher degree of confidence, than trying to figure out a way to pick better stocks.

For most portfolios, beta will drive the majority of returns over the long run.  As such, it will be far more fruitful to first exhaust sources of beta before searching for novel sources of alpha.

By the way, I’m pretty sure I stole this lesson title from someone, but I can’t find the original person who said it.  If it’s you, my apologies.

4.     Diversification has multiple forms.

In 2007, Meb Faber published his paper A Quantitative Approach to Tactical Asset Allocation where he explored the application of a 10-month moving average as a timing model on a variety of asset classes.

It will likely go down in history as one of the most well-timed papers in finance given the 2008 crisis that immediately followed and how well the simple 10-month moving average model would have done in protecting your capital through that event.  It’s likely the paper that launched one-thousand tactical asset allocation models.

In 2013, I wrote a blog post where I showed that the performance of this model was highly sensitive to the choice of rebalance date.  Meb had originally written the paper using an end-of-month rebalance schedule.  In theory, there was nothing stopping someone from running the same model and rebalancing on the 10th trading day of every month.  In the post, I showed the performance of the strategy when applied on every single possible trading day variation, from the 1st to the last trading day of each month.  The short-term dispersion between the strategies was astounding even though the long-run returns were statistically indistinguishable.  

And my obsession with rebalance timing luck was born.

Shortly thereafter my good friend Adam Butler pointed out to me that the choice of a 10-month moving average was just as arbitrary.  Why not 9?  Why not 11?  Why not 200 days?  Why a simple moving average and not an exponential moving average or simple time-series momentum?  Just like what I saw with rebalancing schedule, the long-run returns were statistically indistinguishable but the short-run returns had significant dispersion.

The sort of dispersion that put managers out of business.

Ultimately, I developed my view that diversification was three dimensional: what, how, and when.

What is the traditional diversification almost everyone is certainly familiar with.  This is the diversification across securities or assets.  It’s the what you’re invested in.

How is the process by which investment decisions are made.  This includes diversification across different investment styles – such as value versus momentum – but also within a style.  For example, how are we measuring value?  Or what trend model and speed are we using?

When is the rebalance schedule.

Just as traditional portfolio theory tells us that we should diversify what we invest in because we are not compensated for bearing idiosyncratic risk, I believe the same is true across the how and when axes.

Our aim should be to diversify all uncompensated bets with extreme prejudice.

5.     The philosophical limits of diversification: if you diversify away all the risk, you shouldn’t expect any reward.

One of the most common due diligence questions is, “when doesn’t this strategy work?”  It’s an important question to ask for making sure you understand the nature any strategy.

But the fact that a strategy doesn’t work in certain environments is not a critique.  It should be expected.  If a strategy worked all the time, everyone would do it and it would stop working.

Similarly, if you’re building a portfolio, you need to take some risk.  Whether that risk is some economic risk or process risk or path dependency risk, it doesn’t matter – it should be there, lurking in the background.

If you want a portfolio that has absolutely no scenario risk, you’re basically asking for a true arbitrage or an expensive way of replicating the risk-free rate.

In other words, if you diversify away all the risk in your portfolio – again, think of this as smearing the ball of play-doh really, really, really thin across a very large plane of risk scenarios – return should just converge to the risk-free rate.

If it doesn’t, you’d have an arbitrage: just borrow at the risk-free rate and buy your riskless, diversified portfolio.

But arbitrages don’t come around easy.  Especially for low-frequency strategies and combinations of low-Sharpe asset classes.  There is no magical combination of assets and strategies that will eliminate downside risk in all future states of the world.

A corollary to this point is what I call the frustrating law of active management.  The basic idea is that if an investment idea is perceived both to have alpha and to be “easy”, investors will allocate to it and erode the associated premium.  That’s just basic market efficiency.

So how can a strategy be “hard”?  Well, a manager might have a substantial informational or analytical edge.  Or a manager might have a structural moat, accessing trades others do not have the opportunity to pursue.

But for most major low-frequency edges, “hard” is going to be behavioral.  The strategy has to be hard enough to hold on to that it does not get arbitraged away.

Which means that for any disciplined investment approach to outperform over the long run, it must experience periods of underperformance in the short run.

But we can also invert the statement and say that for any disciplined investment approach to underperform over the long run, it must experience periods of outperformance in the short run.

For active managers, the frustration is not only does their investment approach have to under-perform from time-to-time, but bad strategies will have to out-perform.  The latter may seem confusing, but consider that a purposefully bad strategy could simply be inverted – or traded short – to create a purposefully good one.

6.     It’s usually the unintended bets that blow you up.

I once read a comic – I think it was Farside, but I haven’t been able to find it – that joked that the end of the world would come right after a bunch of scientists in a lab said, “Neat, it worked!”

It’s very rarely the things we intend to do that blow us up.  Rather, it’s the unintended bets that sneak into our portfolio – those things we’re not aware of until it’s too late.

As an example, in the mid-2010s, it became common to say how cheap European equities were versus U.S. equities.  Investors who dove headlong into European equities, however, were punished.

Simply swapping US for foreign equities introduces a significant currency bet.  Europe may have been unjustifiably cheap, but given that valuation reversions typically play out over years, any analysis of this trade should have included either the cost of hedging the currency exposure or, at the very least, an opinion for why being implicitly short the dollar was a bet worth making.

But it could be argued that the analysis itself was simply wrong.  Lawrence Hamtil wrote on this topic many times, pointing out that both cross-country and time-series analysis of valuation ratios can be meaningfully skewed by sector differences.  For example, U.S. equity indices tend to have more exposure to Tech while European indices have more exposure to Consumer Staples.  When normalized for sector differences, the valuation gap narrowed significantly.

People who took the Europe versus US trade were intending to make a valuation bet.  Unless they were careful, they were also taking a currency and sector discrepancy bet.  

Rarely is it the intended bets that blow you up.

7.     It’s long/short portfolios all the way down.

I don’t remember when this one came to me, but it’s one of my favorite mental models.  The phrase is a play off of the “Turtles all the way down” expression.

Every portfolio, and every portfolio decision, can be decomposed into being long something and short something else.

It sounds trivial, but it’s incredibly powerful.  Here’s a few examples:

1.     You’re evaluating a new long-only, active fund.  To isolate what the manager is doing, you can take the fund’s holdings and subtract the holdings of their benchmark.  The result is a dollar-neutral long/short portfolio that reflects the manager’s active bets – it’s long the stuff they’re overweight and short the stuff they’re underweight.  This can help you determine what types of bets they’re making, how big the bets are, and whether the bets are even large stand a chance at covering their fee.

2.     If you’re contemplating selling one exposure to buy another in your portfolio, the trade is equivalent to holding your existing portfolio and overlaying a long/short trade: long the thing you’d buy and short the thing you’d sell.  This allows you to look at the properties of the trade as a whole (both what you’re adding and what you’re subtracting).

3.     If you want to understand how different steps of your portfolio construction process contribute to risk or return, you can treat the changes, stepwise, as long/short portfolios.  For example, for a portfolio that’s equal-weight 50 stocks from the S&P 500, you might compare: (1) Equal-Weight S&P 500 minus S&P 500, and then (2) Equal-Weight 50 Stocks minus Equal-Weight S&P 500.  Isolating each step of your portfolio construction as a long/short allows you to understand the return properties created by that step.

In all of these cases, evaluating the portfolio through the lens of the long/short framework provides meaningful insight.

8.     The more diversified a portfolio is, the higher the hurdle rate for market timing.

Market timing is probably finance’s most alluring siren’s song.  It sounds so simple.  Whether it’s market beta or some investment strategy, we all want to say: “just don’t do the thing when it’s not a good time to do it.”

After all the equity factors were popularized in the 2010s, factor timing came into vogue.  I read a number of papers that suggested that you could buy certain factors at certain parts of the economic cycle.  There was one paper that used a slew of easily tracked economic indicators to contemporaneously define where you were in the cycle, and then rotated across factors depending upon the regime.

And the performance was just ridiculous.

So, to test the idea, I decided to run the counterfactuals.  What if I kept the economic regime definitions the same, but totally randomized the basket of factors I bought in each part of the cycle?  With just a handful of factors, four regimes, and buying a basket of three factors per regime, you could pretty much brute force your way through all the potential combinations and create a distribution of their return results.

No surprise, the paper result was right up there in the top percentiles.  Know what else was?  Just a naïve, equally-weighted portfolio of the factors.  And that’s when you have to ask yourself, “what’s my confidence in this methodology?”

Because the evidence suggests is really, really hard to just beat naïve diversification.

There are a few ways you can get a sense for this, but one of my favorites is just by explicitly looking into the future and asking, “how accurate would I have to be to beat a well-diversified portfolio?”  This isn’t a hard simulation to run, and for reasonable levels of diversification, accuracy numbers creep up quite quickly.

Ultimately, timing is a very low breadth exercise.  To quote Michele Aghassi from AQR, “you’re comparing now versus usual.”  And being wrong compounds forever.

In almost all cases, it’s a lot easier to find something that can diversify your returns than it is to increase your accuracy in forecasting returns.

As a corollary to this lesson, I’ll add that the more predictable a thing is, the less you should be able to profit from it.

For example, let’s say I have a system that allows me to forecast the economic regime we’re in and I have a model for which assets should do well in that economic regime.

If I can forecast the economic regime with certainty, and if the market is reasonably efficient, I probably shouldn’t be able to know which assets will do well in which regime.  Conversely, if I know with perfect certainty which assets will do well in which regime, then I probably shouldn’t be able to forecast the regimes with much accuracy.

If markets are even reasonably efficient, the more easily predictable the thing, the less I should be able to profit from it.

9.     Certain signals are only valuable at extremes.

I was sent a chart recently with a plot of valuations for U.S. large-cap, mid-cap, and small-cap stocks.  The valuations were represented as an average composite of price-to-earnings, price-to-book, and price-to-sales z-scores.  The average z-score of large-caps sat at +1 while the average z-score for both mid- and small-caps sat at -1.

The implication of the chart was that a rotation to small- and mid-caps might be prudent based upon these relative valuations.

Lesson #6 about unintended bets immediately comes to mind.

For example, are historical measures even relevant today?  Before 2008 large-cap equities had a healthy share of financials and energy.  Today, the index is dominated by tech and communication services.  And we went through an entire decade with a zero interest rate policy regime.  How do rates at 5% plus today impact the refinancing opportunities in small-caps versus large-caps?  What about the industry differences between large-caps and small-caps?  Or the profit margins?  Or exposure to foreign revenue sources?  How are negative earners being treated in this analysis?  Is price-to-sales even a useful metric when sales are generated across the entire enterprise?

You might be able to sharpen your analysis and adjust your numbers to account for many of these points.  But there may be many others you simply don’t think of.  And that’s the noise.

Just about every signal has noise.

The question is, “how much noise?”  The more noise we believe a signal to have, the stronger we need the signal to be to believe it has any efficacy.  While we may be comfortable trading precisely measured signals at a single standard deviation, we may only have confidence in coarsely measured signals at much higher significance.

10.  Under strong uncertainty, “halvsies” can be an optimal decision.

During the factor wars of the mid-2010s, a war raged between firms as to what the best portfolio construction approach was: mixed or integrated.

The mixed approach said that each factor should be constructed in isolation and held in its own sleeve.

The integrated approach said that stocks should be scored on all the factors simultaneously, and the stocks with the best aggregate scores should be selected.

There were powerhouses on both sides of the argument.  Goldman Sachs supported mixed while AQR supported integrated.

I spent months agonizing over the right way to do things.  I read papers.  I did empirical analysis.  I even took pen to paper to derive the expected factor efficiency in each approach.

At the end of the day, I could not convince myself one way or another.  So, what did I do?  Halvsies.

Half the portfolio was managed in a mixed manner and half was managed in an integrated manner.

Really, this is just diversification for decision making.  Whenever I’ve had a choice with a large degree of uncertainty, I’ve often found myself falling back on “halvsies.” 

When I’ve debated whether to use one option structure versus another, with no clear winner, I’ve done halvsies.

When I’ve debated two distinctly different methods of modeling something, with neither approach being the clear winner, I’ve done halvsies.

Halvsies provides at least one step in the gradient of decision making and implicitly creates diversification to help hedge against uncertainty.

11.  Always ask: “What’s the trade?”

In July 2019, Greek 10-Year Bonds were trading with a yield that was nearly identical to US 10-Year Bonds.

By December, the yield on Greek 10-year bonds was 40 basis points under US 10-year bonds.  How could that make any sense?  How could a country like Greece make U.S. debt look like it was high yield?

When something seems absurd, ask this simple question: what’s the trade?  If it’s so absurd, how do we profit from it?

In this case, we might consider going long the U.S. 10-year and short the Greek 10-year in a convergence trade.  But we quickly realize an important factor: you don’t actually get paid in percentage points, you get paid in currency.  And that’s where the trade suddenly goes awry.  In this case, you’d receive dollars and owe euros.  And if you tried to explicitly hedge that trade away up front via a cross-currency basis swap, any yield difference largely melted away.

A more relevant financial figure would perhaps have been the spread between 10-year Greek and German bonds, which traded between 150-275bps in the 2nd half of 2019.  Not wholly unreasonable anymore.

When financial pundits talk about things in the market being absurd, ask “what’s the trade?”  Working through how to actual profit from the absurdity often shines a light on why the analysis is wrong.

12.  The trade-off between Type I and Type II errors is asymmetric

Academic finance is obsessed with Type I errors.  The literature is littered with strategies exhibiting alphas significant at a 5% level.  The literature wants to avoid reporting false positives.

In practice, however, there is an asymmetry that has to be considered.

What is the cost of a false positive?  Unless the strategy is adversely selected, the performance of trading a false positive should just be noise minus trading costs.  (And the opportunity cost of capital.)

What is the cost of a false negative?  We miss alpha.

Now consider how a focus on Type I errors can bias the strategies you select.  Are they more likely to be data-mined?  Are they more likely to be crowded?  Are they less likely to incorporate novel market features without meaningful history?

Once we acknowledge this asymmetry, it may actually be prudent to reduce the statistical requirements on the strategies we deploy.

13.  Behavioral Time is decades longer than Statistical Time

I recently stole this one from Cliff Asness.  This point has less to do with any practical portfolio construction thoughts or useful mental models.  It’s just simply acknowledging that managing money in real life is very, very, very different than managing money in a research environment.

It is easy, in a backtest, to look at the multi-year drawdown of a low-Sharpe strategy and say, “I could live through that.”  When it’s a multi-decade simulation, a few years looks like a small blip – just a statistical eventuality on the path.  You live that multi-year drawdown in just a few seconds in your head as your eye wanders the equity curve from the bottom left to the upper right.

In the real world, however, a multi-year drawdown feels like a multi-decade drawdown.  Saying, “this performance is within standard confidence bands for a strategy given our expected Sharpe ratio and we cannot find any evidence that our process is broken,” is little comfort to those who have allocated to you.  Clients will ask you for attribution.  Clients will ask you whether you’ve considered X explanation or Y.  Sales will come screeching to a halt.  Clients will redeem.

For anyone considering a career in managing money, it is important to get comfortable living in behavioral time.

14. Jensen’s Inequality

Jensen’s inequality basically says, “a function applied to a mean does not necessarily equal the mean applied after the function.”

What does that mean and how is it useful?  Consider this example.

You’re building a simple momentum portfolio.  You start with the S&P 500 and rank them by their momentum score, selecting the top 100 and then equally weighting them.

But you remember Lesson #4 and decide to use multiple momentum signals to diversify your how risk.

Here’s the question: do you average all the momentum scores together and then pick the top 100 or do you use each momentum score to create a portfolio and then average those portfolios together.

Jensen’s inequality tells us these approaches will lead to different results.  This is basically the mixed versus integrated debates from Lesson #10.  And the more convex the function is, the more different the results will likely be.  Imagine if instead of picking the top 100 we pick the top 20 or just the top 5.  It’s easy to imagine how different those portfolios could become with different momentum signals.

Here’s another trivial example.  You have 10 buy/sell signals.  Your function is to be long an asset if the signals are positive and short if the signals are negative.

If you average your signals first, your position is binary: always on or off.  But if you apply your function to each signal, and then average the results, you end up with a gradient of weights, the distribution of which will be a function of how correlated your signals are with one another.

You can see how Jensen’s inequality plays a huge role in portfolio construction.  Why?  Because non-linearities show up everywhere.  Portfolio optimization?  Non-linear.  Maximum or minimum position sizes?  Non-linear.  Rank-based cut-offs?  Non-linear.

And the more non-linear the function, the greater the wedge. But this also helps us understand how certain portfolio construction constraints can help us reduce the size of this wedge.

Ultimately, Jensen’s tells us that averaging things together in the name of diversification before or after convex steps in your process will lead to dramatically different portfolio results.

15. A backtest is just a single draw of a stochastic process.

As the saying goes, nobody has ever seen a bad backtest.

And our industry, as a whole, has every right to be skeptical about backtests.  Just about every seasoned quant can tell you a story about naively running backtests in their youth, overfitting and overoptimizing in desperate search of the holy grail strategy.

Less sophisticated actors may even take these backtests and launch products based on them, marketing the backtests to prospective investors.

And most investors would be right to ignore them outright.  I might even be in favor of regulation that prevents them from being shown in the first place.

But that doesn’t mean backtests are ultimately futile.  But we should acknowledge that when we run a single backtest, it’s just a single draw of a larger stochastic process.  Historical prices and data are, after all, just a record of what happened, but not a full picture of what could have happened.

Our job, as researchers, is to use backtesting to try to learn about what the underlying stochastic process looks like.

For example, what happens if we change the parameters of our process?  What happens if we change our entry or exit timing?  Or change our slippage and impact assumptions?

One of my favorite techniques is to change the investable universe, randomly removing chunks of the universe to see how sensitive the process is.  Similarly, randomly removing periods of time from the backtest to test regime sensitivities.

Injecting this randomness into the backtest process can tell us how much of an outlier our singular backtest really is.

Another fantastic technique is to purposefully introduce lookahead bias into your process.  By explicitly using a crystal ball, we can find the theoretical upper limits of achievable results and develop confidence bands for what our results should look like with more reasonable accuracy assumptions.

Backtesting done poorly is worse than not backtesting.  You’d be better off with pen and paper just trying to reason about your process.  But backtesting done well, in my opinion, can teach you quite a bit about the nature of your process, which is ultimately what we want to learn about.

16.  The Market is Usually Right

Did I say 15 ideas and lessons?  Here’s a bonus lesson that’s taken me far longer to learn than I’d care to admit.

The market is, for the most part, usually right.  It took me applying Lesson #11 – “What’s the Trade” – over and over to realize that most things that seem absurd probably aren’t.

That isn’t to say there aren’t exceptions.  If we see $20 on the ground, we might as well pick it up.  The 2021 cash & carry trade in crypto comes to mind immediately.  With limited institutional capacity and a nearly insatiable appetite for leverage from retail investors, the implied financing rates in perps and futures hit 20%+ for highly liquid tokens such as Bitcoin and Ethereum.  I suspect that’s as close to free money as I’ll ever get.

But that’s usually the exception.

This final lesson is about a mental switch for me.  Instead of seeing something and immediately saying, “the market is wrong,” I begin with the assumption that the market is right and I’m the one who is missing something.  This forces me to develop a list of potential reasons I might be missing or overlooking and exhaust those explanations before I can build my confidence that the market is, indeed, wrong.

Conclusion

If you made it this far, thank you.  I appreciate the generosity of your time.  I hope some of these ideas or lessons resonated with you and I hope you enjoyed reading as much as I enjoyed reflecting upon these concepts and putting together this list.  It will be fun for me to look back in another 15 and see how many of these stood the test of time.

Until then, happy investing.

Index Funds Reimagined?

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.

Portfolio Tilts versus Overlays: It’s Long/Short Portfolios All the Way Down

Several years ago, I started using the phrase, “It’s long/short portfolios all the way down.”  I think it’s clever.  Spoiler: it has not caught on.

The point I was trying to make is that the distance between any two portfolios can be measured as a long/short strategy.  This simple point, in my opinion, is a very powerful and flexible mental model for understanding portfolios.

If that sounds like gibberish, consider this practical example: you are a value investor who benchmarks to the S&P 500.  To implement your strategy, you buy the iShares MSCI USA Value ETF (“VLUE”).  If we subtract the weights of holdings in VLUE from the S&P 500, we can identify how much VLUE is over- or underweight any given position.

Figure 1. Relative Weight Differences Between VLUE and S&P 500 for the Top 20 Stocks in the S&P 500 by Weight
 Source: SSGA; iShares.  Calculations by Newfound Research.

Functionally, this is equivalent to saying, “VLUE is equal to the S&P 500 plus a long/short portfolio” where the longs are the overweights and the shorts are the underweights.

This is important for two reasons.  First, it helps us identify our implicit hurdle rate for alpha required to overcome the fee.

If we continue the exercise above for all the holdings of the S&P 500 and VLUE, we find that the longs and shorts both sum up to 86.2%1.  If we normalize the portfolio such that the longs and shorts both add up to 100%, we can say:

VLUE = 100% x S&P 500 + 86.2% x Long/Short

The positions in the long/short capture our active bets while the 86.2% here is our active share.  You may recall articles of years past about whether active share is predictive of alpha.  I believe it is clear, through this decomposition, that it is the active bets that control whether any alpha is generated.  Active share is key, however, in determining whether the strategy can overcome its fee.

For example, the current expense ratio for VLUE is 0.15% and the current expense ratio for the iShares Core S&P 500 ETF (“IVV”) is 0.03%.  Using the formula above, we can say:

0.15% = 0.03% + 86.2% x Fee of Long/Short

Doing some simple arithmetic, we find that the implicit fee of the long/short strategy is 0.139%.  This is the hurdle rate that the long/short portfolio must clear before it adds any excess return.

What if the active share was just 10% (i.e., the fund was a closet benchmarker)?  In that case, the hurdle rate would jump to 1.2%!  While active bets are responsible for generating alpha, the combination of a high fee and a low active share can lead to an unclearable hurdle rate.

The second reason I believe this concept is important is because it demystifies the idea of portfolio overlays.  Through the lens of long/short portfolios all the way down, everything is an overlay.  Buying value stocks?  Equity long/short overlay on broad equity market.  Rebalancing your portfolio?  Multi-asset long/short overlay on top of your prior asset allocation.

Consider the figure below, where I plot the equity curves of two strategies.  In the first, I buy the broad US equity market and overlay a 70% position in the classic Fama-French long/short value factor.2  In the second strategy is simply buying large-cap value stocks.

Figure 2. Equity Market plus Long/Short Value Overlay versus Value Stocks

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Market is the Fama-French Market Factor.  Value Long/Short is the Fama-French HML Factor.  Value Stocks is the Fama-French BIG HiBM. 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 how similar these two approaches are.  Buying value stocks is, effectively, buying the market and adding a big overlay of the long/short value factor.

There are some subtle, and important, differences.  For example, in tilting towards value stocks, the implicit short in any given stock is limited to that stock’s weight in the index (as the weight cannot go below zero).  In tilting towards value stocks, the size of the long/short overlay will also vary over time.3

Nevertheless, over the long run, on a log scale, drawn with a large enough crayon, and if we squint, we see a very similar picture.

This is all well and good on paper, but for many leverage-constrained investors, making room for an interesting equity long/short strategy means having to sell some existing exposure, giving the resulting cash to an alternative manager who holds onto it while implementing their strategy.  In the figure below, I plot two equity lines. In the first, we hold 80% in broad U.S. equities, 20% in cash4, and 20% in the classic Fama-French long/short value factor.  In the second, we buy large-cap value stocks.

Figure 3. Selling Stocks to Buy Alternatives Leads to a Beta Drag

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Market is the Fama-French Market Factor.  Value Long/Short is the Fama-French HML Factor.  Value Stocks is the Fama-French BIG HiBM. 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.

The terminal wealth results are not even close for two reasons.  First, as we saw in Figure 2, the appropriate overlay level is closer to 70%, not 20%.  Second, to make room for the long/short portfolio, we had to sell broad equity beta.  Which means the portfolio can really be thought of as:

100% U.S. Equity + 20% Long Cash / Short U.S. Equity + 20% Value Long/Short

Once again, it’s long/short portfolios all the way down.  That “long cash / short U.S. equity” component is a big drag over a 100-year period and captures what I like to call the “funding problem.”  As attractive as that value long/short may be, can it overcome the hurdle rate of what we had to sell to make room?

Part of the takeaway here is, “implicit leverage is good and may be hard to beat.”  The other takeaway, however, is, “there may be interesting things to invest in that may become more interesting if we can solve the funding problem.”

What are some of those things?  Ideally, we are adding things to a portfolio that have positive expected returns5 and also diversifying our existing holdings.  For most allocators, that means a portfolio of stocks and bonds.  An easy starting point, then, is to consider when stocks and bonds perform poorly and try to identify things that do well in those environments.

Following the methodology of Ilmanen, Maloney, and Ross (2017)6, we identify growth and inflation regimes using a composite of economic growth, inflation, and surprise factors.  Growth and inflation regimes are then combined to create four combined regimes: Growth Up / Inflation Down, Growth Up / Inflation Up, Growth Down / Inflation Down, and Growth Down / Inflation Up.

By design, each of these combined regimes occurs approximately 25% of the time throughout history.  We find that any given decade, however, can exhibit significant variation from the average.  For example, the 2000s were characterized by the Growth Down environment, whereas the 2010s were characterized by an Inflation Down environment.

Figure 4: Regime Classifications

Source: St. Louis Federal Reserve Economic Data; Federal Reserve of Philadelphia Survey of Professional Forecasters.  See Appendix B for regime definitions.

Using these regimes, we can evaluate how different asset classes, equity factors, and trading strategies have historically performed.  In Figures 5, 6, 7, and 8 we do precisely this, plotting the regime-conditional Sharpe ratios of various potential investments.

Note that due to data availability, each figure may cover a different time period.  The 60/40 portfolio is included in each graph as a reference point for that sub-period.

Figure 5: Sharpe Ratio of Equities, Bonds, and a 60/40 Portfolio in Different Economic Regimes (March 1962 to March 2023)

Source: Kenneth French Data Library; Tiingo; FRED; AQR; Bloomberg.  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.  See Appendix B for economic regime definitions.

Figure 6: Sharpe Ratios of Equity Long/Shorts in Different Economic Regimes (March 1962 to December 2022)

Source: Kenneth French Data Library; Tiingo; FRED; AQR; Bloomberg.  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.  See Appendix B for economic regime definitions.

Figure 7: Sharpe Ratios of Hedge Fund Categories in Different Economic Regimes (March 1998 to December 2022)

Source: Kenneth French Data Library; Tiingo; FRED; AQR; Bloomberg; HFRX.  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.  See Appendix B for economic regime definitions.

Figure 8: Sharpe Ratios of Commodities and Managed Futures in Different Economic Regimes  (March 1985 – December 2022)

Source: Kenneth French Data Library; Tiingo; FRED; AQR; Bloomberg.  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.  See Appendix B for economic regime definitions.

There are two standout takeaways:

  1. Stocks and bonds don’t do well during Growth Down / Inflation Up periods.7
  2. Other stuff does.

Specifically, we can see that Quality long/short and Managed Futures have historically been robust across regimes and have provided diversification during Growth Down / Inflation Up regimes.  Unfortunately, while the Quality long/short – or, at least, a proxy for it – can be achieved by tilting our long-only equity exposure, the same cannot be said for Managed Futures.

One question we might pose to ourselves is, “given the possible canvas of tilts and overlays, if we wanted to maximize the Sharpe ratio of our portfolio for a given active risk budget, what would we do?”  We can, at the very least, try to answer this question with the benefit of hindsight.

We’ll make a few assumptions:

  • Our strategic portfolio is 60% stocks and 40% bonds.
  • Our equity tilts can only be up to 60% of the portfolio (i.e., replace long-only equity one-for-one).
  • Our overlays can fill up the rest of the portfolio (i.e., we can replace any remaining long-only stock or bond exposure with capital efficient instruments – like futures or swaps – and allocate the available cash to fund the overlay strategy).

Using these rules, we can run an optimization8 maximizing the realized Sharpe ratio subject to a tracking error constraint.  The results are illustrated in Figure 9.  As the active risk budget increases, so does the allocation to tilts and overlays.  To understand the relative proportional exposure to each, normalized weights are presented in Figure 10.

Without emphasizing the specific allocations, the blue band represents the tilts while the orange, grey, green, purple bands represent the different overlay categories (long/short equity, hedge fund strategies, commodities, and managed futures, respectively).

This whole process uses the benefit of hindsight to measure both returns and covariances, so is by no means a prescriptive endeavor.  Nevertheless, I believe the results point in at least one clear direction: at all levels of active risk, the solution calls for a mix of tilts and overlays.

Figure 9: Maximizing the Realized Sharpe Ratio of a 60/40 Portfolio for a Given Active Risk Budget

Source: AQR Data Library; Kenneth French Data Library; HFRX.  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: Normalized Portfolio Weights

Source: AQR Data Library; Kenneth French Data Library; HFRX.  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 leverage-constrained allocators (e.g. many financial advisors), overlays have historically remained out of reach.  More flexible institutions were able to implement it through a process that became known as “portable alpha,” originally pioneered by PIMCO in the 1970s.  The implementation, on paper, is fairly simple:

  1. Replace passive beta exposure with a capital efficient derivative (e.g. futures or swaps) to free up capital.
  2. Allocate freed up capital to the desired alpha source.

Figure 11: Portable Alpha Example

The net portfolio construction, in effect, retains the beta and “ports” the alpha on as an overlay.

Historically, this required investors to manage a book of derivatives or hire a separate account manager.  Today, mutual funds and ETFs exist that provide pre-packaged capital efficiency.

Figure 12 demonstrates one such example where a 60/40 allocation is packaged into a capital efficient “90/60” fund, allowing an investor to utilize just 2/3rds of their capital to capture the same exposure.  Figure 13 demonstrates that when this freed up capital is allocated, it effectively “stacks” the exposure9 on top of the original 60/40 portfolio.  We have taken to calling this approach Return StackingTM.

Figure 12: Capital Efficient Funds

For illustrative purposes only.

Figure 13: Return StackingTM

For illustrative purposes only.

The other in figure 13 is where we can implement our alternative investment, effectively creating an overlay.  Ideally this is something that has positive expected returns and low correlation to both stocks and bonds.  We’re partial to managed futures for a variety of reasons, but allocators can pick their own adventure here.

Tilts and overlays are not mutually exclusive: it’s long/short portfolios all the way down.  While overlays remained out of reach for many leverage-constrained investors, new capital efficient mutual funds and ETFs enable their implementation.

 


Appendix A: Index Definitions

U.S. Stocks – U.S. total equity market return data from Kenneth French Library until 5/24/2001 when total returns returns from the Vanguard Total Stock Market ETF (VTI) are used.  Returns after 5/24/2021 are net of VTI’s underlying expense ratio.  Data for VTI provided by Tiingo.

10-Year U.S. Treasuries – The 10-Year U.S. Treasury index is a constant maturity index calculated by assuming that a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index, and unmanaged index returns do not reflect any fees, expenses or sales charges. The referenced index is shown for general market comparisons and is not meant to represent any Newfound index or strategy.  Data for 10-year U.S. Treasury yields come from the Federal Reserve of St. Louis economic database (“FRED”).

Value Tilt – BIG HiBM Returns for U.S. Equities (Kenneth French Data Library)

Size Tilt – ME LO 30 Returns for U.S. Equities (Kenneth French Data Library)

Momentum Tilt – BIG HiPRIOR Returns for U.S. Equities (Kenneth French Data Library)

Quality Tilt – 50% BIG LoINV + 50% BIG HiOP Returns for U.S. Equities (Kenneth French Data Library)

Low Beta Tilt – BIG LoBETA Returns for U.S. Equities (Kenneth French Data Library)

Value Long/Short – HML Devil Factor Returns for U.S. Equities (AQR Data Library)

Size Long/Short – SMB Factor Returns for U.S. Equities (Kenneth French Data Library)

Momentum Long/Short – UMD Factor Returns for U.S. Equities (Kenneth French Data Library) 

Quality Long/Short – QMJ Factor Returns for U.S. Equities (AQR Data Library)

Anti-Beta Long/Short – BAB Factor Returns for U.S. Equities (AQR Data Library)

HFRX Equity Long/Short –HFRX Equity Hedge Index (Hedge Fund Research, Inc.)

HFRX Event Driven – HFRX Event Driven Index (Hedge Fund Research, Inc.)

HFRX Macro/CTA – HFRX Macro/CTA Index (Hedge Fund Research, Inc.)

HFRX Relative Value – HFRX Relative Value Arbitrage Index (Hedge Fund Research, Inc.) 

Managed Futures – Time Series Momentum Factor (AQR Data Library). From inception to 2003, a 2% annual management fee and 3% annual estimated transaction cost are applied.  From 2003 to 2013, a 1.5% annual estimated transaction cost is applied.  From inception to 2013, a 20% annual performance fee is applied at the end of each year, so long as the end-of-year NAV exceeds the prior high-water mark.  From 2013 onward a 1.5% annual fee and 0.6% annual estimated transaction cost is applied.

Equal-Weight Commodities – Excess Return of Equal Weight Commodities Portfolio (AQR Data Library)


Appendix B: Regime Classifications

Growth and Inflation are each defined as a composite of two series, which are first normalized to z-scores by subtracting the full-sample historical mean and dividing by the full-sample historical volatility.

“Up” and “Down” regimes are defined as those times when measures are above or below their full sample median.

Growth:

  • Chicago Fed National Activity Index
  • Realized Industrial Production minus prior year Industrial Production forecast from the Survey of Professional Forecasters.

Inflation:

  • Year-over-year CPI change
  • Realized year-over-year CPI minus prior year NGDP forecast from the Survey of Professional Forecasters.

The Hidden Cost in Costless Put-Spread Collars: Rebalance Timing Luck

We have published a new paper on the topic of rebalance timing luck in option strategies: The Hidden Cost in Costless Put-Spread Collars: Rebalance Timing Luck.

Prior research and empirical investment results demonstrate that strategy performance can be highly sensitive to rebalance schedules, an effect called rebalance timing luck (“RTL”). In this paper we extend the empirical analysis to option-based strategies. As a case study, we replicate a popular strategy – the self-financing, three-month put-spread collar – with three implementations that vary only in their rebalance schedule. We find that the annualized tracking error between any two implementations is in excess of 400 basis points. We also decompose the empirically-derived rebalance timing luck for this strategy into its linear and non-linear components. Finally, we provide intuition for the driving causes of rebalance timing luck in option-based strategies.

Return Stacking in an Inverted Yield Curve Environment

Introduction 

When we first started publicly writing and talking about capital efficiency in 2017 – the predecessor conversation to return stackingTM – the 13-week U.S. Treasury Bill rate sat around 1.30%.

The prototypical example at the time was a 1.5x levered 60% stock / 40% bond portfolio (also referred to as a “90/60”).  Such a portfolio would allow investors to achieve the exposure of a 60/40 using just two-thirds of their capital, freeing up valuable portfolio real estate for diversifying alternatives.

Implementing such a portfolio in practice was also trivial: for every $1 invested, $0.9 could be invested in stocks and $0.1 held aside as cash collateral for a $0.6 notional position in U.S. Treasury futures.

Figure 1: One Possible Implementation of a 90/60 Portfolio

Today, the 13-week Treasury Bill rate hovers near 4.5% and the yield curve is severely inverted, causing many to ask, “does return stackingTM still make sense, particularly if we use Treasury futures to achieve our leverage?”

We believe the answer is a resounding “yes,” with four key points to consider.

It’s the portfolio, not the asset

With the yield curve severely inverted, paying short-term financing costs to invest in long-term Treasuries to achieve our leverage may seem like a losing prospect.  We believe this line of thinking is misguided, however; it misses the forest for the trees.

Using U.S. Treasury futures is simply a means to an end.  Sticking with our 90/60 example, what we actually care about is achieving 1.5x levered 60/40 exposure and the flexibility that creates for us in portfolio construction.

Would we have the same concern about an inverted yield curve if for every $1 invested we purchased $0.6 of U.S. Treasuries and held $0.4 in cash as collateral for $0.9 in S&P 500 futures exposure?  What if we simply borrowed money to lever an entire 60/40 portfolio up 1.5x?

Figure 2 plots that the annual returns of these three different approaches.  We can see that they are nearly identical to one another.

Figure 2: Annual Returns for Varying Approaches to Implementing a Levered 60/40 Portfolio

Source: Tiingo, Bloomberg, Barcharts.  Calculations by Newfound Research.  Past performance is backtested and hypothetical.  Returns are gross of all fees, costs, and taxes except for underlying expense ratios.  Returns assume the reinvestment of all distributions.  Past performance is not indicative of future results.  Starting date based upon the availability of pricing data.

To draw this point out further, consider the case of explicitly borrowing money to lever the 60/40 portfolio up 1.5x and the following ways we could implement this portfolio:

  • Hold 90% in stocks, 10% in U.S. Treasuries, and borrow to buy another 50% in U.S. Treasuries;
  • Hold 60% in U.S. Treasuries, 40% in stocks, and borrow to buy another 50% in stocks;
  • Hold 60% in stocks, 40% in U.S. Treasuries, and borrow to buy another 30% in stocks and 20% in U.S. Treasuries.

Figure 3: Different Approaches to Creating a 90/60 Portfolio

Does it matter which we choose?  Does an inverted yield curve make the first choice less attractive than the second?

In theory, we should be indifferent to these choices.  If we are concerned about using U.S. Treasury futures to achieve a levered 60/40, we should be equally concerned about using equity futures (“invert, always invert!”),

Sourcing cheap leverage.

In practice, we do care how we implement a return stackedTM portfolio.  Not because the yield curve is inverted, but because explicitly borrowing at the short-term Treasury Bill rate is difficult for all but the largest institutions.

Treasury futures have historically allowed us to do just that, giving us a very cost-effective source of leverage.  Figure 4 plots the embedded cost of leverage in 10-Year U.S. Treasury Futures relative to 3-Month U.S. Treasury Bill rates. By contrast, at the time of this writing, the current base margin rate is 10.75% at Schwab, 11.33% at Fidelity, and 12.50% at TD Ameritrade.

Figure 4: Embedded Financing Cost in 10-Year U.S. Treasury Futures versus 3-Month U.S. Treasury Bill Rate

Source: Bloomberg.

It’s the excess returns that matter.

But what about the fact that short-term rates have climbed from near-zero to north of 4%.  Is leverage now unattractive because the cost of financing is so high?

Let us return, for a moment, back to basic portfolio theory which says the expected return of an asset can be decomposed into two parts: the risk-free rate and the asset’s risk premium.  For example, the expected return of stocks should be equal to the risk-free rate plus the equity risk premium (“ERP”).  Similarly, the expected return of bonds should be equal to the risk-free rate plus the bond risk premium (“BRP”).

Figure 5: Decomposing Expected Returns into the Risk-Free Rate and Risk Premia

The expected return of a portfolio, then, can simply be thought of as the risk-free rate plus the blended return of risk premia.  For example, the expected return of a 60/40 is:

60% ERStocks + 40% ERBonds

Which can be decomposed as:

60% (Risk-Free Rate + ERP) + 40% (Risk-Free Rate + BRP)

Which equals:

60% ERP + 40% BRP + 100% Risk-Free Rate

Similarly, the 90/60 portfolio becomes:

90% ERP + 60% BRP + 100% Risk-Free Rate

= 1.5x (60% ERP + 40% BRP) + 100% Risk-Free Rate

What about a 45% Stock / 30% Bond / 25% Cash portfolio?  No surprise:

30% ERP + 20% BRP + 100% Risk-Free Rate

= 0.5x (60% ERP + 40% BRP) + 100% Risk-Free Rate

Whether we’re holding cash, fully invested, or levered, all we are doing is scaling the risk premium exposure!  It is the returns in excess of the risk-free rate that matter.

The important implication here is that if we believe the levered portfolio is unattractive to invest in, it must also mean we believe the unlevered portfolio is unattractive to invest in.1  If 60% ERP + 40% BRP is negative, no amount of scaling up or down will change it; we’d be better off just holding cash.

The null hypothesis is that markets are efficient.

None of this negates the fact that an investor may hold the active view that intermediate- to long-term U.S. Treasuries are unattractive to hold relative to cash today.  Such a view, however, is not unique to a levered portfolio: it would affect levered and unlevered portfolios alike.  To remain consistent with such a view, an investor should sell down their long-duration bonds in preference for short-duration exposure, regardless of leverage.

The only point we will stress here is that we believe the prudent approach is to assume, as a null hypothesis, that markets are generally efficient.  After all, if everyone held the same active view that long duration bonds are currently unattractive, they would sell those bonds, driving up the yield until the point they are attractive.  If we believe markets are generally in equilibrium, the current long-term yield should be equally attractive as the short yield when appropriately adjusted for their risks.

How can that be the case when the short-term rate is higher than the long-term rate?  The pure expectations hypothesis states that the yield curve embeds the expected path of short rates.  It is important to remember that the expected return of a longer-dated Treasury should be compared to the expected return of a constantly rolled shorter-dated Treasury.  An inverted yield curve, then, expresses the aggregate view that short rates should be lower in the future, which would bring down the return of the constantly rolled short-rate series.

Nevertheless, if an investor does have an active view about the relative expected returns of short- versus longer-dated Treasuries, that view would be expressed regardless of whether the portfolio is levered or not.

Conclusion

In this note we have attempted to address the question as to whether return stackingTM still makes sense when the cost of financing goes up, particularly if we’re accessing that financing through longer-dated Treasury futures during an inverted yield curve environment.

We believe the answer is ‘yes’, and four key points help illustrate this fact.  First, philosophically, we care less about the specific asset we are levering than the make-up of the levered portfolio.  Second, in practice we want to choose an asset to lever that provides us with a cost of financing as close to the risk-free rate as possible.  Third, it is the return in excess of the risk-free rate that ultimately matters.  Finally, an active view about the relative attractiveness of Treasuries applies regardless of whether the portfolio is levered or not.

As a final point, we want to zoom out once more to emphasize the portfolio view.  Consider the investor who uses a 90/60 portfolio to free up capital, and that freed up capital is invested for alpha exposure.  Very frequently, alpha exposures are packaged in a way they provide cash plus alpha returns.  For example, a managed futures fund is effectively U.S. T-Bills plus the return of an active futures trading strategy.

Which means the cash positions effectively net out.  Assume we put 66.6% of our portfolio in a 90/60 and 33.3% of our portfolio in a managed futures fund.  If we x-ray the former position, we effectively have 60% stocks plus 40% bonds minus 33.3% U.S. T-Bills.  If we x-ray the latter, we effectively have 33.3% T-Bills plus 33.3% of the active futures strategy.  Taken together, we’re left with 60% stocks plus 40% bonds plus 33.3% of the active futures strategy.

More than anything, it’s the net portfolio allocation that matters.

 


 

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