Is Managed Futures Value-able?

On June 19, 2023

In Craftsmanship, Inflation, Portfolio Construction, Trend, Value

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

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

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

Diversifying Value

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

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

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

Figure 1: Excess Return Correlation

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

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

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

Figure 2: Value Relative Drawdowns Greater than 10%

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

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

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

Figure 3: Univariate Regression Coefficients

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

But How Much?

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

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

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

Figure 4: Information Ratio Frontier

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

Figure 5: MAR Ratio Frontier

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

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

Figure 6: Max Information and MAR Ratios

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

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

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

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

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

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

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

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

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

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

What About Other Factors?

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

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

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

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

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

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

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

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

Conclusion

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

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

Appendix A: Index Definitions

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

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

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

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

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

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

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

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

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

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

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

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

What Is Managed Futures?

By Steven Braun

On February 2, 2023

In Craftsmanship, Portfolio Construction, Risk Management, Trend

Summary

Much like in 2008, managed futures as an investment strategy had an impressive year in 2022. With most traditional asset classes struggling to navigate the inflationary macroeconomic environment, managed futures has been drawing interest as a potential diversifier.
Managed futures is a hedge fund category that uses futures contracts as their primary investment vehicle. Managed futures managers can engage in many different investment strategies, but trend following is the most common.
Trend following as an investment strategy has a substantial amount of empirical evidence promoting its efficacy as an investment strategy. There also exist several behavioral arguments for why this anomaly exists, and why we might expect it to continue.
As a diversifier, multi-asset trend following has provided diversification benefits when compared to both stocks and bonds. Additionally, trend following has posted positive returns in the four major drawdowns in equities since 2000.

Cut short your losses, and let your winners run. – David Ricardo, 1838

What is Managed Futures?

Managed futures is a hedge fund category originating in the 1980s, named for the ability to trade (both long and short) global equity, bond, commodity, and currency futures contracts. Today, these strategies have been made available to investors in both mutual fund and ETF wrappers. The predominate strategy of most managed futures managers is trend following, so much so, that the terms are often used synonymously.

While trend following is by far the largest and most pronounced strategy in the category, it is not the only strategy used in the space.¹ Managed futures can engage in trend following, momentum trading, mean reversion, carry-focused strategies, relative value trading, macro driven strategies, or any combination thereof. Any individual managed futures manager may have a certain bias towards one of the strategies, though, trend following is by far the most utilized strategy of the group².

Figure 1: The Taxonomy of Managed Futures

Adapted from Kaminski (2014). The most common characteristics are highlighted in orange.

What is Trend Following?

Simply put, trend following is a strategy that buys (‘goes long’) assets that have been rising in price and sells (‘goes short’) assets that have been decreasing in price, based on the premise that this trend will continue. The precise method of measuring trends varies widely, but each primarily relies on the difference between an asset’s price today and the price of the same asset previously. Some common methods of measuring trends include total return measurements, moving averages, and regression lines. These different approaches are all mathematically linked, and empirical evidence does not suggest that one method is necessarily better than another³.

Trend following has a rich history in financial markets, with centuries of evidence supporting the idea that markets tend to trend. The obvious question to then ask is: why? The past few decades of academic research has focused on explaining theories such as the Efficient Market Hypothesis and research into explanatory market factors (such as value and size), diminishing the amount of research being conducted on trend following.

Figure 2: The Life Cycle of a Trend

Adapted from AQR. For illustrative purposes only.

The classification of trend following as an anomaly, however, has not left it without theories for why it works. There are a number of generally accepted explanations for why trend following works, and more importantly, why the anomaly might continue to persist.

Anchoring Bias: When new data enters the marketplace, investors can overly rely on historical data, thereby underreacting to the new information. This can be seen in Figure 3 where, after the catalyst of new information enters the market, the price of a security will directionally follow the fair value of the asset, but not with a large enough magnitude to match the fair value precisely.

Disposition Effect: Investors have a tendency to take gains on their winning positions too early and hold onto their losing positions too long.

Herding: After a noticeable trend has been established, investors “bandwagon” into the trade, prolonging the directional trend, and potentially pushing the price past the asset’s fair value⁴.

Confirmation Bias: Investors tend to ignore information that is contrary to an their beliefs. A positive (or negative) signal will be ignored if the investor has a differing view, extending the time frame for the convergence of an asset’s price to its fair value.

Rational Inattention Bias: Investors cannot immediately digest all information due to a lack of information processing resources (or mental capacity). Consequently, prices move towards fair value more slowly as the information is processed by all investors.

As previously mentioned, methodologies may vary widely when analyzing an asset’s trend, but the general theme is to view an asset’s current price relative to some measure of its recent history. For example, one common example of this is to observe an asset’s current price versus its 200-day moving average: initiating a long position when the price is above its moving average or a short position when it is below. Extending Figure 2, we can graphically depict the trade cycle attempting to take advantage of such a trend.

Figure 3: The Life Cycle of a Trade

Source: Newfound Research, AQR. For illustrative purposes only

Of course, using such an idealized description of a trend is not typically what is found in the market, which leads to many false-starts, The risk-management decisions made to reduce the impact of these false-starts begins to highlight part of the attractiveness of the strategy as a diversifier.

Consider that the fair value of an asset is generally never known with a high degree of certainty. A trend following manager is thus reliant on the perceived direction of trend at any given time, and so, must make choices based on how the trend evolves or not.

Figure 4: Heads I Trend, Tails I Don’t

Adapted from Michael Covel. For illustrative purposes only.

When the model indicates that a trend has formed, the manager will initiate a position in the direction of the indicated trend (either short or long – blue line in Figure 4). As long as the trend continues, the strategy will hold that position, and only exit when the signal indicates that the trend no longer exists. At that time, the manager will remove the position, potentially taking the opposite position⁵.

The second case (red line in Figure 4) is one in which the trend reverses shortly after a position has been initiated. After establishing a position in the asset, the price of the asset reverts to its previous levels, possibly completely reversing in direction. In such a case, the signal will indicate that the trend no longer exists and recommend that the position be removed.

Historically, by quickly cutting losers and letting winning trades run, trend following has created a positively skewed return profile. Managed futures strategies tend to trade many different markets and underlying assets. This minimizes the impact of trends being rejected but may increase the probability of taking a position in an asset that has an outlier trend occurring that might be out of the scope of a traditional portfolio.

Kaminski (2014) refers to this characteristic as divergent risk taking⁶, where a divergent investor “profess[es] their own ignorance to the true structure of potential risks/benefits with some level of skepticism for what is knowable or is not dependable”.

This divergent risk behavior results in a positively skewed return distribution by not risking too much on a trade, removing the position if it goes against you, and allowing a trade to run if it is winning⁷.

The structural nature of trend following minimizes the size of any bets taken, and quickly eliminates a position if the bet is not paying off. By diversifying across many markets, asset classes, and economic goods, while maintaining sensible positions without directional bias, the strategy maintains staying power by not swinging for the fences and staying with a time-proven approach⁸, in a well-diversified manner.

Using Managed Futures as A Diversifier

The traditional investor portfolio has typically been dominated by two assets: stocks and bonds. In recent history, investors have even been able to use fixed income to buffer equity risk as high-quality bonds have exhibited flight-to-safety characteristics in times of extreme market turmoil. In the first two decades of the 2000s, this pairing has worked extremely well given that interest rates declined over the period, inflation remained low, and the bonds were resilient during the fallout of the tech bubble and the Great Financial Crisis.

In Figure 5, we chart the relationship between the year-over-year Consumer Price Index for All Urban Consumers (“CPIAUCSL”) versus the 12-month correlation between U.S. Stocks and 10-Year U.S. Treasuries⁹. We can see that negative correlation is most pronounced when inflation is low. Positive correlation regimes, on the other hand, have historically occurred in all realized ranges of CPI changes, the most striking occurring when inflation was extraordinarily high.

Figure 5: The Relationship Between Inflation and Equity-Bond Correlation

Source: FRED, Kenneth French Data Library, Tiingo. For illustrative purposes only.

Since trend following can hold both long and short positions, it has the potential to trade price trends in assets in any direction that may emerge from increasing inflation risks. This is highlighted by the performance of trend following in 2022, where the year-to-date real returns of U.S. equities¹⁰, 10-Year U.S. Treasuries, and the SG CTA Trend Index as of December 31, 2022 , were -19.5%, -16.5%, and +27.4%, respectively. During 2022, trend following strategies were generally long the U.S. Dollar, short fixed income securities, and short equity indices. Additionally, the managers tended to hold mixed positions in the commodity space, taking long and short positions in the individual commodity contracts exhibiting both positive and negative trends.

Importantly, the dynamics exhibited throughout different economic regimes (such as monetary inflation vs supply/demand inflation) will unfold differently, so positions that were profitable in 2022 will likely not be the same in all environments. Trend following as a strategy, is dynamic in nature, and will adjust positioning as trends emerge and fade, regardless of the economic regime.

In addition to historically providing a ballast in inflationary regimes, one of managed futures’ claims to fame stems from the strategy’s ability to provide negative correlation in times of financial stress, specifically, in equity crises. The net result of including an allocation to trend following strategies during these periods has been a reduction in portfolio drawdowns and portfolio volatility.

Though managed futures have been in existence since the 1980’s, the strategy garnered its popularity coming out of the Great Financial Crisis, as it was one of the few investment strategies to provide a positive return. While this event shot the strategy to prominence, it was not an isolated incident. In fact, this relationship has been repeated frequently throughout history.

Table 1 shows the cumulative nominal returns of stocks, bonds, and managed futures when the equity market realized a greater-than 20% drawdown.

Table 1: Nominal Return of Equities, Bonds, and Managed Futures During Equity Crises

Source: FRED, Kenneth French Data Library, BarclayHedge. Calculations by Newfound Research. Time period is based on data availability. Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise Past performance is not a reliable indicator of future performance.

Since the inception of the SG CTA Trend Index¹¹, bonds have provided diversification benefits in three of the four large drawdowns. 2022, however, was the first period in which inflation has been a concern in the market, and U.S. Treasuries were insufficient to reduce risk in a traditional portfolio.

We can see, though, that the SG CTA Trend Index provided similar diversification benefits during the drawdowns in the first two decades of the century, but also proved capable while inflation shocks rose to prominence in 2022.

Figure 6: Performance From 1999 to 2022

Source: BarclayHedge, Tiingo. 60/40 Portfolio is the Vanguard Balance Index Fund (“VBINX”) and returns presented are net of the management fee of the fund. Time period is based on data availability. Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise. Past performance is not a reliable indicator of future performance.

Conclusion

Traditional portfolios consisting of equity and fixed income exposure have enjoyed two decades of strong performance due to favorable economic tailwinds. With the changing economic regime and uncertainty facing markets ahead, however, investors have begun searching for potential additions to their portfolios to protect against inflation and to provide diversifying exposure to other macroeconomic headwinds.

Trend following as a strategy has extensive empirical evidence supporting both its standalone performance, as well as the diversifying benefits in relation to traditional asset classes such as stocks and bonds. In addition, trend following is mechanically convex in that it can provide positive returns in both bull and bear markets.

Managed futures is a strong contender as an addition to a stock-and-bond heavy portfolio. Finding its roots in the 1980s, the strategy has a tenured history in the investment landscape with a demonstrated history of providing diversifying exposure in times of equity crisis.

In this paper, we have shown that trend following is a robust trading strategy with behavioral underpinnings, suggesting that the strategy has staying power in the long-run, as well as desirable characteristics due to the mechanical nature of the strategy.

As a potential addition to a traditional investment portfolio, managed futures provides a source of diversification beyond that of mainstream asset classes, as well as strong absolute returns on a standalone basis.

APPENDIX A: TREND FOLLOWING AS AN OPTIONS STRADDLE

A trend following strategy can benefit from both positive and negative price trends. If prices are increasing, then a long position can be initiated; if prices are decreasing, then a short position can be initiated. Said differently: a trend following strategy can potentially profit from both increases or decreases in price.

This characteristic is immediately reminiscent of a long position in an option straddle, where a put and call option are purchased with the same strike price. This option position would, thereby, benefit if the price moves largely either positive or negative¹².

Figure A1: Long Straddle Payoff Profile

Source: Newfound Research. For illustrative purposes only.

Empirically, these strategies have in fact performed remarkably similar. To illustrate this, we will create two simple strategies.

The first strategy is a simple trend following strategy that takes a long position in the S&P 500 when its prior 12-month return is positive, and a short position when its negative.

The second strategy will attempt to replicate the delta-position of a straddle expiring in one month, struck at the close price of the S&P 500 twelve months ago. We then compute the delta of this position using the Black-Scholes model¹³ and take a position in the S&P 500 equal to the computed delta. For example, if the price of the S&P 500 12-months ago was $3,000, we would calculate the delta of a straddle struck at $3,000. Since the delta of this position will range between -1 and 1, the strategy will use this as an allocation to the S&P 500.

Figure A2: Replicating Trend Following with Straddles

Source: Tiingo. Calculations by Newfound Research. Returns assume the reinvestment of all dividends. The S&P 500 is represented by the Vanguard 500 Index Fund Investor Shares (“VFINX”). For illustrative purposes only. Past performance is not a reliable indicator of future performance.

For both strategies, we will assume that any excess capital is held in cash, returning 0%. Figure A2 plots the growth of $1 invested in each strategy.

As we can see, the option strategy and the trend following strategy provide a roughly equivalent return profile. In fact, if we compare the quarterly returns of the two strategies to the S&P 500, an important pattern emerges. Both strategies exhibit convex relationships in relation to the S&P 500.

Figure A3: Trend Following Relationship to the Underlying

Source: Newfound Research. For illustrative purposes only.

Figure A4: Straddle Replication Relationship to the Underlying

Source: Newfound Research. For illustrative purposes only.

APPENDIX B: Index Definitions

U.S. Stocks: U.S. total equity market return data from Kenneth French Library. 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.

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 comparison 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”).

SG Trend Index: The SG Trend Index is designed to track the largest 10 (by AUM) CTAs and be representative of the managed futures trend-following space.

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

A long/flat tactical equity strategy with a portable beta bond overlay – a tactical 90/60 portfolio – has many moving parts that can make attribution and analysis difficult.
By decomposing the strategy into its passive holdings (a 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 can explore the historical performance of each component and diversification benefits across each piece of the strategy.
Using a mean-variance framework, we are also able to construct an efficient frontier of the strategy components and assess the differences between the optimal portfolio and the tactical 90/60.
We find that the tactical 90/60 is relatively close to the optimal portfolio for its volatility level and that its drawdown risk profile is close to that of an unlevered 60/40 portfolio.
By utilizing a modest amount of leverage and pairing it will risk management in both equities and bonds, investors may be able to pursue capital efficiency and maximize portfolio returns while simultaneously managing risk.

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).

Tightening the Uncertain Payout of Trend-Following

By Nathan Faber

On January 28, 2019

In Craftsmanship, Portfolio Construction, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

Long/flat trend-following strategies have historically delivered payout profiles similar to those of call options, with positive payouts for larger positive underlying asset returns and slightly negative payouts for near-zero or negative underlying returns.
However, this functional relationship contains a fair amount of uncertainty for any given trend-following model and lookback period.
In portfolio construction, we tend to favor assets that have a combination of high expected returns or diversifying return profiles.
Since broad investor behavior provides a basis for systematic trend-following models to have positive expected returns, taking a multi-model approach to trend-following can be used to reduce the variance around the expected payout profile.

Introduction

Over the past few months, we have written much about model diversification as a tactic for managing specification risk, even with specific case studies. When we consider the three axes of diversification, model diversification pertains to the “how” axis, which focuses on strategies that have the same overarching objective but go about achieving it in different ways.

Long/flat trend-following, especially with equity investments, aims to protect capital on the downside while maintaining participation in positive markets. This leads to a payout profile that looks similar to that of a call option.¹

However, while a call option offers a defined payout based on the price of an underlying asset and a specific maturity date, a trend-following strategy does not provide such a guarantee. There is a degree of uncertainty.

The good news is that uncertainty can potentially be diversified given the right combinations of assets or strategies.

In this commentary, we will dive into a number of trend-following strategies to see what has historically led to this benefit and the extent that diversification would reduce the uncertainty around the expected payoff.

Diversification in Trend-Following

The justification for a multi-model approach boils down to a simple diversification argument.

Say you would like to include trend-following in a portfolio as a way to manage risk (e.g. sequence risk for a retiree). There is academic and empirical evidence that trend-following works over a variety of time horizons, generally ranging from 3 to 12 months. And there are many ways to measure trends, such as moving average crossovers, trailing returns, deviations from moving averages, risk adjusted returns, etc.

The basis for deciding ex-ante which variant will be the best over our own investment horizon is tenuous at best. Backtests can show one iteration outperforming over a given time horizon, but most of the differences between strategies are either noise from a statistical point of view or realized over a longer time period than any investor has the lifespan (or mettle) to endure.

However, we expect each one to generate positive returns over a sufficiently long time horizon. Whether this is one year, three years, five years, 10 years, 50 years… we don’t know. What we do know is that out of the multitude the variations of trend-following, we are very likely to pick one that is not the best or even in the top segment of the pack in the short-term.

From a volatility standpoint, when the strategies are fully invested, they will have volatility equal to the underlying asset. Determining exactly when the diversification benefits will come in to play – that is, when some strategies are invested and others are not – is a fool’s errand.

Modern portfolio theory has done a disservice in making correlation seem like an inherent trait of an investment. It is not.

Looking at multiple trend-following strategies that can coincide precisely for stretches of time before behaving completely differently from each other, makes many portfolio construction techniques useless. We do not expect correlation benefits to always be present. These are nonlinear strategies, and fitting them into a linear world does not make sense.

If you have pinned up ReSolve Asset Management’s flow chart of portfolio choice above your desk (from Portfolio Optimization: A General Framework for Portfolio Choice), then the decision on this is easy.

Source: ReSolve Asset Management. Reprinted with permission

From this simple framework, we can break the different performance regimes down as follows:

The Math Behind the Diversification

The expected value of a trend-following strategy can be thought of as a function of the underlying security return:

Where the subscript i is used to indicate that the function is dependent on the specific trend-following strategy.

If we combine multiple trend-following strategies into a portfolio, then the expectation is the average of these functions (assuming an equal weight portfolio per the ReSolve chart above):

What’s left to determine is the functional form of f.

Continuing in the vein of the call option payoff profile, we can use the Black-Scholes equation as the functional form (with the risk-free rate set to 0). This leaves three parameters with which to fit the formula to the data: the volatility (with the time to expiration term lumped in, i.e. sigma * sqrt(T-t)), the strike, and the initial cost of the option.

where d₁ and d₂ are defined in the standard fashion and N is the cumulative normal distribution function.

r_K is the strike price in the option formula expressed as a percent relative to the current value of the underlying security.

In the following example, we will attempt to provide some meaning to the fitted parameters. However, keep in mind that any mapping is not necessarily one-to-one with the option parameters. The functional form may apply, but the parameters are not ones that were set in stone ex-ante.²

An Example: Trend-Following on the S&P 500

As an example, we will consider a trend-following model on the S&P 500 using monthly time-series momentum with lookback windows ranging from 4 to 16 months. The risk-free rate was used when the trends were negative.

The graph below shows an example of the option price fit to the data using a least-squares regression for the 15-month time series momentum strategy using rolling 3-year returns from 1927 to 2018.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The volatility parameter was 9.5%, the strike was 2.3%, and the cost was 1.7%.

What do these parameters mean?

As we said before this can be a bit tricky. Painting in broad strokes:

The volatility parameter describes how “elbowed” payoff profile is. Small values are akin to an option close to expiry where the payoff profile changes abruptly around the strike price. Larger values yield a more gentle change in slope.
The strike represents the point at which the payoff profile changes from participation to protection using trend-following lingo. In the example where the strike is 2.3%, this means that the strategy would be expected to start protecting capital when the S&P 500 return is less than 2.3%. There is some cost associated with this value being high.
The cost is the vertical shift of the payoff profile, but it is not good to think of it as the insurance premium of the trend-following strategy. It is only one piece. To see why this is the case, consider that the fitted volatility may be large and that the option price curve may be significantly above the final payout curve (i.e. if the time-scaled volatility went to zero).

So what is the actual “cost” of the strategy?

With trend-following, since whipsaw is generally the largest potential detractor, we will look at the expected return on the strategy when the S&P 500 is flat, that is, an absence of an average trend. It is possible for the cost to be negative, indicating a positive expected trend-following return when the market was flat.

Looking at the actual fit of the data from a statistical perspective, the largest deviations from the expected value (the residuals from the regression) are seen during large positive returns for the S&P 500, mainly coming out of the Great Depression. This characteristic of individual trend-following models is generally attributable to the delay in getting back into the market after a prolonged, severe drawdown due to the time it takes for a new positive trend to be established.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Part of the seemingly large number of outliers is simply due to the fact that these returns exhibit autocorrelation since the periods are rolling, which means that the data points have some overlap. If we filtered the data down into non-overlapping periods, some of these outliers would be removed.

The outliers that remain are a fact of trend-following strategies. While this fact of trend-following cannot be totally removed, some of the outliers may be managed using multiple lookback periods.

The following chart illustrates the expected values for the trend-following strategies over all the lookback periods.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The shorter-term lookback windows have the expected value curves that are less horizontal on the left side of the chart (higher volatility parameter).

As we said before the cost of the trend-following strategy can be represented by the strategy’s expected return when the S&P 500 is flat. This can be thought of as the premium for the insurance policy of the trend-following strategies.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The blend does not have the lowest cost, but this cost is only one part of the picture. The parameters for the expected value functions do nothing to capture the distribution of the data around – either above or below – these curves.

The diversification benefits are best seen in the distribution of the rolling returns around the expected value functions.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Now with a more comprehensive picture of the potential outcomes, a cost difference of even 3% is less than one standard deviation, making the blended strategy much more robust to whipsaw for the potential range of S&P 500 returns.

As a side note, the cost of the short window (4 and 5 month) strategies is relatively high. However, since there are many rolling periods when these models are the best performing of the group, there can still be a benefit to including them. With them in the blend, we still see a reduction in the dispersion around the expected value function.

Expanding the Multitude of Models

To take the example even further down the multi-model path, we can look at the same analysis for varying lookback windows for a price-minus-moving-average model and an exponentially weighted moving average model.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

And finally, we can combine all three trend-following measurement style blends into a final composite blend.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

As with nearly every study on diversification, the overall blend is not the best by all metrics. In this case, its cost is higher than the EWMA blended model and its dispersion is higher than the TS blended model. But it exhibits the type of middle-of-the-road characteristics that lead to results that are robust to an uncertain future.

Conclusion

Long/flat trend-following strategies have payoff profiles similar to call options, with larger upsides and limited downsides. Unlike call options (and all derivative securities) that pay a deterministic amount based on the underlying securities prices, the payoff of a trend-following strategy is uncertain,

Using historical data, we can calculate the expected payoff profile and the dispersion around it. We find that by blending a variety of trend-following models, both in how they measure trend and the length of the lookback window, we can often reduce the implied cost of the call option and the dispersion of outcomes.

A backtest of an individual trend-following model can look the best over a given time period, but there are many factors that play into whether that performance will be valid going forward. The assets have to behave similarly, potentially both on an absolute and relative basis, and an investor has to hold the investment for a long enough time to weather short-term underperformance.

A multi-model approach can address both of these.

It will reduce the model specification risk that is present ex-ante. It will not pick the best model, but then again, it will not pick the worst.

From an investor perspective, this diversification reduces the spread of outcomes which can lead to an easier product to hold as a long-term investment. Diversification among the models may not always be present (i.e. when style risk dominates and all trend-following strategies do poorly), but when it is, it reduces the chance of taking on uncompensated risks.

Taking on compensated risks is a necessary part of investing, and in the case of trend-following, the style risk is something we desire. Removing as many uncompensated risks as possible leads to more pure forms of this style risk and strategies that are robust to unfavorable specifications.

Measuring the Benefit of Diversification

By Nathan Faber

On November 5, 2018

In Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

The benefits of diversification are often touted, but many investors feel disappointed in diversified portfolios because of the dispersion in performance of the individual holdings.
In the context of three different unconstrained sleeves, we look at a way to measure and visualize the benefit (or detriment) of diversification based on achieving different objectives.
Through this lens, we get a picture of how good or bad the results might have been, which can lead to confidence either in the robustness of the allocation or in the need to take a different approach.
Since we only experience one path of history, it is difficult to assess the benefit of diversification unless we consider what could have happened.
We believe that taking a systematic approach does not fully remove the art of the analysis but can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

Introduction

Diversification is a standard risk management tool in any portfolio. Reducing the impact of idiosyncratic risks in individual investments by holding a suite of stocks, asset classes, strategies, etc. produces a smoother investment ride most of the time and reduces the risk of negative surprises.

But in a world where we only experience one outcome out of the multitude of possibilities, gauging the benefit of diversification is difficult. It is even hard to do in hindsight, not so much because we can’t but more often that we won’t. The results already happened.

Over a single time period with no rebalancing, a diversified portfolio will underperform the best asset that it holds. This is a mathematical fact when there is any dispersion in the returns of the assets and it is why we have said that diversification will always disappoint. Our natural behavioral tendencies can often get the better of us, despite the fact that diversification might be doing a great job, especially when examined through the appropriate lens and measured in the context of what could have happened.

Last summer, we published a presentation entitled Building an Unconstrained Sleeve. In it, we looked at ways to combine traditional and non-traditional assets and strategies to target specific objectives: equity hedging, absolute return, and equity-like with downside management.

Now that we have 15 months of subsequent data for all the underlying strategies, we want to revisit that piece and explore the benefit of diversification in the context of hindsight.

A Recap of the Process

As a quick refresher, we included seven strategies and asset classes in the construction of our unconstrained sleeves:

Long/flat trend-following equities
Minimum volatility equities
Macro trend-following (managed futures)
Macro risk parity
Macro value
Macro income
Intermediate U.S. Treasuries

While these strategies are surely not exhaustive, they cover a range of factors (value, momentum, low volatility, etc.) and a global set of asset classes (equities, bonds, commodities, and currencies) commonly included in unconstrained sleeves. They were also selected because many of these strategies are conveniently packaged as ETFs or mutual funds, making the resulting sleeves more easily implementable.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees.

Over the 15 months, world equity was by far the best performer and the spread between best-performing and worst-performing positions exceeded 20 percentage points. If you wanted high returns – and going back to our statement about how diversification will always disappoint – you could have just held world equities and been quite content.

But putting ourselves back in June 2017, we did not know a priori that simply holding equities would have generated the highest returns. Looking at this type of chart in November 2008 would have led to a very different emotional conclusion.

The aim of our original study was to develop unconstrained sleeves that would meet their objectives regardless of how the future played out. Therefore, we employed a simulation-based method that aimed to preserve some of the unique correlation structure between the strategies across different market environments and reduce the risk of overfitting to a single realization of history. With this approach, we constructed portfolios that targeted three different objectives that investors might be interested in:

Equity hedge – designed to offset significant equity losses.
Absolute return – designed to create a stable and consistent return stream in all environments.
Equity-like – designed to capture significant equity upside with reduced downside.

(Note: Greater detail about portfolio construction process, strategy descriptions, and performance attributes of each strategy can be found in our original presentation.)

But were our constructed portfolios successful in achieving their objectives out-of-sample? To analyze this question, as well as explore the benefits/detractors of diversification for each objective, we will calculate the distribution of what could have happened. The hope is that, each strategy would perform well relative to all other possible portfolios that could have been chosen for the sleeve.

Saying exactly what portfolios we could have chosen is where a little art comes into play. For example, in the equity-like strategies, it is difficult to say that a 100% bond portfolio would have ever been a viable option and therefore may not be an apt out-of-sample comparison.

However, since our original process did not have any specific override for these intuitive constraints, and since we do not wish to assert after-the-fact which portfolios would have been rejected, we will allow the entire potential allocation space to be fair game in our comparison.

There are a number of ways to sample the set of allocations over the 7 asset classes that could have formed the portfolios for each sleeve. Perhaps the most obvious choice would be to sample uniformly over the possible allocations. The issue to balance in this case is coverage of the space (a 6-dimensional simplex) with the number of samples. To be 95% confident that we sampled an allocation above 95% for only a single asset class would require nearly 200 million samples. We have used modified Sobol sequences in the past to ensure coverage of more of the space with fewer points. However, in the current case, to mimic the rounding that is often found in portfolio allocations, we will use a lattice of points spaced 2.5% apart covering the entire space. This requires just under 10 million points in the simulations.

Equity Hedge

This sleeve was designed to offset significant equity losses by limiting downside capture. The resulting optimized portfolio was relatively concentrated in two main positions that historically have exhibited low-to-negative correlations to equities and exhibited potential crisis alpha during significant and prolonged drawdowns.Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

The down capture this portfolio during the out-of-sample period was 0.44. This result falls in the 70^th percentile (that is, better than 70% of the other sample portfolios and where lower down-capture is better) when compared to the 10 million possible other portfolios we could have originally selected. Not surprisingly, the 100% intermediate-term Treasury portfolio had the best down capture (-0.05) over the out-of-sample. Of the portfolios with better down capture, Intermediate Treasuries and Macro – Income were generally the highest allocations.

This does not come as much of a surprise to anyone who has followed the managed futures space for the last 15 months. The category largely remains in a multi-year drawdown (peaking in early 2014), but it has also done little to offset the rapid sell-offs seen in equities in 2018. Therefore, with the full benefit of hindsight, any allocation to Macro – Trend in the original portfolio would be a detriment realizing our out-of-sample objective.

Yet even with this lackluster performance, an out-of-sample realized 70^th percentile result over a short, 15-month horizon is a result to be pleased with.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees.

Absolute Return

This sleeve was designed to seek a stable and consistent return stream in all market environments. We aimed to accomplish this by utilizing a risk parity approach. As expected, this sleeve holds all asset classes and is very well diversified across them.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

To measure the success of the risk parity over the live period, we will look at the Gini coefficient for each of the ten million potential portfolios we could have initially selected. The Gini coefficient quantifies the equality of the distribution, with a value of 1 representing 100% concentration and 0 representing perfect equality.

The Gini coefficient of the actual portfolio was 0.25 which was in the 99.8^th percentile of possible outcomes (i.e. highly diversified on a relative basis). Here, the percentile estimate is padded by the fact that many of the simulated portfolios (e.g. the 100% ones) would clearly not be close to equal risk contribution.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees.

Did our original portfolio achieve its out-of-sample goal? Here, we can evaluate success as to whether the realized contribution to risk of each exposure was close to equivalent; i.e. did we actually achieve risk parity as desired? We can see below that indeed we did, with the main exception of Macro – Trend, which was the most volatile asset class over the period.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Over the sample space of potential portfolios, the portfolio with the minimum out-of-sample Gini coefficient (0.08) was tilted toward the less volatile and more diversifying asset classes (Intermediate Treasuries and Macro – Income). Even so, due to the limited granularity of the sampled portfolios, the risk contribution of Macro – Income was still half of that for each of the other strategies.

It is also worth noting how similar this solution is – generated with the complete benefit of hindsight – to our originally constructed portfolio.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Equity-like with Downside Management

This sleeve was designed in an effort to capture equity market growth while managing the risk of severe and prolonged drawdowns. It was tilted toward the equity-like exposures with a split among risk management styles (trend, minimum volatility, macro strategies, etc.). The allocation to U.S. Treasuries is very small.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

For this portfolio, we have two variables to analyze: the up capture relative to global equities and the Ulcer index, a measure of the severity and duration of drawdowns. In the construction of the sleeve, the target was to keep the Ulcer index less than 25% of the value for global equities. The joint distribution of these quantities over the live period is shown below with the actual values over the live period for the sleeve indicated.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees.

The realized Ulcer level was 68% of that of world equity – a far cry from the 25% that the portfolio was optimized for – and was in the 42^nd percentile while the up capture of 0.60 was in the 93^rd percentile.

With the explicit goal of achieving a relative Ulcer level, a comparison against the entire potential allocation space of 10 million portfolios is not appropriate. Therefore, we reduce the set of 10 million comparative portfolios to only those that would have given a relative Ulcer index less than 25% compared to world equities, eliminating approximately 40% of possible portfolios.

The distributions of allocations to each of the strategies in the acceptable subset are shown below. We can see that the more diversifying strategies take on a larger range of allocations.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees.

Interestingly, looking only over this subset of the original 10 million portfolios improves the out-of-sample up capture of our originally constructed portfolio to the 99^th percentile but does not change the percentile of the Ulcer index over the live period. Why is this?

The correlation of the relative Ulcer index over the live period with that over the historical period is only 0.1, indicating that the out of sample data did not line up with our expectations at first glance. However, this makes sense when we recall that the optimization was carried out using data from much more extreme market environments (think 2001 and 2008). It is a good reminder that, just because you optimize for a certain parameter value does not mean you will get it over the live data.

Higher up-capture typically goes hand-in-hand with a higher Ulcer index, as higher return often requires bearing more risk. Therefore, one way to standardize our measures across the potential set of portfolios is to calculate the ratio of up-capture to the Ulcer index. With this transformation, the risk-adjusted up capture falls in the 87^th percentile over the set of sample allocations, indicating a very high realized risk-adjusted return.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees.

Conclusion

We only experience one path of the world and do not know the infinite alternate course history could have taken. But it is exactly this infinitude of alternate states that diversification is meant to address.

Diversification generally has no apparent benefit unless we envision what could have happened. Unfortunately our innate natures make this difficult. We do not often value our realized path in this context. After all, none of these alternate states actually happened, so it is difficult to picture what we did not experience.

A quantitative approach can yield a systematic way to evaluate the benefit (or detriment) of diversification. This way, we are not relying as much on intuition – how did our performance feel? – and are looking through a more objective lens at our initial decisions.

In the examples using the Unconstrained Sleeves, diversification focused on more than just returns. The objectives that initially went in to the portfolio construction were the parameters of interest.

Taking a systematic approach does not fully remove the art of the analysis, as was evident in the construction of the potential sample of portfolios used in the comparisons, but having a process can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

The Research Library of Newfound Research

Tag: portfolio construction Page 1 of 2

Is Managed Futures Value-able?

What Is Managed Futures?

Summary

What is Managed Futures?

What is Trend Following?

Using Managed Futures as A Diversifier

Conclusion

APPENDIX A: TREND FOLLOWING AS AN OPTIONS STRADDLE

APPENDIX B: Index Definitions

Diversification with Portable Beta

Summary

Diversification Among Components

Finding the Optimal Blend

Conclusion

Tightening the Uncertain Payout of Trend-Following

Summary

Introduction

Diversification in Trend-Following

The Math Behind the Diversification

An Example: Trend-Following on the S&P 500

Expanding the Multitude of Models

Conclusion

Measuring the Benefit of Diversification

Summary

Introduction

A Recap of the Process

Equity Hedge

Absolute Return

Equity-like with Downside Management

Conclusion

Tag: portfolio construction Page 1 of 2

Is Managed Futures Value-able?

What Is Managed Futures?

Summary

What is Managed Futures?

What is Trend Following?

Using Managed Futures as A Diversifier

Conclusion

APPENDIX A: TREND FOLLOWING AS AN OPTIONS STRADDLE

APPENDIX B: Index Definitions

Diversification with Portable Beta

Summary

Diversification Among Components

Finding the Optimal Blend

Conclusion

Tightening the Uncertain Payout of Trend-Following

Summary­

Introduction

Diversification in Trend-Following

The Math Behind the Diversification

An Example: Trend-Following on the S&P 500

Expanding the Multitude of Models

Conclusion

Measuring the Benefit of Diversification

Summary­

Introduction

A Recap of the Process

Equity Hedge

Absolute Return

Equity-like with Downside Management

Conclusion

Summary

Summary