Flirting with Models™ | The Blog of Newfound Research

One Hedge to Rule Them All

On March 30, 2020

In Craftsmanship, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

About two years ago, we compared and contrasted different approaches to risk managing equity exposure; including fixed income, risk parity, managed futures, tactical equity, and options-based strategies.
Given the recent market events as the world navigates through the COVID-19 crisis, we revisit this analysis to see how these strategies would have fared over the past two years.
We find that all eight strategies studied have continued to successfully reduce risk, with two of the previously underperforming options-based strategies now jumping to the forefront of the pack.
Over time, performance of the risk management strategies still varies significantly both relative to the S&P 500 and compared to the other strategies. Generally, risk-managed strategies tend to behave like insurance, underperforming on the upside and outperforming on the downside.
Diversifying your diversifiers by blending a number of complementary risk-managed strategies together – even at random – can be a powerful method of improving long-term outcomes.

“The primary requirement of historical time is that inly one of the possible alternatives coming at you from the future can be actualized in the present where it will flow into the pat and remain forever after unalterable. You may sometimes have “another chance” and be able to make a different choice in some later present, but this can in no way change the choice you did in fact make in the first instance.”

– Dr. William G. Pollard, Prof. of Physics, Manhattan Project

23 trading days.

In a little over a month, the S&P 500 dropped nearly 35% from all-time highs in a sell-off that was one of the fastest in history. Many investors experienced the largest drawdowns their portfolios had seen since the Financial Crisis.

While the market currently sits in a drawdown closer to 25% (as of the time of this writing), the future remains could take any path. Following the relative calm in the market over the preceding year, we are now living through a historic time with the uncertainty and severity of the growing COVID-19 pandemic and its far-reaching ramifications.

However, as a firm that focuses on managing risk, we are used to not knowing the answers.

In the summer of 2018, we published a piece entitled The State of Risk Management where we examined the historical trade-offs in terms of returns during market downturns versus returns during calm market environments of a variety of risk management methods.

Since that time, especially with the benefit of hindsight, one might argue that risk management was unnecessary until this past month. While the S&P 500 experienced a 19% drawdown in Q4 of 2018, it quickly recovered and went on to post a gain of 32% in 2019, rewarding those who stayed the course (or, better yet, bought the dip).

Source: Tiingo. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions. Data through 3/27/2020.

With the future poised to follow a variety of uncertain paths, we think it is a prudent time to check in on some of the more popular ways to manage risk and see how they are handling the current events.

The Updated Historical Track Record

For risk management, we examine eight strategies that roughly fit into four categories:

Diversification Strategies: strategic 60/40 stock/bond mix¹and risk parity²
Options Strategies: equity collar³, protective put⁴, and put-write⁵,⁶
Equity Strategies: long-only defensive equity that blends a minimum volatility strategy⁷, a quality strategy⁸, and a dividend growth strategy⁹ in equal weights
Trend-Following Strategies: managed futures¹⁰ and tactical equity¹¹

Index data was used prior to fund inception when necessary, and the common inception data is December 1997.

The following charts show the return and risk characteristics of the strategies over the entire historical period. Previously, we had used maximum drawdown as a measure of risk but have now switched to using the ulcer index to quantify both the duration and severity of drawdowns.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.

Relative to when we previously presented these statistics (as of July 2018), the most notable changes are that the 95-100 Collar index and Risk Parity have improved and that Managed Futures moved into the top-performing spot up from the middle of the pack. Trend Equity dropped slightly in the rankings, which is partially attributable to our switching over to using the Newfound Trend Equity Index, which includes exposure to small- and mid-cap companies and invests in cash rather than corporate bonds for the defensive position.

Six of the eight strategies still exhibit strong risk-adjusted performance relative to the S&P over the entire time period.

But as we also showed in 2018, the dispersion in strategy performance is significant.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.

This chart also highlights the current trailing one-year performance for each strategy as of 3/27/2020.

Both the 95-110 Collar and the 5% Put Protection indices are in the top 10% of their historical one-year returns, with the put protection index forging new maximum territory. Trend equity and defensive equity have exhibited returns closer to their median levels, while managed futures, strategic diversification with bonds, and risk parity have had returns above their medians.

When we examine the current market environment, this makes sense. Many options were relatively cheap (i.e. implied volatility was low) heading into and early in February, and the option rollover date was close to when the drawdown began (positive timing luck). Equity trends were also very strong coming out of 2019.

With the sharp reversal in equity prices, option strategies provided a strong static hedge that any investors had been paying premiums for through the previous years of bull market returns.

Trend equity strategies were slower to act as trends took time to reverse before cash was introduced into the portfolio, and managed futures were eventually able to capitalize on short positions and diversification once these trends were established.

Zooming in more granularly, we can see the trade-offs between the hedging performance of each strategy in down markets and the premiums paid through negative returns in up-markets. This chart shows the returns relative to the S&P 500 (SPY). When the lines are increasing (decreasing), the hedge is outperforming (underperforming). A flatter line during periods of calm markets indicates lower premiums if we think of these strategies as insurance policies.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.

All eight strategies have provided hedging in both Q4 2018 and the current downturn. The -95-100 Collar- provided some of the lowest premiums. -Trend Equity- also provided low premiums but had a slower time getting back in the market after the hedging period in 2018.

-Managed Futures- have provided some of the best hedging through both down periods but had the highest premium during the strong market of 2019.

With the continued dispersion in performance, especially with the “new” market crisis, this highlights the importance of diversification.

Diversifying Your Diversifiers

Not every risk management strategy will perfectly hedge every downturn while also having a low cost during up markets.

We see the power of diversifying your diversifiers when we test simple equal-weight blends of the risk management strategies. In our 2018 update, we had used an equal weight blend of all eight strategies and a blend of the six strategies that had historical Sharpe ratios above the S&P 500. This latter selection was admittedly biased with hindsight. The two excluded strategies – the 95-110 Collar and the 5% Put Protection indices – were some of the best performing over the period from August 2018 to March 2020!

Our own biases notwithstanding, we still include both blends for comparison.

Both blends have higher Sharpe ratios than 6 of the 8 individual strategies and higher excess return to ulcer index ratios than all of the eight individual strategies.

This is a very powerful result, indicating that naïve diversification is nearly as good as being able to pick the best individual strategies with perfect foresight.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.

But holding eight – or even six – strategies can be daunting, especially for more aggressive investors who may only want to allocate a small portion of their portfolio to a risk management sleeve.

How much diversification is enough?

The following charts show the distribution of risk-adjusted returns from randomly choosing any number of the 8 strategies and holding them in equal weight.

As is to be expected, the cost of choosing the “wrong” blend of strategies decreases as the number of strategies held increases. The potential benefits initially increase and then back off as the luck of choosing the “right” strategy blend is reduced through holding a greater number of strategies.

Both charts show the distributions converging for the single choice for an 8-strategy portfolio.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.

Even holding 3 or 4 of the eight risk management strategies, chosen at random, leads to robust results, in general, with narrowed bands in the distribution (e.g. 25^th to 75^th percentiles).

Blending strategies from each of the different categories – static diversification, options, equity, and trend-following – can further reduce concentration risk verses selection at random and ensure that a variety of risk factors within the hedging strategies (e.g. interest rates from bonds, volatility from options, beta from equity, and whipsaw from trend-following) are mitigated.

Conclusion

We’ve said it many times before: There is no holy grail when it comes to risk management. While finding the perfect hedge that beats all others in every environment is enticing, it is impossible via the simple fact that risk cannot be destroyed, only transformed.

In an uncertain world where we cannot predict exactly what the next crisis will look like – or even what the current crisis will look like after today – diversifying your diversifiers by combining a number of complementary risk-managed strategies may be a prudent course of action.

We believe that this type of balanced approach has the potential to deliver compelling results over a full market cycle while managing the idiosyncratic risk of any one manager or strategy.

Diversification can also help to increase the odds of an investor sticking with their risk management plan as the short-term performance lows won’t be quite as low as they would be with a single strategy (conversely, the highs won’t be as high either).

Developing a plan and sticking with it is the most important first step in risk management. It is obviously desirable to keep premiums in strong markets as low as possible while having efficient hedges in down markets, but simple diversification can go a long way to provide a robust results.

Risk management is, by definition, required to be in place before risks are realized. Even when the market is currently down, risks in the future are still present. Therefore, we must periodically ask ourselves, “What risks are we willing to bear?”

One potential path has been locked into history, but the next time potential risks become reality – and they inevitably will – we must be comfortable with our answer.

Why Trend Models Diverge

By Corey Hoffstein

On March 9, 2020

In Risk & Style Premia, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

During the week of February 23^rd, the S&P 500 fell more than 10%.
After a prolonged bullish period in equities, this tumultuous decline caused many trend-following signals to turn negative.
As we would expect, short-term signals across a variety of models turned negative. However, we also saw that price-minus-moving-average models turned negative across a broad horizon of lookbacks where the same was not true for other models.
In this brief research note, we aim to explain why common trend-following models are actually mathematically linked to one another and differ mainly in how they place weight on recent versus prior price changes.
We find that price-minus-moving-average models place the greatest weight on the most recent price changes, whereas models like time-series momentum place equal-weight across their lookback horizon.

In a market note we sent out last weekend, the following graphic was embedded:

What this table intends to capture is the percentage of trend signals that are on for a given model and lookback horizon (i.e. speed) on U.S. equities. The point we were trying to establish was that despite a very bearish week, trend models remained largely mixed. For frequent readers of our commentaries, it should come as no surprise that we were attempting to highlight the potential specification risks of selecting just one trend model to implement with (especially when coupled with timing luck!).

But there is a potentially interesting second lesson to learn here which is a bit more academic. Why does it look like the price-minus (i.e. price-minus-moving-average) models turned off, the time series momentum models partially turned off, and the cross-over (i.e. dual-moving-average-cross) signals largely remained positive?

While this note will be short, it will be somewhat technical. Therefore, we’ll spoil the ending: these signals are all mathematically linked.

They can all be decomposed into a weighted average of prior log-returns and the primary difference between the signals is the weighting concentration. The price-minus model front-weights, the time-series model equal weights, and the cross-over model tends to back-weight (largely dependent upon the length of the two moving averages). Thus, we would expect a price-minus model to react more quickly to large, recent changes.

If you want the gist of the results, just jump to the section The Weight of Prior Evidence, which provides graphical evidence of these weighting schemes.

Before we begin, we want to acknowledge that absolutely nothing in this note is novel. We are, by in large, simply re-stating work pioneered by Bruder, Dao, Richard, and Roncalli (2011); Marshall, Nguyen and Visaltanachoti (2012); Levine and Pedersen (2015); Beekhuizen and Hallerbach (2015); and Zakamulin (2015).

Decomposing Time-Series Momentum

We will begin by decomposing a time-series momentum value, which we will define as:

We will begin with a simple substitution:

Which implies that:

Simply put, time-series momentum puts equal weight on all the past price changes¹ that occur.

Decomposing Dual-Moving-Average-Crossover

We define the dual-moving-average-crossover as:

We assume m is less than n (i.e. the first moving average is “faster” than the second). Then, re-writing:

Here, we can make a cheeky transformation where we add and subtract the current price, P_t:

What we find is that the double-moving-average-crossover value is the difference in two weighted averages of time-series momentum values.

Decomposing Price-Minus-Moving-Average

This decomposition is trivial given the dual-moving-average-crossover. Simply,

The Weight of Prior Evidence

We have now shown that these decompositions are all mathematically related. Just as importantly, we have shown that all three methods are simply re-weighting schemes of prior price changes. To gain a sense of how past returns are weighted to generate a current signal, we can plot normalized weightings for different hypothetical models.

For TSMOM, we can easily see that shorter lookback models apply more weight on less data and therefore are likely to react faster to recent price changes.
PMAC models apply weight in a linear, declining fashion, with the most weight applied to the most recent price changes. What is interesting is that PMAC(50) puts far more weight on recent prices changes than the TSMOM(50) model does. For equivalent lookback periods, then, we would expect PMAC to react much more quickly. This is precisely why we saw PMAC models turn off in the most recent sell-off when other models did not: they are much more front-weighted.
DMAC models create a hump-shaped weighting profile, with increasing weight applied up until the length of the shorter lookback period, and then descending weight thereafter. If we wanted to, we could even create a back-weighted model, as we have with the DMAC(150, 200) example. In practice, it is common to see that m is approximately equal to n/4 (e.g. DMAC(50, 200)). Such a model underweights the most recent information relative to slightly less recent information.

Conclusion

In this brief research note, we demonstrated that common trend-following signals – namely time-series momentum, price-minus-moving-average, and dual-moving-average-crossover – are mathematically linked to one another. We find that prior price changes are the building blocks of each signal, with the primary differences being how those prior price changes are weighted.

Time-series momentum signals equally-weight prior price changes; price-minus-moving-average models tend to forward-weight prior price changes; and dual-moving-average-crossovers create a hump-like weighting function. The choice of which model to employ, then, expresses a view as to the relative importance we want to place on recent versus past price changes.

These results align with the trend signal changes seen over the past week during the rapid sell-off in the S&P 500. Price-minus-moving-average models appeared to turn negative much faster than time-series momentum or dual-moving-average-crossover signals.

By decomposing these models into their most basic and shared form, we again highlight the potential specification risks that can arise from electing to employ just one model. This is particularly true if an investor selects just one of these models without realizing the implicit choice they have made about the relative importance they would like to place on recent versus past returns.

Ensembles and Rebalancing

By Corey Hoffstein

On February 24, 2020

In Portfolio Construction, Weekly Commentary

This post is available as a PDF download here.

Summary

While rebalancing studies typically focus on the combination of different asset classes, we evaluate a combination of two naïve trend-following strategies.
As expected, we find that a rebalanced fixed-mix of the two strategies generates a concave payoff profile.
More interestingly, deriving the optimal blend of the two strategies allows the rebalanced portfolio to out-perform either of the two underlying strategies.
While most rebalancing literature has focused on the benefits of combining asset classes, we believe this literature can be trivially extended to ensembles of strategies.

Two weeks ago, we wrote about the idea of payoff diversification. The notion is fairly trivial, though we find it is often overlooked. Put simply, any and all trading decisions – even something as trivial as rebalancing – create a “payoff profile.” These profiles often fall into two categories: concave strategies that do well in stable environments is maintained and convex strategies that do better in the tails.

For example, we saw that rebalancing a 60/40 stock/bond portfolio earned a premium against a buy-and-hold approach when the spread between stock and bond returns remained narrow. Conversely, when the spread in return between stocks and bonds was wide, rebalancing created a drag on returns. This is a fairly trivial and obvious conclusion, but we believe it is important for investors to understand these impacts and why payoff is a meaningful axis of diversification.

In our prior study, we compared two different approaches to investing: strategic rebalancing and momentum investing. In this (very brief) study, we want to demonstrate that these results are also applicable when applied to different variations of the same strategy.

Specifically, we will look at two long/short trend following strategies applied to broad U.S. equities. When trend signals are positive, the strategy will be long U.S. equities and short the risk-free rate; when trend signals are negative the strategy will be short U.S. equities and long the risk-free rate. We will use a simple time-series momentum signal. The first model (“21D”) will evaluate trailing 21-day returns and hold for 1 day and the second model (“168D”) will evaluate trailing 168-day returns and holds for 14 days (with 14 overlapping portfolios).¹ Both strategies implement a full skip day before allocating and assuming implementation at closing prices.

Source: Kenneth French Data Library. Calculations by Newfound Research. 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. Past performance is not indicative of future results.

So, what happens if we create a portfolio that holds both of these strategies, allocating 50% of our capital to each? Readers of our prior note will likely be able to guess the answer easily: we create a concave payoff profile that depends upon the relative performance between the two strategies. How, specifically, that concave shape manifests will be path dependent, but will also depend upon the rebalance frequency. For example, below we plot the payoff profiles for the 50/50 blend rebalanced weekly and monthly.

Source: Kenneth French Data Library. Calculations by Newfound Research. 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. Past performance is not indicative of future results.

If we stop thinking of these as two strategies applied to the same asset and just think of them as two assets, the results are fairly standard and intuitive. What is potentially appealing, however, is that the same literature and research that applies to the potential to create a rebalancing premium between assets can apply to a portfolio of strategies (whether a combination of distinct strategies, such as value and momentum, or an ensemble of the same strategy).

Below, we plot the annualized return of weekly rebalanced portfolios with different fixed-mix allocations to the 21D and 168D strategies. We can see that the curve peaks at approximately 45%, suggesting that a 45% allocation to the 21D strategy and a 55% allocation to the 168D strategy actually maximizes the compound annualized growth rate of the portfolio.

If we follow the process of Dubikovsky and Susinno (2017)² to derive the optimal blend of these two assets – using the benefit of hindsight to measure their annualized returns (7.28% and 7.61% respectively), volatility (17.55% and 17.97% respectively), and correlation (0.1318) – we derive an optimal weight of 45.33%.

Perhaps somewhat surprisingly, even if the correlation between these two strategies was 0.9, the optimal blend would still recommend about 10% to the 21D variation. And, as extreme as it may seem, even if the annualized return of the 21D strategy was just 5.36% – a full 225 basis points below the 168D strategy – the optimal blend would still recommend about 10%. Diversification can create interesting opportunities to harvest return; at least, in expectation.

And, as we would expect, if we have no view as to a difference in return or volatility between the two specifications, we would end up with a recommended allocation of 50% to each.

Conclusion

While most studies on rebalancing consider the potential benefits of combining assets, we believe that these benefits are trivially extended to strategies. Not just different strategies, however, but even strategies of the same style.

In this brief note, we explore the payoff profile created by combining two naïve long/short trend following strategies applied to broad U.S. equities. Unsurprisingly, rebalancing a simple mixture of the two specifications creates a concave payoff that generally profits when the spread between the two strategies is narrow and loses when the spread is wide.

More interestingly, however, we demonstrate that by rebalancing a fixed-mix of the two strategies, we can generate a return that is greater than either strategy individually. We believe that this potential benefit of ensemble approaches has been mostly overlooked by existing literature and deserves further analysis.

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).

Payoff Diversification

By Corey Hoffstein

On February 10, 2020

In Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

At Newfound, we adopt a holistic view of diversification that encompasses not only what we invest in, but also how and when we make those investment decisions.
In this three-dimensional perspective, what is correlation-based, how is payoff-based, and when is opportunity-based.
In this piece, we provide an example of what we mean by payoff-based diversification, using a simple strategically rebalanced portfolio and a naïve momentum strategy.
We find that the strategically rebalanced portfolio exhibits a payoff structure that is concave in nature whereas the momentum-based approach exhibits a convex profile.
By combining the two approaches – being careful in how we size positions – we can develop a portfolio that is less sensitive to the co-movement of underlying assets.

At Newfound, we embrace a holistic view of diversification that covers not just what we invest in, but also how and when we make those decisions. What is the diversification most investors are well-versed in and covers traditional, correlation-based diversification between securities, assets, macroeconomic factors, and geographic regions.

We identify when as “opportunity diversification” because it captures the opportunities that are available when we make investment decisions. This often goes overlooked in public markets (which is why we spend so much time writing about rebalance timing luck) but is well acknowledged in private markets where investors often allocate to multiple fund “vintages” to create diversification.

How is generally easy to understand, but sometimes difficult to visualize. We call it “payoff diversification” to acknowledge that when viewed through he appropriate lens, every investment style creates a particular shape. For example, when the return of a call option is plotted against the return of the underlying security, it generates a hockey-stick-like payoff profile.

In this short research note, we are going to demonstrate the payoff profiles of a strategically allocated portfolio and a naïve momentum strategy. We will then show that by combining these two approaches we can create a portfolio that exhibits significantly less sensitivity to the co-movement of underlying assets.

The Payoff Profile of a Strategic Portfolio

Few investors consider a strategically allocated portfolio to be an active strategy. And it isn’t; at least not until we introduce rebalancing. Once we institute a process to systematically returning our drifted weights back to their original fixed mix, we create a strategy and a corresponding payoff profile.

But what does this payoff profile look like? As an example, consider a U.S. 60/40 portfolio comprised of broad U.S. equities and a constant maturity 10-year U.S. Treasury index. If equities out-perform bonds, our equity allocation will increase and our bond allocation will decrease. If equities continue to out-perform bonds, we will benefit relative to our original policy weights. Similarly, if equities under-perform bonds, then our relative equity allocation will decrease. Again, should they continue to underperform, we are well positioned.

However, if we were to rebalance back to our original 60/40 allocation, we would eliminate the opportunity to benefit from the continuation of the relative performance.

On the other hand, consider the case where equities out-perform, our relative allocation to equities increases due to drift, and then equities subsequently under-perform. Now allowing drift has hurt us and we would have been better off rebalancing.

We can visualize this relationship by plotting the return spread between stocks and bonds (x-axis) versus the return spread between a monthly-rebalanced portfolio and a buy-and-hold (drifted) approach (y-axis) over rolling 1-year periods.

Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. 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. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The rebalanced variation is rebalanced at the end of each month whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming 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. Past performance is not indicative of future results.

What we can see is a concave payoff function. When equities significantly out-perform bonds (far right side of the graph), the rebalanced portfolio under-performs the drifted portfolio. Similarly, when bonds significantly out-perform equities (far left side of the graph), the rebalanced portfolio under-performs the drifted portfolio. When the return spread between stocks and bonds is small– a case likely to be more indicative of mean-reversion than positive autocorrelation in the spread – we can see that rebalancing actually generates a positive return versus the drifted portfolio.

Those versed in options will note that this payoff looks incredibly similar to a 1-year strangle sold on the spread between stocks and bonds and struck at 0%. The seller captures the premium when the realized spread remains small but loses money when the spread is more extreme.

The Payoff Profile of Naïve Momentum Following

We can now take the exact same approach to evaluating the payoff profile of a naïve momentum strategy. Each month, the strategy will simply invest in either stocks or bonds based upon whichever had the highest trailing 12-month return

As this approach is explicitly trying to capture auto-correlation in the return spread between stocks and bonds, we would expect to see almost mirror behavior to the payoff profile we saw with strategic rebalancing.

Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. 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. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The momentum portfolio is rebalanced monthly and selects the asset with the highest prior 12-month returns whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming 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. Past performance is not indicative of future results.

While the profile may not be as tidy as before, we can see a convex payoff profile that tends to profit when the return spread is more extreme and lose money when the spread is narrow. Again, those familiar with options will recognize this as similar to the payoff of a 1-year straddle based upon the return spread between stocks and bonds. The buyer pays a premium but captures the spread when it is extreme.

Note, however, the scale of the y-axis. Whereas the payoff profile for the rebalanced portfolio was between -3.0% and +2.0%, the payoff profile for this momentum approach is much larger, ranging between -30.0% and 40.0%.

Creating Payoff Diversification

We have seen that whether we strategically rebalance or adopt a momentum-based approach, both approaches create a payoff profile that is sensitive to the return spread in underlying assets. But what if we do not want to take such a specific payoff bet? One simple answer is diversification.

If we allocate to both the strategically rebalanced portfolio and the naïve momentum portfolio, we will realize both their payoff profiles simultaneously. As their profiles are close mirrors of one another, we may be able to achieve a more neutral outcome.

We have to be careful, however, as to size the allocations appropriate. Recall that the payoff profile of the strategically rebalanced portfolio was approximately 1/10^th the size of the naïve momentum strategy. For both profiles to contribute equally, we would want to allocate approximately 90% of our capital to the strategic rebalancing strategy and 10% of our capital to the momentum strategy.

Below we plot the payoff structure of such a mix.

Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. 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. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The mixed portfolio is rebalanced monthly and is a 90% allocation to a rebalanced 60/40 and a 10% allocation to a naïve momentum strategy; whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming 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. Past performance is not indicative of future results.

We can see that diversifying how we make decisions results in a payoff structure that is far more neutral to the co-movement of underlying securities in the portfolio. The holy grail, of course, is not just to find strategies whose combination neutralizes sensitivity to the spread in returns, but actually creates a higher likelihood of positive outcomes in all environments.

Conclusion

In this research note, we aimed to provide greater insight into the idea of payoff diversification, the how in our what-how-when diversification framework. To do so, we explored two simple examples: a strategically rebalanced 60/40 allocation and a naïve momentum strategy.

We found that the strategically rebalanced portfolio generates a payoff profile that is convex with respect to the spread in returns between stocks and bonds. In general, the larger the spread, the more likely that rebalancing generates a negative return versus a buy-and-hold approach. Conversely, the smaller the spread, the more likely that rebalancing generates a positive return.

The naïve momentum strategy – which simply bought the asset with the greatest prior 12-month returns – exhibited a convex profile. When the return spread between stocks and bonds was large, the naïve momentum strategy was more likely to out-perform buy-and-hold. Conversely, when the return spread was small, the naïve momentum strategy tended to under-perform.

Importantly, the magnitudes of the payoffs are significantly different, with the naïve momentum strategy generating returns nearly 10x larger than strategic rebalancing in the tails. This difference has important implications for strategy sizing, and we find a portfolio mixture of 90% strategic rebalancing and 10% naïve momentum does a reasonably good job of neutralizing portfolio payoff sensitivity to the spread in stock and bond returns.