In past research we have explored the potential benefits of how-based diversification through the lens of pay-off functions.
Specifically, we explored how strategic rebalancing created a concave payoff while momentum / trend-following created a convex payoff. By combining these two approaches, total portfolio payoff became more neutral to the dispersion in return of underlying assets.
We have also spent considerable time exploring when-based diversification through our writing on rebalance timing luck.
To manage rebalance timing luck, we advocate for a tranching methodology that can be best distilled as rebalancing “a little but frequently.”
Herein, we demonstrate that the resulting payoff profile of a tranche-based rebalancing strategy closely resembles that of a portfolio that combines both strategic rebalancing and momentum/trend-following.
While we typically think of tranching as simply a way to de-emphasize the impact of a specific rebalancing date choice, this research suggests that for certain horizons, tranching may also be effective because it naturally introduces momentum/trend-following into the portfolio.
In Payoff Diversification (February 10th, 2020), we explored the idea of combining concave and convex payoff profiles. Specifically, we demonstrated that rebalancing a strategic asset allocation was inherently concave (i.e. mean reversionary) whereas trend-following and momentum was inherently convex. By combining the two approaches together, we could neutralize the implicit payoff profile of our portfolio with respect to performance of the underlying assets.
Source: Newfound Research. Payoff Diversification (February 10th, 2020). 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 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.
The intuition behind why rebalancing is inherently mean-reversionary is fairly simple. Consider a simple 50% stock / 50% bond portfolio. Between rebalances, this allocation will drift based upon the relative performance of stocks and bonds. When we rebalance, to right-size our relative allocations we must sell the asset that has out-performed and buy the one that has under-performed. “Sell your winners and buy your losers” certainly sounds mean-reversionary to us.
In fact, one way to think about a rebalance is as the application of a long/short overlay on your portfolio. For example, if the 50/50 portfolio drifted to a 45/55, we could think about rebalancing as holding the 45/55 and overlaying it with a +5/-5 long/short portfolio. This perspective explicitly expresses the “buy the loser, short the winner” strategy. In other words, we’re actively placing a trade that benefits when future returns between the two assets reverts.
While we may not be actively trying to express a view or forecast about future returns when we rebalance, we should consider the performance implications of our choice based upon whether the relative performance of these two assets continues to expand or contract:
Relative Performance Expands
Relative Performance Contracts
Rebalance
–
+
Do Not Rebalance
+
–
Our argument in Payoff Diversification was that by combining strategic rebalancing and momentum / trend following, we could help neutralize this implicit bet.
What we can also see in the table above, though, is that the simple act of not rebalancing benefits from a continuation of relative returns just as trend/momentum does.
Let’s keep that in the back of our minds and switch gears, for a moment, to portfolio tranching. Frequent readers of our research notes will know we have spent considerable time researching the implications of rebalance timing luck. We won’t go into great detail here, but the research can be broadly summarized as, “when you rebalance your portfolio can have meaningful implications for performance.”
Given the discussion above, why that result holds true follows naturally. If two people hold 60/40 portfolios but rebalance them at different times in the year, their results will diverge based upon the relative performance of stocks and bonds between the rebalance periods.
As a trivial example, consider two 60/40 investors who each rebalance once a year. One chooses to rebalance every March and one chooses to rebalance every September. In 2008, the September investor would have re-upped his allocation to equities only to watch them sell-off for the next six months. The March investor, on the other hand, would have rebalanced earlier that year and her equity allocation would have drifted lower as the 2008 crisis wore on.
Even better, she would rebalance in March 2009, re-upping her equity allocation near the market bottom and almost perfectly timing the performance mean-reversion that would unfold. The September investor, on the other hand, would be underweight equities due to drift at this point.
Below we plot hypothetical drifted equity allocations for these investors over time.
Source: Tiingo. Calculations by Newfound Research.
The implications are that rebalancing can imbed large, albeit unintentional, market-timing bets.
The whole concept of tranching can be summarized with the phrase: “a little but frequently.” In other words, rebalance your portfolio more frequently, but only make small changes. As an example, rather than rebalance once a year, we could rebalance 1/12th of our portfolio every month. If our portfolio had drifted from a 60/40 to a 55/45, rather than rebalancing all the way back, we would just correct 1/12th of the drift, trading to a 55.42/44.58.1
Another way to think about this approach is as a collection of sub-portfolios. For example, if we elected to implement a 12-month tranche, we might think of it as 12 separate sub-portfolios, each of which rebalances every 12 months but does so at the end of a different month (e.g. one rebalances in January, one in February, et cetera).
But why does this approach work? It helps de-emphasize the mean-reversion bet for any given rebalance date. We can see this by constructing the same payoff plots as before for different tranching speeds. The 1-month tranche reflects a full monthly rebalance; a 3-month tranche reflects rebalancing 33.33% of the portfolio; a 6-month tranche reflects rebalancing 16.66% of the portfolio each month; et cetera.
Source: Newfound Research. Payoff Diversification (February 10th, 2020). 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 partially 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.
Note how the concave payoff function appears to “unbend” and the 12-month tranche appears similar in shape to payoff of the 90% strategic rebalance / 10% momentum strategy portfolio we plotted in the introduction.
Why might this be the case? Recall that not rebalancing can be effective so long as there is continuation (i.e. momentum / trend) in the relative performance between stocks and bonds. By allowing our portfolio to drift, our portfolio will naturally tilt itself towards the out-performing asset. Furthermore, drift serves as an interesting amplifier to the momentum signal: the more persistent the relative out-performance, and the larger the relative out-performance in magnitude, the greater the resulting tilt.
While tranching naturally helps reduce rebalance timing luck by de-emphasizing each specific rebalance, we can also see that we may be able to naturally embed momentum into our process.
Conclusion
In portfolio management research, the answer we find is often a reflection of the angle by which a question is asked.
For example, in prior research notes, we have spent considerable time documenting the impact of rebalance timing luck in strategic asset allocation, tactical asset allocation, and factor investing. The simple choice of when, though often overlooked in analysis, can have a significant impact upon realized results. Therefore, in order to de-emphasize the choice of when, we introduce portfolio tranching.
We have also spent a good deal of time discussing the how axis of diversification (i.e. process). Not only have we research this topic through the lens of ensemble techniques, but we have also explored it through the payoff profiles generated by each process. We find that by combining diversifying concave and convex profiles – e.g. mean-reversion and momentum – we can potentially create a return profile that is more robust to different outcomes.
Herein, we found that tranching the rebalance of a strategic asset allocation may, in fact, allow us to naturally embed momentum without having to explicitly introduce a momentum strategy. What we find, then, is that the two topics may not actually be independent avenues of research about when and how. Rather, they may just different ways of exploring how to diversify the impacts of convexity and concavity in portfolio construction.
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.
The bond risk premium is the return that investors earn by investing in longer duration bonds.
While the most common way that investors can access this return stream is through investing in bond portfolios, bonds often significantly de-risk portfolios and scale back returns.
Investors who desire more equity-like risk can tap into the bond risk premium by overlaying bond exposure on top of equities.
Through the use of a leveraged ETP strategy, we construct a long-only bond risk premium factor and investigate its characteristics in terms of rebalance frequency and timing luck.
By balancing the costs of trading with the risk of equity overexposure, investors can incorporate the bond risk premium as a complementary factor exposure to equities without sacrificing return potential from scaling back the overall risk level unnecessarily.
The discussion surrounding factor investing generally pertains to either equity portfolios or bond portfolios in isolation. We can calculate value, momentum, carry, and quality factors for each asset class and invest in the securities that exhibit the best characteristics of each factor or a combination of factors.
There are also ways to use these factors to shift allocations between stocks and bonds (e.g. trend and standardizing based on historical levels). However, we do not typically discuss bonds as their own standalone factor.
The bond risk premium – or term premium – can be thought of as the premium investors earn from holding longer duration bonds as opposed to cash. In a sense, it is a measure of carry. Its theoretical basis is generally seen to be related to macroeconomic factors such as inflation and growth expectations.1
While timing the term premium using factors within bond duration buckets is definitely a possibility, this commentary will focus on the term premium in the context of an equity investor who wants long-term exposure to the factor.
The Term Premium as a Factor
For the term premium, we can take the usual approach and construct a self-financing long/short portfolio of 100% intermediate (7-10 year) U.S. Treasuries that borrows the entire portfolio value at the risk-free rate.
This factor, shown in bold in the chart below, has exhibited a much tamer return profile than common equity factors.
Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
But over the entire time period, its returns have been higher than those of both the Size and Value factors. Its maximum drawdown has been less than 40% of that of the next best factor (Quality), and it is worth acknowledging that its volatility – which is generally correlated to drawdown for highly liquid assets with non-linear payoffs – has also been substantially lower.
The term premium also has exhibited very low correlation with the other equity factors.
Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
A Little Free Lunch
Whether we are treating bonds as factor or not, they are generally the primary way investors seek to diversify equity portfolios.
The problem is that they are also a great way to reduce returns during most market environments through their inherently lower risk.
Anytime that an asset with lower volatility is added to a portfolio, the risk will be reduced. Unless the asset class also has a particularly high Sharpe ratio, maintaining the same level of return is virtually impossible even if risk-adjusted returns are improved.
In a 2016 paper2, Salient broke down this reduction in risk into two components: de-risking and the “free lunch” affect.
The reduction in risk form the free lunch effect is desirable, but the risk reduction from de-risking may or may not be desirable, depending on the investor’s target risk profile.
The following chart shows the volatility breakdown of a range of portfolios of the S&P 500 (IVV) and 7-10 Year U.S. Treasuries (IEF).
Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
Moving from an all equity portfolio to a 50/50 equity reduces the volatility from 14.2% to 7.4%. But only 150 bps of this reduction is from the free lunch effect that stems from the lower correlation between the two assets (-0.18). The remaining 530 bps of volatility reduction is simply due to lower risk.
In this case, annualized returns were dampened from 9.6% to 7.8%. While the Sharpe ratio climbed from 0.49 to 0.70, an investor seeking higher risk would not benefit without the use of leverage.
Despite the strong performance of the term premium factor, risk-seeking investors (e.g. those early in their careers) are generally reluctant to tap into this factor too much because of the de-risking effect.
How do investors who want to bear risk commensurate with equities tap into the bond risk premium without de-risking their portfolio?
One solution is using leveraged ETPs.
Long-Only Term Premium
By taking a 50/50 portfolio of the 2x Levered S&P 500 ETF (SSO) and the 2x Levered 7-10 Year U.S. Treasury ETF (UST), we can construct a portfolio that has 100% equity exposure and 100% of the term premium factor.3
But managing this portfolio takes some care.
Left alone to drift, the allocations can get very far away from their target 50/50, spanning the range from 85/15 to 25/75. Periodic rebalancing is a must.
Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
Of course, now the question is, “How frequently should we rebalance the portfolio?”
This boils down to a balancing act between performance and costs (e.g. ticket charges, tax impacts, operational burden, etc.).
On one hand, we would like to remain as close to the 50/50 allocation as possible to maintain the desired exposure to each asset class. However, this could require a prohibitive amount of trading.
From a performance standpoint, we see improved results with longer holding periods (take note of the y-axes in the following charts; they were scaled to highlight the differences).
Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
The returns do not show a definitive pattern based on rebalance frequency, but the volatility decreases with increasing time between rebalances. This seems like it would point to waiting longer between rebalances, which would be corroborated by a consideration of trading costs.
The issues with waiting longer between the rebalance are twofold:
Waiting longer is essentially a momentum trade. The better performing asset class garners a larger allocation as time progresses. This can be a good thing – especially in hindsight with how well equities have done – but it allows the portfolio to become overexposed to factors that we are not necessarily intending to exploit.
Longer rebalances are more exposed to timing luck. For example, a yearly rebalance may have done well from a performance perspective, but the short-term performance could vary by as much as 50,000 bps between the best performing rebalance month and the worst! The chart below shows the performance of each iteration relative to the median performance of the 12 different monthly rebalance strategies.
Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
As the chart also shows, tranching can help mitigate timing luck. Tranching also gives the returns of the strategies over the range of rebalance frequencies a more discernible pattern, with longer rebalance period strategies exhibiting slightly higher returns due to their higher average equity allocations.
Under the assumption that we can tranche any strategy that we choose, we can now compare only the tranched strategies at different rebalance frequencies to address our concern with taking bets on momentum.
Pausing for a minute, we should be clear that we do not actually know what the true factor construction should be; it is a moving target. We are more concerned with robustness than simply trying to achieve outperformance. So we will compare the strategies to the median performance of the previously monthly offset annual rebalance strategies.
The following charts shows the aggregate risk of short-term performance deviations from this benchmark.
The first one shows the aggregate deviations, both positive and negative, and the second focuses on only the downside deviation (i.e. performance that is worse than the median).4
Both charts support a choice of rebalance frequency somewhere in the range of 3-6 months.
Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
With the rebalance frequency set based on the construction of the factor, the last part is a consideration of costs.
Unfortunately, this is more situation-specific (e.g. what commissions does your platform charge for trades?).
From an asset manager point-of-view, where we can trade with costs proportional to the size of the trade, execute efficiently, and automate much of the operational burden, tranching is our preferred approach.
We also prefer this approach over simply rebalancing back to the static 50/50 allocation more frequently.
In our previous commentary on constructing value portfolios to mitigate timing luck, we described how tranching monthly is a different decision than rebalancing monthly and that tranching frequency and rebalance frequency are distinct decisions.
We see the same effect here where we plot the monthly tranched annually rebalanced strategy (blue line) and the strategy rebalanced back to 50/50 every month (orange line).
Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to manager fees, transaction costs, and taxes. Past performance is not an indicator of future results.
Tranching wins out.
However, since the target for the term premium factor is a 50/50 static allocation, running a simple allocation filter to keep the portfolio weights within a certain tolerance can be a way to implement a more dynamic rebalancing model while reducing costs.
For example, rebalancing when the allocations for SSO and UST we outside a 5% band (i.e. the portfolio was beyond a 55/45 or 45/55) achieved better performance metrics than the monthly rebalanced version with an average of only 3 rebalances per year.
Conclusion
The bond term premium does not have to be reserved for risk-averse investors. Investors desiring portfolios tilted heavily toward equities can also tap into this diversifying return stream as a factor within their portfolio.
Utilizing leveraged ETPs is one way to maintaining exposure to equities while capturing a significant portion of the bond risk premium. However, it requires more oversight than investing in other factors such as value, momentum, and quality, which are typically packaged in easy-to-access ETFs.
If a fixed frequency rebalance approach is used, tranching is an effective way to reduce timing risk, especially when markets are volatile. Aside from tranching, we find that, historically, holding periods between 3 and 6 months yield results close in line with the median rolling short-term performance of the individual strategies. Implementing a methodology like this can reduce the risk of poor luck in choosing the rebalance frequency or starting the strategy at an unfortunate time.
If frequent rebalances – like those seen with tranching – are infeasible, a dynamic schedule based on a drift in allocations is also a possibility.
Leveraged ETPs are often seen as risk trading instruments that are not fit for retail investors who are more focused on buy-and-hold systems. However, given the right risk management, these investment vehicles can be a way for investors to access the bond term premium, getting a larger free lunch, and avoiding undesired de-risking along the way.
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. 
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. 
Tranching, Trend, and Mean Reversion
By Corey Hoffstein
On April 27, 2020
In Craftsmanship, Momentum, Portfolio Construction, Weekly Commentary
This post is available as a PDF download here.
Summary
In Payoff Diversification (February 10th, 2020), we explored the idea of combining concave and convex payoff profiles. Specifically, we demonstrated that rebalancing a strategic asset allocation was inherently concave (i.e. mean reversionary) whereas trend-following and momentum was inherently convex. By combining the two approaches together, we could neutralize the implicit payoff profile of our portfolio with respect to performance of the underlying assets.
Source: Newfound Research. Payoff Diversification (February 10th, 2020). 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 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.
The intuition behind why rebalancing is inherently mean-reversionary is fairly simple. Consider a simple 50% stock / 50% bond portfolio. Between rebalances, this allocation will drift based upon the relative performance of stocks and bonds. When we rebalance, to right-size our relative allocations we must sell the asset that has out-performed and buy the one that has under-performed. “Sell your winners and buy your losers” certainly sounds mean-reversionary to us.
In fact, one way to think about a rebalance is as the application of a long/short overlay on your portfolio. For example, if the 50/50 portfolio drifted to a 45/55, we could think about rebalancing as holding the 45/55 and overlaying it with a +5/-5 long/short portfolio. This perspective explicitly expresses the “buy the loser, short the winner” strategy. In other words, we’re actively placing a trade that benefits when future returns between the two assets reverts.
While we may not be actively trying to express a view or forecast about future returns when we rebalance, we should consider the performance implications of our choice based upon whether the relative performance of these two assets continues to expand or contract:
Relative Performance Expands
Relative Performance Contracts
–
+
+
–
Our argument in Payoff Diversification was that by combining strategic rebalancing and momentum / trend following, we could help neutralize this implicit bet.
What we can also see in the table above, though, is that the simple act of not rebalancing benefits from a continuation of relative returns just as trend/momentum does.
Let’s keep that in the back of our minds and switch gears, for a moment, to portfolio tranching. Frequent readers of our research notes will know we have spent considerable time researching the implications of rebalance timing luck. We won’t go into great detail here, but the research can be broadly summarized as, “when you rebalance your portfolio can have meaningful implications for performance.”
Given the discussion above, why that result holds true follows naturally. If two people hold 60/40 portfolios but rebalance them at different times in the year, their results will diverge based upon the relative performance of stocks and bonds between the rebalance periods.
As a trivial example, consider two 60/40 investors who each rebalance once a year. One chooses to rebalance every March and one chooses to rebalance every September. In 2008, the September investor would have re-upped his allocation to equities only to watch them sell-off for the next six months. The March investor, on the other hand, would have rebalanced earlier that year and her equity allocation would have drifted lower as the 2008 crisis wore on.
Even better, she would rebalance in March 2009, re-upping her equity allocation near the market bottom and almost perfectly timing the performance mean-reversion that would unfold. The September investor, on the other hand, would be underweight equities due to drift at this point.
Below we plot hypothetical drifted equity allocations for these investors over time.
Source: Tiingo. Calculations by Newfound Research.
The implications are that rebalancing can imbed large, albeit unintentional, market-timing bets.
In Rebalance Timing Luck: The Difference between Hired and Fired we derived that the optimal solution for avoiding the impact of these rebalance decisions is portfolio tranching. This is the same solution proposed by Blitz, van der Grient, and van Vliet (2010).
The whole concept of tranching can be summarized with the phrase: “a little but frequently.” In other words, rebalance your portfolio more frequently, but only make small changes. As an example, rather than rebalance once a year, we could rebalance 1/12th of our portfolio every month. If our portfolio had drifted from a 60/40 to a 55/45, rather than rebalancing all the way back, we would just correct 1/12th of the drift, trading to a 55.42/44.58.1
Another way to think about this approach is as a collection of sub-portfolios. For example, if we elected to implement a 12-month tranche, we might think of it as 12 separate sub-portfolios, each of which rebalances every 12 months but does so at the end of a different month (e.g. one rebalances in January, one in February, et cetera).
But why does this approach work? It helps de-emphasize the mean-reversion bet for any given rebalance date. We can see this by constructing the same payoff plots as before for different tranching speeds. The 1-month tranche reflects a full monthly rebalance; a 3-month tranche reflects rebalancing 33.33% of the portfolio; a 6-month tranche reflects rebalancing 16.66% of the portfolio each month; et cetera.
Source: Newfound Research. Payoff Diversification (February 10th, 2020). 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 partially 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.
Note how the concave payoff function appears to “unbend” and the 12-month tranche appears similar in shape to payoff of the 90% strategic rebalance / 10% momentum strategy portfolio we plotted in the introduction.
Why might this be the case? Recall that not rebalancing can be effective so long as there is continuation (i.e. momentum / trend) in the relative performance between stocks and bonds. By allowing our portfolio to drift, our portfolio will naturally tilt itself towards the out-performing asset. Furthermore, drift serves as an interesting amplifier to the momentum signal: the more persistent the relative out-performance, and the larger the relative out-performance in magnitude, the greater the resulting tilt.
While tranching naturally helps reduce rebalance timing luck by de-emphasizing each specific rebalance, we can also see that we may be able to naturally embed momentum into our process.
Conclusion
In portfolio management research, the answer we find is often a reflection of the angle by which a question is asked.
For example, in prior research notes, we have spent considerable time documenting the impact of rebalance timing luck in strategic asset allocation, tactical asset allocation, and factor investing. The simple choice of when, though often overlooked in analysis, can have a significant impact upon realized results. Therefore, in order to de-emphasize the choice of when, we introduce portfolio tranching.
We have also spent a good deal of time discussing the how axis of diversification (i.e. process). Not only have we research this topic through the lens of ensemble techniques, but we have also explored it through the payoff profiles generated by each process. We find that by combining diversifying concave and convex profiles – e.g. mean-reversion and momentum – we can potentially create a return profile that is more robust to different outcomes.
Herein, we found that tranching the rebalance of a strategic asset allocation may, in fact, allow us to naturally embed momentum without having to explicitly introduce a momentum strategy. What we find, then, is that the two topics may not actually be independent avenues of research about when and how. Rather, they may just different ways of exploring how to diversify the impacts of convexity and concavity in portfolio construction.