Flirting with Models

The Research Library of Newfound Research

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Tranching, Trend, and Mean Reversion

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On April 27, 2020

In Craftsmanship, Momentum, Portfolio Construction, Weekly Commentary

This post is available as a PDF download here.

Summary

  • 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.

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.

 

 

One Hedge to Rule Them All

By

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.

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.

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. 25th to 75th 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.

Diversification with Portable Beta

By

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).

Timing Trend Model Specification with Momentum

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On December 23, 2019

In Craftsmanship, Risk & Style Premia, Trend, Weekly Commentary

A PDF version of this post is available here.

Summary

  • Over the last several years, we have written several research notes demonstrating the potential benefits of diversifying “specification risk.”
  • Specification risk occurs when an investment strategy is overly sensitive to the outcome of a single investment process or parameter choice.
  • Adopting an ensemble approach is akin to creating a virtual fund-of-funds of stylistically similar managers, exhibiting many of the same advantages of traditional multi-manager diversification.
  • In this piece, we briefly explore whether model specification choices can be timed using momentum within the context of a naïve trend strategy.
  • We find little evidence that momentum-based parameter specification leads to meaningful or consistent improvements beyond a naively diversified approach.

Over the last several years, we’ve advocated on numerous occasions for a more holistic view of diversification: one that goes beyond just what we invest in, but also considers how those decisions are made and when they are made.

We believe that this style of thinking can be applied “all the way down” our process.  For example, how-based diversification would advocate for the inclusion of both value and momentum processes, as well as for different approaches to capturing value and momentum.

Unlike correlation-based what diversification, how-based diversification often does little for traditional portfolio risk metrics.  For example, in Is Multi-Manager Diversification Worth It? we demonstrated that within most equity categories, allocating across multiple managers does almost nothing to reduce  portfolio volatility.  It does, however, have a profound impact on the dispersion of terminal wealth that is achieved, often by avoiding manager-specific tail-risks.  In other words, our certainty of achieving a given outcome may be dramatically improved by taking a multi-manager approach.

Ensemble techniques to portfolio construction can be thought of as adopting this same multi-manager approach by creating a set of virtual managers to allocate across.

In late 2018, we wrote two notes that touched upon this:  When Simplicity Met Fragility and What Do Portfolios and Teacups Have in Common?  In both studies we injected a bit of randomness into asset returns to measure the stability of trend-following strategies.  We found that highly simplistic models tended to exhibit significant deviations in results with just slightly modified inputs, suggesting that they are highly fragile.  Increasing diversification across what, how, and when axes led to a significant improvement in outcome stability.

As empirical evidence, we studied the real-time results of the popular Dual Momentum GEM strategy in our piece Fragility Case Study: Dual Momentum GEM, finding that slight deviations in model specification lead to significantly different allocation conclusions and therefore meaningfully different performance results.  This was particularly pronounced over short horizons.

Tying trend-following to option theory, we then demonstrated how an ensemble of trend following models and specifications could be used to increase outcome certainty in Tightening the Uncertain Payout of Trend-Following.

Yet while more diversification appears to make portfolios more consistent in the outcomes they achieve, empirical evidence also suggests that certain specifications can lead to superior results for prolonged periods of time.  For example, slower trend following signals appear to have performed much, much better than fast trend following signals over the last two decades.

One of the benefits of being a quant is that it is easy to create thousands of virtual managers, all of whom may follow the same style (e.g. “trend”) but implement with a different model (e.g. prior total return, price-minus-moving-average, etc) and specification (e.g. 10 month, 200 day, 13 week / 34 week cross, etc).  An ancillary benefit is that it is also easy to re-allocate capital among these virtual managers.

Given this ease, and knowing that certain specifications can go through prolonged periods of out-performance, we might ask: can we time specification choices with momentum?

Timing Trend Specification

In this research note, we will explore whether momentum signals can help us time out specification choices as it relates to a simple long/flat U.S. trend equity strategy.

Using data from the Kenneth French library, our strategy will hold broad U.S. equities when the trend signal is positive and shift to the risk-free asset when trends are negative.  We will develop 1023 different strategies by employing three different models – prior total return, price-minus-moving-average, and dual-moving-average-cross-over – with lookback choices spanning from 20-to-360 days in length.

After constructing the 1023 different strategies, we will then apply a momentum model that ranks the models based upon prior returns and equally-weights our portfolio across the top 10%.  These choices are made daily and implemented with 21 overlapping portfolios to reduce the impact of rebalance timing luck.

It should be noted that because the underlying strategies are only allocating between U.S. equities and a risk-free asset, they can go through prolonged periods where they have identical returns or where more than 10% of models share the highest prior return.  In these cases, we select all models that have returns equal-to-or-greater-than the model identified at the 10th percentile.

Before comparing performance results, we think it is worthwhile to take a quick look under the hood to see whether the momentum-based approach is actually creating meaningful tilts in specification selection.  Below we plot both aggregate model and lookback weights for the 126-day momentum strategy.

Source: Kenneth French Data Library. Calculations by Newfound Research.

We can see that while the model selection remains largely balanced, with the exception of a few periods, the lookback horizon selection is far more volatile.  On average, the strategy preferred intermediate-to-long-term signals (i.e. 181-to-360 day), but we can see intermittent periods where short-term models carried favor.

Did this extra effort generate value, though?  Below we plot the ratio of the momentum strategies’ equity curves versus the naïve diversified approach.

We see little consistency in relative performance and four of the five strategies end up flat-to-worse.  Only the 252-day momentum strategy out-performs by the end of the testing period and this is only due to a stretch of performance from 1950-1964.  In fact, since 1965 the relative performance of the 252-day momentum model has been negative versus the naively diversified approach.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all distributions.

This analysis suggests that naïve, momentum-based specification selection does not appear to have much merit against a diversified approach for our simple trend equity strategy.

The Potential Benefits of Virtual Rebalancing

One potential benefit of an ensemble approach is that rebalancing across virtual managers can generate growth under certain market conditions.  Similar to a strategically rebalanced portfolio, we find that when returns across virtual managers are expected to be similar, consistent rebalancing can harvest excess returns above a buy-and-hold approach.

The trade-off, of course, is that when there is autocorrelation in specification performance, rebalancing creates a drag.   However, given that the evidence above suggests that relative performance between specifications is not persistent, we might expect that continuously rebalancing across our ensemble of virtual managers may actually allow us to harvest returns above and beyond what might be possible with just selecting an individual manager.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all distributions.

Conclusion

In this study, we explored whether we could time model specification choices in a simple trend equity strategy using momentum signals.

Testing different lookback horizons of 21-through-378 days, we found little evidence of meaningful persistence in the returns of different model specifications.  In fact, four of the five momentum models we studied actually under-performed a naïve, diversified.  The one model that did out-perform only seemed to do so due to strong performance realized over the 1950-1964 period, actually relatively under-performing ever since.

While this evidence suggests that timing specification with momentum may not be a fruitful approach, it does suggest that the lack of return persistence may benefit diversification for a second reason: rebalancing.  Indeed, barring any belief that one specification would necessarily do better than another, consistently re-pooling and distributing resources through rebalancing may actually lead to the growth-optimal solution.1 This potentially implies an even higher hurdle rate for specification-timers to overcome.

 

 

Re-specifying the Fama French 3-Factor Model

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On December 16, 2019

In Craftsmanship, Portfolio Construction, Risk & Style Premia, Risk Management, Value, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • The Fama French three-factor model provides a powerful tool for assessing exposures to equity risk premia in investment strategies.
  • In this note, we explore alternative specifications of the value (HML) and size (SMB) factors using price-to-earnings, price-to-cash flow, and dividend yield.
  • Running factor regressions using these alternate specifications on a suite of value ETFs and Newfound’s Systematic Value strategy, lead to a wide array of results, both numerically and directionally.
  • While many investors consider the uncertainty of the parameter estimates from the regression using the three-factor model, most do not consider the uncertainty that comes from the assumption of how you construct the equity factors in the first place.
  • Understanding the additional uncertainty is crucial for manager and investors who must consider what risks they are trying to measure and control by using tools like factor regression and make sure their assumptions align with their goals.

In their 1992 paper, The Cross-Section of Expected Stock Returns, Eugene Fama and Kenneth French outlined their three-factor model to explain stock returns.

While the Capital Asset Pricing Model (CAPM) only describes asset returns in relation to their exposure to the market’s excess return through the stock’s beta and identifies any return beyond that as alpha, Fama and French’s three-factor model reattributed some of that supposed alpha to exposures to a value factor (High-minus-low or HML) based on returns stratified by price-to-book ratios and a size factor (small-minus-big or SMB) based on returns stratified by market capitalization.

This gave investors a tool to judge investment strategies based on the loadings to these risk factors. A manager with a seemingly high alpha may have simply been investing in value and small-cap stocks historically.

The notion of compensated risk premia has also opened the floodgate of many additional factors from other researchers (such as momentum, quality, low beta, etc.) and even two more factors from Fama and French (investment and profitability).

A richer factor universe opens up a wide realm of possibilities for analysis and attribution. However, setting further developments aside and going back to the original three-factor model, we would be remiss if we didn’t dive a bit further into its specification.

At the highest level, we agree with treating “value” and “size” as risk factors, but there is more than one way to skin a factor.

What is “value”?

Fama and French define it using the price-to-book ratio of a stock. This seems legitimate for a broad swath of stocks, especially those that are very capital intensive – such as energy, manufacturing, and financial firms – but what about industries that have structurally lower book values and may have other potential price drivers? For example, a technology company might have significant intangible intellectual property and some utility companies might employ leverage, which decreases their book value substantially.

To determine value in these sectors, we might utilize ratios that account for sales, dividends, or earnings. But then if we analyzed these strategies using the Fama French three-factor model as it is specified, we might misjudge the loading on the value factor.

“Size” seems more straightforward. Companies with low market capitalizations are small. However, when we consider how the size factor is defined based on the value factor, there might even be some differences in SMB using different value metrics.

In this commentary, we will explore what happens when we alter the definition of value for the value factor (and hence the size factor) and see how this affects factor regressions of a sample of value ETFs along with our Systematic Value strategy.

HML Factor Definitions

In the standard version of the Fama French 3-factor model, HML is constructed as a self-financing long/short portfolio using a 2×3 sort on size and value. The investment universe is split in half based on market capitalization and in three parts (30%/40%/30%) based on valuation, in this base case, price-to-book ratio.

Using additional data from the Kenneth French Data Library and the same methodology, we will construct HML factors using sorts based on size and:

  • Price-to-earnings ratios
  • Price-to-cash flow ratios
  • Dividend yields

The common inception date for all the factors is June 1951.

The chart below shows the growth of each of the four value factor portfolios.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all distributions. 

Over the entire time period – and for many shorter time horizons – the standard HML factor using price-to-book does not even have the most attractive returns. Price-to-earnings and price-to-cash flow often beat it out.

On the other hand, the HML factor formed using dividend yields doesn’t look so hot.

One of the reasons behind this is that the small, low dividend yield companies performed much better than the small companies that were ranked poorly by the other value factors. We can see this effect borne out in the SMB chart for each factor, as the SMB factor for dividend yield performed the best.

(Recall that we mentioned previously how the Fama French way of defining the size factor is dependent on which value metric we use.)

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all distributions.

Looking at the statistical significance of each factor through its t-statistic, we can see that Price-to-Earnings and Price-to-Cash Flow yielded higher significance for the HML factor than Price-to-Book. And those two along with Dividend Yield all eclipsed the Price-to-Book construction of the SMB factor.

T-Statistics for HML and SMB Using Various Value Metrics

 Price-to-BookDividend YieldPrice-to-EarningsPrice-to-Cash Flow
HML2.90.03.73.4
SMB1.02.41.61.9

Assuming that we do consider all metrics to be appropriate ways to assess the value of companies, even if possibly under different circumstances, how do different variants of the Fama French three-factor model change for each scenario with regression analysis?

The Impact on Factor Regressions

Using a sample of U.S. value ETFs and our Systematic Value strategy, we plot the loadings for the different versions of HML. The regressions are carried out using the trailing three years of monthly data ending on October 2019.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

For each different specification of HML, the differences in the loading between investments is generally directionally consistent. For instance, DVP has higher loadings than FTA for all forms of HML.

However, sometimes this is not the case.

VLUE looks more attractive than VTV based on price-to-cash flow but not dividend yield. FTA is roughly equivalent to QVAL in terms of loading when price-to-book is used for HML, but it varies wildly when other metrics are used.

The tightest range for the four models for any of the investments is 0.09 (PWV) and the widest is 0.52 (QVAL). When we factor in that these estimates each have their own uncertainty, distinguishing which investment has the better value characteristic is tough. Decisions are commonly made on much smaller differences.

We see similar dispersion in the SMB loadings for the various constructions.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

Many of these values are not statistically significant from zero, so someone who has a thorough understanding of uncertainty in regression would likely not draw a strict comparison between most of these investments.

However, one implication of this is that if a metric is chosen that does ascribe significant size exposure to one of these investments, an investor may make a decision based on not wanting to bear that risk in what they desire to be a large-cap investment.

Can We Blend Our Way Out?

One way we often mitigate model specification risk is by blending a number of models together into one.

By averaging all of our HML and SMB factors, respectively, we arrive at blended factors for the three-factor model.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

All of the investments now have HML loadings in the top of their range of the individual model loadings, and many (FTA, PWV, RPV, SPVU, VTV, and the Systematic Value strategy) have loadings to the blended HML factor that exceed the loadings for all of the individual models.

The opposite is the case for the blended SMB factor: the loadings are in the low-end of the range of the individual model loadings.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees.  Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios.  Returns assume the reinvestment of all distributions.

So which is the correct method?

That’s a good question.

For some investments, it is situation-specific. If a strategy only uses price-to-earnings as its value metric, then putting it up against a three-factor model using the P/E ratio to construct the factors is appropriate for judging the efficacy of harvesting that factor.

However, if we are concerned more generally about the abstract concept of “value”, then the blended model may be the best way to go.

Conclusion

In this study, we have explored the impact of model specification for the value and size factor in the Fama French three-factor model.

We empirically tested this impact by designing a variety of HML and SMB factors based on three additional value metrics (price-to-earnings, price-to-cash flow, and dividend yield). These factors were constructed using the same rules as for the standard method using price-to-book ratios.

Each factor, with the possible exceptions of the dividend yield-based HML, has performance that could make it a legitimate specification for the three-factor model over the time that common data is available.

Running factor regressions using these alternate specifications on a suite of value ETFs and Newfound’s Systematic Value strategy, led to a wide array of results, both numerically and directionally.

While many investors consider the uncertainty of the parameter estimates from the regression using the three-factor model, most do not consider the uncertainty that comes from the assumption of how you construct the equity factors in the first place.

Understanding the additional uncertainty is crucial for decision-making. Managers and investors alike must consider what risks they are trying to measure and control by using tools like factor regression and make sure their assumptions align with their goals.

“Value” is in the eye of the beholder, and blind applications of two different value factors may lead to seeing double conclusions.

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