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Diversifying the What, How, and When of Trend Following

This post is available as a PDF download here.

Summary

  • Naïve and simple long/flat trend following approaches have demonstrated considerable consistency and success in U.S. equities.
  • While there are many benefits to simplicity, an overly simplistic implementation can leave investors naked to unintended risks in the short run.
  • We explore how investors can think about introducing greater diversification across the three axes of what, how, and when in effort to build a more robust tactical solution.

In last week’s commentary – Protect & Participate: Managing Drawdowns with Trend Following – we explored the basics of trend following and how a simple “long/flat” investing approach, when applied to U.S. equities, has historically demonstrated considerable ability to limit extreme drawdowns.

While we always preach the benefits of simplicity, an evaluation of the “long run” can often overshadow many of the short-run risks that can materialize when a model is overly simplistic.  Most strategies look good when plotted over a 100-year period in log-scale and drawn with a fat enough marker.

With trend following in particular, a naïve implementation can introduce uncompensated risk factors that, if left unattended, can lead to performance gremlins.

We should be clear, however, that left unattended, nothing could happen at all.  You could get lucky.  That’s the funny thing about risk: sometimes it does not materialize and correcting for it can actually leave you worse off.

But hope is not a strategy and without a crystal ball at our disposal, we feel that managing uncompensated risks is critical for creating more consistent performance and aligning with investor expectations.

In light of this, the remainder of this commentary will be dedicated to exploring how we can tackle several of the uncompensated risks found in naïve implementations by using the three axes of diversification: what, how, and when. 

The What: Asset Diversification

The first axis of diversification is “what,” which encompasses the question, “what are we allocating across?”

As a tangent, we want to point out that there is a relationship between tactical asset allocation and underlying opportunities to diversify, which we wrote about in a prior commentary Rising Correlations and Tactical Asset Allocation.  The simple take is that when there are more opportunities for diversification, the accuracy hurdle rate that a tactical process has to overcome increases.  While we won’t address that concept explicitly here, we do think it is an important one to keep in mind.

Specifically as it relates to developing a robust trend following strategy, however, what we wish to discuss is “what are we generating signals on?”

A backtest of a naively implemented trend following approach on U.S. equities over the last century has been exceptionally effective.  Perhaps deceivingly so.  Consider the following cumulative excess return results from 12/1969 to present for a 12-1 month time-series momentum strategy.

 

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.  Benchmark is 50% U.S. equity index / 50% risk-free rate.

While the strategy exhibits a considerable amount of consistency, this need not be the case.

Backtests demonstrate that trend following has worked in a variety of international markets “over the long run,” but the realized performance can be much more volatile than we have seen with U.S. equities.  Below we plot the growth of $1 in standard 12-1 month time-series momentum strategies for a handful of randomly selected international equity markets minus their respective benchmark (50% equity / 50% cash).

Note: Things can get a little whacky when working with international markets.  You ultimately have to consider whose perspective you are investing from.  Here, we assumed a U.S. investor that uses U.S. dollar-denominated foreign equity returns and invests in the U.S. risk-free rate.  Note that this does, by construction, conflate currency trends with underlying trends in the equity indices themselves.  We will concede that whether the appropriate measure of trend should be local-currency based or not is debatable.  In this case, we do not think it affects our overall point.

Source: MSCI.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.  Benchmark is 50% respective equity index / 50% U.S. risk-free rate.

The question to ask ourselves, then, is, “Do we believe U.S. equities are special and naive trend following will continue to work exceptionally well, or was U.S. performance an unusual outlier?”

We are rarely inclined to believe that exceptional, outlier performance will continue.  One approach to providing U.S. equity exposure while diversifying our investments is to use the individual sectors that comprise the index itself.  Below we plot the cumulative excess returns of a simple 12-1 time-series momentum strategy applied to a random selection of underlying U.S. equity sectors.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.  Benchmark is 50% respective sector index / 50% U.S. risk-free rate.

While we can see that trend following was successful in generating excess returns, we can also see that when it was successful varies depending upon the sector in question.  For example, Energy (blue) and Telecom (Grey) significantly diverge from one another in the late 1950s / early 1960s as well as in the late 1990s / early 2000s.

If we simply equally allocate across sector strategies, we end up with a cumulative excess return graph that is highly reminiscent of the of the results seen in the naïve U.S. equity strategy, but generated with far more internal diversification.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.

A potential added benefit of this approach is that we are now afforded the flexibility to vary sector weights depending upon our objective.  We could potentially incorporate other factors (e.g. value or momentum), enforce diversification limits, or even re-invest capital from sectors exhibiting negative trends back into those exhibiting positive trends.

The How: Process Diversification

The second axis of diversification is “how”: the process in which decisions are made.  This axis can be a bit of a rabbit hole: it can start with high-level questions such as, “value or momentum?” and then go deeper with, “which value measure are you using?” and then even more nuanced with questions such as, “cross-market or cross-industry measures?”  Anecdotally, the diversification “bang for your buck” decreases as the questions get more nuanced.

With respect to trend following, the obvious question is, “how are you measuring the trend?”

One Signal to Rule Them All?

There are a number of ways investors can implement trend-following signals.  Some popular methods include:

  • Prior total returns (“time-series momentum”)
  • Price-minus-moving-average (e.g. price falls below the 200 day moving average)
  • Moving-average double cross-over (e.g. the 50 day moving average crosses the 200 day moving average)
  • Moving-average change-in-direction (e.g. the 200 day moving average slope turns positive or negative)

One question we often receive is, “is there one approach that is better than another?”  Research over the last decade, however, actually shows that they are highly related approaches.

Bruder, Dao, Richard, and Roncalli (2011) united moving-average-double-crossover strategies and time-series momentum by showing that cross-overs were really just an alternative weighting scheme for returns in time-series momentum.[1] To quote,

“The weighting of each return … forms a triangle, and the biggest weighting is given at the horizon of the smallest moving average. Therefore, depending on the horizon n2 of the shortest moving average, the indicator can be focused toward the current trend (if n2 is small) or toward past trends (if n2 is as large as n1/2 for instance).”

Marshall, Nguyen and Visaltanachoti (2012) proved that time-series momentum is related to moving-average-change-in-direction.[2] In fact, time-series momentum signals will not occur until the moving average changes direction.  Therefore, signals from a price-minus-moving-average strategy are likely to occur before a change in signal from time-series momentum.

Levine and Pedersen (2015) showed that time-series momentum and moving average cross-overs are highly related.[3] It also found that time-series momentum and moving-average cross-over strategies perform similarly across 58 liquid futures and forward contracts.

Beekhuizen and Hallerbach (2015) also linked moving averages with returns, but further explored trend rules with skip periods and the popular MACD rule.[4] Using the implied link of moving averages and returns, it showed that the MACD is as much trend following as it is mean-reversion.

Zakamulin (2015) explored price-minus-moving-average, moving-average-double-crossover, and moving-average-change-of-direction technical trading rules and found that they can be interpreted as the computation of a weighted moving average of momentum rules with different lookback periods.[5]

These studies are important because they help validate the approach of traditional price-based systems (e.g. moving averages) with the growing body of academic literature on time-series momentum.

The other interpretation, however, is that all of the approaches are simply a different way of trying to tap into the same underlying factor.  The realized difference in their results, then, will likely have to do more with the inefficiencies in capturing that factor and which specific environments a given approach may underperform.  For example, below we plot the maximum return difference over rolling 5-year periods between four different trend following approaches: (1) moving-average change-in-direction (12-month), (2) moving-average double-crossover (3-month / 12-month), (3) price-minus-moving-average (12-month), and (4) time-series momentum (12-1 month).

We can see that during certain periods, the spread between approaches can exceed several hundred basis points.  In fact, the long-term average spread was 348 basis points (“bps”) and the median was 306 bps.  What is perhaps more astounding is that no approach was a consistent winner or loser: relative performance was highly time-varying.  In fact, when ranked 1-to-4 based on prior 5-year realized returns, the average long-term ranks of the strategies were 2.09, 2.67, 2.4, and 2.79 respectively, indicating that no strategy was a clear perpetual winner or loser.

 Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Without the ability to forecast which model will do best and when, model choice represents an uncompensated risk that we bear as a manager.  Using multiple methods, then, is likely a prudent course of action.

Identifying the Magic Parameter

The academic and empirical evidence for trend following (and, generally, momentum) tends to support a formation (“lookback”) period of 6-to-12 months.  Often we see moving averages used that align with this time horizon as well.

Intuition is that shorter horizons tend to react to market changes more quickly since new information represents a larger proportion of the data used to derive the signal.  For example, in a 6-month momentum measure a new monthly data point represents 16.6% of the data, whereas it only represents 8.3% of a 12-month moving average.

A longer horizon, therefore, is likely to be more “stable” and therefore less susceptible to whipsaw.

Which particular horizon achieves the best performance, then, will likely be highly regime dependent.  To get a sense of this, we ran six time-series momentum strategies, with look-back periods ranging from 6-months to 12-months.  Again, we plot the spread between the best and worst performing strategies over rolling 5-year periods.

 Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Ignoring the Great Depression for a moment, we can see that 5-year annualized returns between parameterizations frequently deviate by more than 500 bps.  If we dig under the hood, we again see that the optimal parameterization is highly regime dependent.

For example, coming out of the Great Depression, the longer-length strategies seemed to perform best.  From 8/1927 to 12/1934, an 11-1 time-series momentum strategy returned 136% while a 6-1 time-series momentum strategy returned -25%.  Same philosophy; very different performance.

Conversely, from 12/1951 to 12/1971, the 6-1 strategy returned 723% while the 11-1 strategy returned 361%.

Once again, without evidence that we can time our parameter choice, we end up bearing unnecessary parameterization risk, and diversification is a prudent action.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

The When: Timing Luck

Long-time readers of our commentary will be familiar with this topic.  For those unfamiliar, we recommend a quick glance over our commentary Quantifying Timing Luck (specifically, the section What is “Timing Luck”?).

The simple description of the problem is that investment strategies can be affected by the investment opportunities they see at the point at which they rebalance.  For example, if we rebalance our tactical strategies at the end of each month, our results will be subject to what our signals say at that point.  We can easily imagine two scenarios where this might work against us:

  1. Our signals identify no change and we remain invested; the market sells off dramatically over the next month.
  2. The market sells off dramatically prior to our rebalance, causing us to move to cash. After we trade, the market rebounds significantly, causing us to miss out on potential gains.

As it turns out, these are not insignificant risks.  Below we plot four identically managed tactical strategies that each rebalance on a different week of the month.  While one of the strategies turned $1 into $4,139 another turned it into $6,797.  That is not an insignificant difference.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Fortunately, the cure for this problem is simple: diversification.  Instead of picking a week to rebalance on, we can allocate to multiple variations of the strategy, each rebalancing at a different point in time.  One variation may rebalance on the 1st week of the month, another on the 2nd week, et cetera.  This technique is called “overlapping portfolios” or “tranching” and we have proven in past commentaries that it can dramatically reduce the impact that timing luck can have on realized results.

Conclusion

Basic, naïve implementations of long/flat trend following exhibit considerable robustness and consistency over the long run when applied to U.S. equities.  The short run, however, is a different story.  While simple implementations can help ensure that we avoid overfitting our models to historical data, it can also leave us exposed to a number of unintended bets and uncompensated risks.

Instead of adding more complexity, we believe that the simple solution to combat these risks is diversification.

Specifically, we explore diversification across three axes.

The first axis is “what” and represents “what we invest across.”  We saw that while trend following worked well on U.S. equities, the approach had less consistency when applied to international indices.  Instead of presuming that the U.S. represents a unique candidate for this type of strategy, we explored a sector-based implementation that may allow for greater internal diversification.

The second axis is “how” and captures “how we implement the strategy.”  There are a variety of approaches practitioners use to measure and identify trends, and each comes with its own pros and cons.  We explore four popular methods and find that none consistently reigns supreme, indicating once again that diversification of process is likely a prudent approach.

Similarly, when it comes to parameterizing these models, we find that a range of lookback periods are successful in the long run, but have varying performance in the short run.  A prudent solution once again, is diversification.

The final axis is “when” and represents “when we rebalance our portfolio.”  Long-time readers recognize this topic as one we frequently write about: timing luck.  We demonstrate that merely shifting what week of the month we rebalance on can have considerable long-term effects.  Again, as an uncompensated risk, we would argue that it is best diversified away.

While a naïve trend following process is easy to implement, we believe that a robust one requires thinking along the many dimensions of risk and asking ourselves which risks are worth bearing (hopefully those that are compensated) and which risks we should seek to hedge or diversify away.

 


 

[1] Bruder, Benjamin and Dao, Tung-Lam and Richard, Jean-Charles and Roncalli, Thierry, Trend Filtering Methods for Momentum Strategies (December 1, 2011). Available at SSRN: http://ssrn.com/abstract=2289097

[2] Marshall, Ben R. and Nguyen, Nhut H. and Visaltanachoti, Nuttawat, Time-Series Momentum versus Moving Average Trading Rules (December 22, 2014). Available at SSRN: http://ssrn.com/abstract=2225551

[3] Levine, Ari and Pedersen, Lasse Heje, Which Trend Is Your Friend? (May 7, 2015). Financial Analysts Journal, vol. 72, no. 3 (May/June 2016). Available at SSRN: https://ssrn.com/abstract=2603731

[4] Beekhuizen, Paul and Hallerbach, Winfried G., Uncovering Trend Rules (May 11, 2015). Available at SSRN: http://ssrn.com/abstract=2604942

[5] Zakamulin, Valeriy, Market Timing with Moving Averages: Anatomy and Performance of Trading Rules (May 13, 2015). Available at SSRN: http://ssrn.com/abstract=2585056

Protect & Participate: Managing Drawdowns with Trend Following

This post is available as PDF download here.

Summary

  • Trend following is an investment strategy that buys assets exhibiting strong absolute performance and sells assets exhibiting negative absolute performance.
  • Despite its simplistic description, trend following has exhibited considerable empirical robustness as a strategy, having been found to work in equity indices, bonds, commodities, and currencies.
  • A particularly interesting feature about trend following is its potential ability to avoid significant losses. Evidence suggests that trend following approaches can be used as alternative risk management techniques.
  • However, if investors expect to fully participate with asset growth while receiving significant protection, they are likely to be disappointed.
  • Relative to other risk management techniques, even very simple trend following strategies have exhibited very attractive return profiles.

What is Trend Following?

At its core, trend following – also called “absolute” or “time-series” momentum – is a very basic investment thesis: investments exhibiting positive returns tend to keep exhibiting positive returns and those exhibiting negative returns tend to keep exhibiting negative returns.

While the approach may sound woefully simplistic, the empirical and academic evidence that supports it extends back nearly two centuries.  Lempérière, Deremble, Seager, Potters, and Bouchard (2014), for example, test trend following approaches on commodities, currencies, stock indices, and bonds going back to 1800 and find that “the existence of trends [is] one of the most statistically significant anomalies in financial markets.”[1]

While LDSPB (2014) may have one of the longest backtests to date, a variety of other authors have demonstrated the existence of trends, and the success of trend following, in a variety of environments and markets.  We won’t list them here, but for those interested, a more thorough history can be found in our own paper Two Centuries of Momentum.

The driving theory behind trend following is that investor (mis-)behavior causes the emergence of trends.  When new information enters the market, investors underreact due to an anchoring bias that causes them to overweight prior information.  As price begins to drift towards fair value, herding takes over and causes investors to overreact.  This under and subsequent over-reaction is what causes a trend to emerge.

While somewhat contradictory to the notion that investors should not “chase performance” or “time markets,” evidence suggests that when systematically applied, trend following approaches can create a potentially significant return premium and potentially help investors avoid significant losses.

The Basic Trend Following Setup

In our experience, the two most popular methods of implementing a trend following signal are (1) a simple moving average cross-over system and (2) a measure of trailing total return.

In a simple moving average system cross-over system, when price is above the simple moving average, the system stays invested.  When price falls below, the strategy divests (usually into a risk-free asset, like U.S. Treasury Bills).  This sort of “in-or-out” system is often called “long/flat.”  For example, below we show a 12-month simple moving average and highlight when the system would buy and sell based upon when price crosses over.

The second form of trend following is more commonly referred to as “time-series momentum.”  In this approach, prior realized returns are calculated and the signal is generated depending upon whether returns were positive or negative.  For example, a popular academic approach is to use a “12-1” model, which takes the prior 12-month returns and subtracts the most recent month’s return (to avoid short-term mean reversion effects).  If this value is positive, the system invests and if the value is negative, it divests.

By looking at the example graphs, we can see that while these systems are similar, they are not exactly equal.  Nor are they the only way trend following approaches are implemented by practitioners.  What is important here is not the specific methodology, but that these methodologies attempt to capture the same underlying dynamics.

Empirical Evidence: Trend Following in a Crisis

To explore how a simple 12-1 time-series momentum system has worked in the past, we will apply the process to a broad U.S. equity index.  At the end of each month, we will calculate the trend following signal.  If the signal is positive, we will remain invested in the index (i.e. we are “long”).  If the signal is negative, we will divest into U.S. Treasury Bills (i.e. we are “flat”).

To explore the potential risk management capabilities of trend following, we will define a “crisis” as any period over which the broad U.S. equity market suffers a drawdown exceeding 25% from a recent market high.  We will then measure the maximum peak-to-trough drawdown of U.S. equities over the period and compare it to the maximum peak-to-trough drawdown of the 12-1 time series momentum strategy.

Since the early 1900s, we identify eight such scenarios.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not indicative of future returns.  All performance is hypothetical and backtested.  Performance assumes the reinvestment of all distributions.  Returns are gross of all fees, including management fees, transaction costs, and taxes.

A few important takeaways:

  • Trend following is not a risk panacea. Even with trend following applied, drawdowns in excess of 15% occurred in each of these cases.  This is the cost of market participation, which will address a bit later.
  • Trend following did not limit losses in all cases. The market sell-off in October 1987 was so rapid that there was not sufficient time for trends to emerge and the system to be able to exit.  When trend following ends up protecting from quick sell-offs, it is more likely a function of luck than skill.
  • In many cases, trend following did help cut losses significantly. In the bear markets of the 1970s and 2000s, trend following helped reduce realized losses by over 50%.

Of course, the experience of these losses is very different than the summary numbers.  Below we plot the actual returns of equities versus a trend following overlay for several of the scenarios.

 

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not indicative of future returns.  All performance is hypothetical and backtested.  Performance assumes the reinvestment of all distributions.  Returns are gross of all fees, including management fees, transaction costs, and taxes.

We can see that the in many cases, when the trend following system got out, the market subsequently rallied, meaning that a trend follower would have a larger drawdown.  For example, in the Great Depression after the trend following system divested into U.S. Treasury Bills, the equity market rallied significantly.  This left the trend follower with a realized loss of -32% while a buy-and-hold investor would only be down -19%.

It is only with the benefit of hindsight that we can see that markets continued to fall and the patient trend follower was rewarded.

Ex-Ante Expectations About Participation

Of course, protecting capital is only half of the equation.  If we only cared about capital preservation, we could invest in short-term inflation-protected Treasuries and, barring a default by the U.S. government, sleep very well at night.

Before we demonstrate any empirical evidence about trend following’s ability to participate in growth, we want to use one of our favorite exercises – a coin flip game – to help establish reasonable expectations.

Imagine that we approach you with the offer to play a game.  We are going to flip a coin and you are going to try to guess how it lands.  If the coin lands on heads and you guess heads, the game is a push.  If it lands on tails and you guess tails, we give you $1.  If you guess wrong, you give us $1.

Does this sound like a game you would want to play?  Our guess is “no.”

Yet when we talk to many investors about their expectations for trend following strategies, this is the game they have created by choosing the U.S. equity market as a benchmark.

Consider the four scenarios that can happen:

  • The market goes up and trend following participates.
  • The market goes down and trend following goes down.
  • The market goes up and trend following is in cash.
  • The market goes down and trend following is in cash.

In the first scenario, even though trend following got the call right, we created a mental “push.”  In the middle two scenarios, trend following was incorrect and either participates on the downside or fails to participate on the upside (i.e. we “lose”).  It is only in the last scenario that trend following adds value.

In other words, by choosing U.S. equities as our benchmark for a long/flat trend following strategy, the strategy can only add value when the market is going down.  If we believe that the market will go up over the long run, that leaves very few scenarios for trend following to add value and plenty of scenarios for it to be a detractor.

Which is, unsurprisingly, exactly what you see if you plot the growth of a buy-and-hold investor versus a time-series momentum strategy: success in periods of significant market drawdown and relative underperformance in other periods.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not indicative of future returns.  All performance is hypothetical and backtested.  Performance assumes the reinvestment of all distributions.  Returns are gross of all fees, including management fees, transaction costs, and taxes.

We can see, for example, that the trend following strategy lost its entire lead to the buy-and-hold investor from 1942 to 1962.  That is a frustratingly long period of underperformance for any investor to weather.

Determining the appropriate benchmark, however, is often a matter of preference.  We believe the appropriate way to address the problem is by asking whether trend following materially outperforms U.S. equities on a risk-adjusted basis.

To answer this question, we calculate the strategy’s full-period sensitivity to the U.S. equity index (i.e. its “beta”) and then re-create a new index that is comprised of a mixture U.S. equities and U.S. Treasury Bills that shares the same beta.  In this case, that index is 50% U.S. equities and 50% U.S. Treasury Bills.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not indicative of future returns.  All performance is hypothetical and backtested.  Performance assumes the reinvestment of all distributions.  Returns are gross of all fees, including management fees, transaction costs, and taxes.

We can see that compared to a risk-adjusted benchmark, trend following exhibits a significant return premium without necessarily materializing significant excess downside risk.

Our take away from this is simple: investors who expect long/flat trend following strategies to keep up with equities are sure to be disappointed eventually.  However, if we use a benchmark that allows both “in” and “flat” decisions to add value (e.g. a 50% U.S. equity index + 50% U.S. Treasury Bill portfolio), trend following has historically added significant value.

One interpretation may be that trend following may be best suited as a “risk pivot” within the portfolio, rather than as an outright replacement for U.S. equity.  For example, if an investor has a 60% equity and 40% bond portfolio, rather than replacing equity with a trend strategy, the investor could replace a mix of both stocks and bonds.  By taking 10% from stocks and 10% from bonds to give to the trend allocation, the portfolio now has the ability to pivot between a 70/30 and a 50/50.  You can read more about this idea in our whitepaper Achieving Risk Ignition.

Another potential interpretation of this data is that long/flat trend following is a risk management technique and should be compared in light of alternative means of managing risk.

Pre-2008 versus Post-2008 Experience

Unfortunately, many investors have had their expectations for long/flat trend following strategies set by the period leading up to the 2008 financial crisis as well as the crisis itself, only to find themselves disappointed by subsequent performance.

Several years of whipsaws (including 2011, 2015 and 2016) leading to relative underperformance have caused many to ask, “is trend following broken?”

When we evaluate the data, however, we see that it is not the post-2008 period that is unique, but rather the pre-2008 period.

In fact, the pre-2008 period is unique in how calm a market environment it was, with drawdowns rarely eclipsing 10%.  While the post-2008 period has had its calm years (e.g. 2013 and 2017), it has also been punctuated by periods of volatility.  We can see the difference by plotting the drawdowns over the two periods.

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

The unfortunate reality is that the calm period of pre-2008 and the strong performance of trend following in 2008 gave investors the false confidence that trend following had the ability to nearly fully participate on the upside and protect almost entirely on the downside.

Unfortunately, this simply is not true.  As we have said many times in the past, “risk cannot be destroyed, only transformed.”  While trend following tends to do well in environments where trends persist, it does poorly in those periods that exhibit sharp and sudden price reversals.

However, if we compare our trend following system against the more appropriate long-term risk-adjusted benchmark, we still see a significant return premium earned.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not indicative of future returns.  All performance is hypothetical and backtested.  Performance assumes the reinvestment of all distributions.  Returns are gross of all fees, including management fees, transaction costs, and taxes.

One question we may ask ourselves is, “if we are using trend following to manage risk, how did other risk management techniques perform over the same period?”

Annualized Return
(2009 – 2017)
Annualized Volatility
(2009 – 2017)
Maximum Drawdown
(2007 – 2009)
S&P 50014.4%12.0%-52.3%
12-1 TS Momentum11.7%12.3%-10.9%
80/2012.3%9.4%-42.5%
60/4010.1%6.9%-32.0%
CBOE S&P 500 5% Put Protection Index10.2%10.1%-36.6%
Salient Trend Index (Managed Futures)1.2%10.3%-14.3%
Salient Risk Parity Index6.6%8.7%-30.8%
HFRX Global Hedge Fund Index1.5%4.0%-23.4%

Source: Kenneth French Data Library, CSI, Salient, HFRI, CBOE.  Calculations by Newfound Research.  Past performance is not indicative of future returns.  Performance assumes the reinvestment of all distributions.  Returns are gross of all fees, including management fees, transaction costs, and taxes.  60/40 and 80/20 portfolios are mixtures of the SPDR S&P 500 ETF (“SPY”) and iShares Core U.S. Bond ETF (“AGG”) in 60%/40% and 80%/20% proportional allocations, rebalanced annually.

We can see that while trend following has failed to keep up with U.S. equities in the post-crisis period (again, we would expect this), it has kept up much better than other potential risk management alternatives while providing significantly more protection during the crisis period.

Another important takeaway is that during the post crisis period, the trend following strategy had the highest volatility of any of the strategies measured.  In other words, while we might be able to rely on trend following for crisis risk management (i.e. avoiding the large left tail of returns), it is not necessarily going to reduce volatility during a bull market.

Conclusion

As an investment strategy, trend following has a long history of academic and empirical support.  Evidence suggests that trend following can be an effective means of avoiding large negative returns that coincide with traditional bear markets.

However, trend following is not a panacea.  In line with our philosophy that “risk cannot be destroyed, only transformed,” the risk management benefit often seen in trend following strategies comes with higher risks in other environments (i.e. “whipsaw”).

Investors who have relied upon the realized participation of trend following strategies during the pre-crisis period (2003-2007), as well as the protection afforded during the 2008 crisis itself, may have unrealistic expectations for forward performance.  Simply put: long/flat trend following strategies are very likely to underperform the underlying asset during strong bull markets.  In this case, replacing traditional equity exposure with a long/flat trend following strategy will likely lead to long-term underperformance.

However, when compared against other means of risk management, trend following has historically exhibited considerable downside protection for the upside participation it has realized.  Compared to a risk-adjusted benchmark, a long/flat U.S. equity trend following strategy exhibits an annualized excess return of 2.89%.

For investors looking to diversify how they manage risk, we believe the trend following represents a high transparent, and historically effective, alternative.

 


 

[1] https://arxiv.org/pdf/1404.3274.pdf

Thinking in Long/Short Portfolios

This post is available as a PDF download here.

Summary­

  • Few investors hold explicit shorts in their portfolio, but all active investors hold them
  • We (re-)introduce the simple framework of thinking about an active portfolio as a combination of a passive benchmark plus a long/short portfolio.
  • This decomposition provides greater clarity into the often confusing role of terms like active bets, active share, and active risk.
  • We see that while active share defines the quantity of our active exposure, the active bets themselves define the quality.

Ask the average investor if they employ shorting in their portfolios and “no” is likely the answer.

Examine the average portfolio, however, and shorts abound.  Perhaps not explicitly, but certainly implicitly.  But what in the world is an implicit short?

As investors, if we held no particular views about the market, our default position would be a market-capitalization weighted portfolio.  Any deviation from market-capitalization weighted, then, expresses some sort of view (intentional or not).

For example, if we hold a portfolio of 40 blue-chip stocks instead of a total equity market index, we have expressed a view.  That view is in part determined by what we hold, but equally important is what we do not.

In fact, we can capture this view – our active bets ­– by looking at the difference between what we hold in our portfolio and the market-capitalization weighted index.  And we quite literally mean the difference.  If we take the weights of our portfolio and subtract the weights of the index, we will be left with a dollar-neutral long/short portfolio.  The long side will express those positions that we are overweight relative to the index, and the short side will express those positions we are underweight.

Below is a simple example of this idea.

PortfolioBenchmarkImplied Long/Short
Stock A25%50%-25%
Stock B75%50%25%

 

“Dollar-neutral” simply means that the long and short legs will be of notional equal size (e.g. in the above example they are both 25%).

While our portfolio may appear to be long only, in reality it expresses a view that is captured by a long/short portfolio.  As it turns out, our portfolio has an implicit short.

This framework is important because it allows us to go beyond evaluating what we hold and instead evaluate both the bets we are taking and the scale of those bets.  Generically speaking, we can say:

Portfolio = Benchmark + b x Long/Short

Here, the legs of the Long/Short portfolio are assumed to have 100% notional exposure.  Using the example above, this would mean that the long/short is 100% long Stock B, 100% short Stock A, and b is equal to 25%.

This step is important because it allows us to disentangle quantity from quality.  A portfolio that is very overweight AAPL and a portfolio that is slightly overweight AAPL are expressing the same bet: it is simply the magnitude of that bet that is different.

So while the Long/Short portfolio captures our active bets, b measures our active share.  In the context of this framework, it is easy to see that all active share determines is how exposed our portfolio is to our active bets.

We often hear a good deal of confusion about active share.  Is more active share a good thing?  A bad thing?  Should we pay up for active share?  Is active share correlated with alpha?  This framework helps illuminate the answers.

Let’s slightly re-write our equation to more explicitly highlight the difference between our portfolio and the benchmark.

Portfolio – Benchmark = b x Long/Short

This means that the difference in returns between the portfolio and the benchmark will be entirely due to the return generated by the Long/Short portfolio of our active bets and how exposed we are to the active bets.

RPortfolio – RBenchmark = b x RLong/Short

Our expected excess return is then quite easy to think about: it is quite simply the expected return of our active bets (the Long/Short portfolio) scaled by how exposed we are to them (i.e. our active share):

E[RPortfolio – RBenchmark] = b x E[RLong/Short]

Active risk (also known as “tracking error”) also becomes quite easy to conceptualize.  Active risk is simply the standard deviation of differences in returns between our Portfolio and the Benchmark.  Or, as our framework shows us, it is just the volatility of our active bets scaled by how exposed we are to them.

s[RPortfolio – RBenchmark] = b x s[RLong/Short]

We can see that in all of these cases, both our active bets as well as our active share play a critical role.  A higher active share means that the fee we are paying provides us more access to the active bets.  It does not mean, however, that those active bets are necessarily any good.  More is not always better.

Active share simply defines the quantity.  The active bets, expressed in the long/short portfolio, will determine the quality.  That quality is often captured by the Information Ratio, which is the expected excess return of our portfolio versus the benchmark divided by how much tracking error we have to take to generate that return.

IR = E[RPortfolio – RBenchmark] / s[RPortfolio – RBenchmark]

Re-writing these terms, we have:

IR = E[RLong/Short] / s[RLong/Short]

Note that the active share component cancels out.  The information ratio provides us a pure measure of the quality of our active bets and ignores how much exposure our portfolio actually has to those bets.

Both quantity and quality are ultimately important in determining whether the portfolio will be able to overcome the hurdle rate set by the portfolio’s fee.

b x E[RLong/Short] > FeePortfolio – FeeBenchmark

The lower our active share, the higher our expectation for our active bets needs to be to overcome the fee spread.  For example, if the spread in fee between our portfolio and the benchmark is 1% and our active share is just 25%, then we have to believe that our active bets can generate a return in excess of 4% to justify paying the fee spread.  If, however, our active share is 75%, then the return needed falls to 1.33%.

Through this equation we can also understand the implications of fee pressure.  If the cost of the active portfolio and the cost of the benchmark are equivalent, there is zero hurdle rate to overcome.  We would choose active so long as we expect a positive return from our active bets.[1]

However, through its organizational structure and growth, Vanguard has been able to continually lower the fee of the passive benchmark over the last several decades.  All else held equal, this means that the hurdle rate for active managers goes up.

Thus as the cost of passive goes down, active managers must lower their fee in a commensurate manner or boost the quality of their active bets.

Conclusion

For long-only “smart beta” and factor portfolios, we often see a focus on what the portfolio holds.  While this is important, it is only a piece of the overall picture.  Just as important in determining performance relative to a benchmark is what the portfolio does not hold.

In this piece, we explicitly calculate active bets as the difference between the active portfolio and its benchmark.  This framework helps illuminate that our active return will be a function both of the quality of our active bets as well as the quantity of our exposure to them.

Finally, we can see that if our aim is to outperform the benchmark, we must first overcome the fee we are paying.  The ability to overcome that fee will be a function of both quality and quantity.  By scaling the fee by the portfolio’s active share, we can identify the hurdle rate that our active bets must overcome.

[1] More technically, theory tells us we would need a positive marginal expected utility from the investment in the context of our overall portfolio.

Quantifying Timing Luck

This blog post is available as a PDF download here.

Summary­­

  • When two managers implement identical strategies, but merely choose to rebalance on different days, we call variance between their returns “timing luck.”
  • Timing luck can easily be overcome by using a method of overlapping portfolios, but few firms do this in practice.
  • We believe the magnitude of timing luck impact is much larger than most believe, particularly in tactical strategies.
  • We derive a model to estimate the impact of timing luck, using only values that can be easily estimated from portfolios implemented without the overlapping portfolio technique.
  • We find that timing luck looms large in many different types of strategies.

As a pre-emptive warning, this week’s commentary is a math derivation.  We think it is a very relevant derivation – one which we have not seen before – but a derivation nonetheless.  If math is not your thing, this might be one to skip.

If math is your thing: consider this a request for comments.  The derivation here will be rather informal sketch, and we think there are other improvements still lingering.

What is “Timing Luck?”

The basic concept of timing luck is that when we choose to rebalance can have a profound impact on our performance results.  For example, if we rebalance an investment strategy once a month, the choice to rebalance at the end of the month will lead to different performance than had we elected to rebalance mid-month.

We call this performance differential “timing luck,” and we believe it is an overlooked, non-negligible portfolio construction risk.

As an example, consider a simple stock/cash timing model that rebalances monthly, investing in a broad U.S. equity index when its 12-1 month return is positive, and a constant maturity 1-year U.S. Treasury index otherwise.  Depending on which day of the month you choose to rebalance (we will assume 21 variations to represent 21 trading days), your results may be dramatically different.

Source: Kenneth French Data Library, Federal Reserve of St. Louis.  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.

The best performing strategy had an annualized return of 11.1%, while the worst returned just 9.6%.  Compounded over 55 years, and that 150 basis point (“bps”) differential leads to an astounding difference in final wealth.  With a standard deviation between 50-year annualized returns of 0.42%, the 1-year annualized estimate of performance variation due to timing luck is 314bps!

Again, an identical process is employed: the only difference between these results is the choice of what day of the month to rebalance.

That small choice, and the good luck or misfortune it realizes, can easily be the difference between “hired” and “fired.”

Is There a Solution to Timing Luck?

In the past, we have argued that overlapping portfolios can be utilized to minimize the impact of timing luck.  The idea of overlapping portfolios is as follows: given an investment process and a holding period, we can invest across multiple managers that invest utilizing the same process but have offset holding periods.[1]

For example, below each manager has a four time-step holding period, and we utilize four managers to minimize timing luck from a single implementation.

The proof that this approach minimizes timing luck is as follows.

Assume that we have N managers, all following an identical investment process with identical holding period, but whose rebalance points are offset from one another by one period.

Consider that at any point in time, we can define the portfolio of Manager #2 to be the portfolio of Manager #1 plus a dollar-neutral long/short portfolio that captures the differences in holdings between them.  Similarly, Manager #3’s portfolio can be thought of as Manager #2’s portfolio plus a dollar-neutral long/short portfolio.  This continues in a circular manner, where Manager #1’s portfolio can be thought of as Manager #N’s portfolio plus a dollar-neutral long/short.

Given that the managers all follow an identical process, we would expect them to have the same long-term expected return.  Thus, the expected return of the dollar-neutral long/short portfolios is zero.

However, the variance of the dollar-neutral long/short portfolios captures the risk of timing luck.

In allocating capital between the N portfolios, our goal is to minimize timing luck.  Put another way, we want to find the allocation that results in the minimum variance portfolio of the long/short portfolios.  Fortunately, there is a simple, closed form solution for calculating the minimum variance portfolio:

Here, w is our solution (an Nx1 vector of weights), Sigma is the covariance matrix and  is an Nx1 vector of 1s.  To solve this equation, we need the covariance matrix between the long/short portfolios.  Since each portfolio is employing an identical process, we can assume that each of the long/short portfolios should have equal variance.  Without loss of generality, we can assume variances are equal to 1 and replace our covariance matrix, Sigma, with a correlation matrix, C.

The correlations between long/short portfolios will largely depend on the process in question and the amount of overlap between portfolios.  That said, because each manager runs an identical process, we would expect that the long-term correlation between Portfolio #2’s long/short and Portfolio #1’s long/short to be identical to the correlation between Portfolio #3’s long/short and Portfolio #2’s.  Similarly, the correlation between Portfolio #3’s and Portfolio #1’s long/shorts should be the same as the correlation between Portfolio #N’s and Portfolio #2’s.

Following this logic (and remembering the circular nature of the rebalances), we can ignore exact numbers and fill in a correlation matrix using variables:

This correlation matrix has two special properties.  First, being a correlation matrix, it is symmetric.  Second, it is circulant: each row is rotated one element to the right of the preceding row.  A special property of a symmetric circulant matrix is that its inverse – in this case C-1 – is also symmetric circulant.  This property guarantees that C-11 is equal to k1 for some constant k.

Which means we can re-write our minimum variance solution as:

Since the constant  will cancel out, we are left with:

Thus, our optimal solution is an equal-weight allocation to all N portfolios.

Highlighted in gold below, we can see the result of this approach using the same stock/cash example as before.  Specifically, the gold portfolio uses each of the 21 variations as a different sub-portfolio.

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.

While we have a solution for timing luck, a question that lingers is: “how much will timing luck affect my particular strategy?”

The Setup

We assume an active investment strategy with constant portfolio of variance (S2), constant and continuous annualized turnover (T; e.g. 0.5 for 50% annual turnover), and consistent rebalances at discrete frequency (f; e.g. 1/12 for monthly).

We will also assume that the portfolio contains no static components.  This allows us to interpret 100% turnover as meaning that the entire portfolio was turned over, rather than that 50% of the portfolio was turn over twice.

To quantify the magnitude of timing luck, we will calculate the variance of a dollar-neutral, long/short portfolio that is long a discrete implementation (i.e. rebalancing at a fixed interval) of this strategy (D) and short the theoretically optimal infinite overlapping portfolio implementation (M – for “meta”).

As before, the expected return of this long/short is zero, but its variance captures the return differences created by timing luck.

Differences between the Discrete and Continuous Portfolios

The long/short portfolio is defined as (D – M).  However, we would expect the holdings of D to overlap with the holdings of M.  How much overlap will depend on both portfolio turnover and rebalance frequency.

Assume, for a moment, that M does not have infinite overlapping portfolios, but a finite number N, each uniformly spaced across the holding period.

If we assume 100% turnover that is continuous, we would expect that the first overlapping portfolio, implemented at t=1/N, to have (1 – 1/N) percent of its holdings identical to D (i.e. not “turned over”).  On the other hand, the portfolio implemented at t = (N-1)/N will have just 1/N percent of its holdings identical to D.

Thus, we can say that if M contains N discrete overlapping portfolios, we can expect M and D to overlap by:

Which we can reduce,

If we take the limit as N goes to infinity – i.e. we have infinite overlapping portfolios – then we are simply left with:

Thus, the overlap we expect between our discretely implemented portfolio, D, and the portfolio with infinite overlapping portfolios, M, is a simple function of the expected turnover during the holding period.

We can then define our long/short portfolio:

Where Q is the portfolio of holdings in M that are not in D.

We should pause here, for a moment, as this is where our assumption of “no static portfolio elements” becomes relevant.  We defined (1) to be the amount M and D overlap.   Technically, if we allow securities to be sold and then repurchased, (1) represents a lower limit to how much M and D overlap.  As an absurd example, consider a portfolio that creates 100% turnover by buying and selling the same 1% of the portfolio 100 times.  Thus, Q in (6) need not necessarily be unique from D; part of D could be contained in Q.

By assuming that no part of the portfolio is static, we are assuming that over the (very) long run, the average turnover experience over a holding period does not include repurchase of sold securities, and thus (1) is the amount of overlap and D and Q are independent holdings.

This assumption is likely fairer for traditionally active portfolios that focus on security selection, but potentially less realistic for tactical strategies that often sell and re-purchase the same exposure.  More on this later.

Defining,

We can re-write,

Solving for Timing Luck

We can then solve for the variance of the long/short portfolio,

Expanding:

As D and Q both represent viable allocation schemes for the portfolio, we will assume that they share the same long-term portfolio variance, S2.  This assumption may be fair, over the long run, for traditional stock-selection portfolios, but likely less fair for highly tactical portfolios that can meaningfully shift their portfolio risk exposures.

Thus,

Replacing back our definition for a, we are left with:

Or, that the annualized volatility due to timing luck (L) is:

What is Corr(D,Q)?

The least easily interpreted – or calculated – term in our equation is the correlation between our discrete portfolio, D, and the non-overlapping securities found in the infinite overlapping portfolios implementation, Q.

The intuitive interpretation here is that when the securities held in our discrete portfolio are highly correlated to those that are not held but the optimal strategy recommends we hold, then we would expect the difference to have less impact.  On the other hand, if those securities are negatively correlated, then the discrete rebalance choice could lead to significant additional volatility.

Estimating this value, however, may be difficult to do empirically.

One potential answer is to use the intra-portfolio correlation (“IPC”) of an equal-weight portfolio of representative assets or securities.  The intuition here is that we expect each asset to experience, on average, an equivalent amount of turnover due to our assumption that there are no static positions in the portfolio.

Thus, taking the IPC of an equal-weight portfolio of representative securities allows us to express the view that while we do not know which securities will be different at any given point in time, we expect over the long-run that all securities will be “missing” with equal frequency and magnitude, and therefore the IPC is representative of the long-term correlation between D and Q.

Estimating Timing Luck in our Stock/Cash Tactical Strategy

The assumptions required for our estimate of timing luck may work well with traditional security selection portfolios (or, at least, quantitative implementations of factors like value, momentum, defensive etc.), but will it work with tactical portfolios?

Using our prior stock/cash example, let’s estimate the expected magnitude of timing luck.  Using one of the discrete implementations, we estimate that turnover is 67% per year.  Our rebalance frequency is monthly (1/12) and the intra-portfolio correlation between stocks and bonds is assumed to be 0%.  Finally, the long-term volatility of the strategy is about 12.2%.

Using these figures, we estimate:

This is a somewhat disappointing result, as we had calculated prior that the actual timing luck was 314bps.  Our estimate is less than 1/6th of the actual figure!

Part of the problem may be that many of the assumptions we outlined are violated with our example tactical strategy.  We think the bigger problem is that our estimates for these variables, when using a highly tactical strategy, are simply wrong.

In our equation, we assumed that turnover would be continuous.  This is because we are using turnover as a proxy for the decay speed of our alpha signal.

What does this mean?  As an example, value strategies rely on value signals that tend to decay slowly.  When a stock is identified as being a value stock, it tends to stay that way for some time.  Therefore, if you build a portfolio off of these signals, you would expect low turnover.  Momentum signals, on the other hand, tend to decay more quickly.  A stock that is labeled as high momentum this month may no longer be high momentum in three months’ time.  Thus, momentum strategies tend to be high turnover.

This relationship does not necessarily hold for tactical strategies.

In our tactical example, we rebalance monthly because we believe the time-series momentum has a short forecast horizon.  However, with only two assets, the strategy can go years without turnover.  Worse, the same strategy might miss a signal because it is only sampling in a discrete manner and therefore understate true turnover in a continuous framework.

If we were to look at the turnover of a tactical strategy implemented with the same rules but rebalanced daily, we would see a turnover rate over 300%.  This would increase our estimate up to 215bps.  Still well below the realized 314bps, but certainly high enough to raise eyebrows about the impact of timing luck in tactical portfolios not implemented using overlapping portfolios.

We should also remember that timing luck is determined by the difference in holdings between the discrete strategy and the meta strategy.  We had assumed that the portfolios D and Q would have the same volatility, but in a strategy that shifts between stocks and bonds, this most certainly is not the case.  This means that long-run volatility in such a tactical strategy can actually be misleadingly low.

Consider the situation when the tactical strategy goes to cash based upon a short-lived signal; i.e. the meta strategy will not build a significant cash position.  The realized volatility of the strategy will dampen the perceived timing luck, when in reality the volatility difference between the two portfolios is quite large.

In our specific tactical example, we know that when D is stocks, Q is bonds and vice versa.  With this insight, we can re-write equation (10):

Which we can simplify as:

Which is simply just a constant times the variance of a portfolio that is 100% long stocks and -100% short bonds (or vice versa; the variance will be the same).

If we use this equation and the variance of a long/short stock/bond portfolio and our prior estimate of 300% turnover, we get an estimate of timing luck volatility of 191bps.

Note that using this concept, there may be a more generic solution that is possible using some measure of active variance (likely scaled by active share).

Conclusion

In this piece we have demonstrated the potentially massive impact of timing luck, addressed how to solve for it, and derived a model that can be used to estimate the magnitude of timing luck risk in strategies that do not employ an overlapping portfolios technique.

While our derived approach is not perfect – as we saw in its application with our tactical example – we believe it is an important step forward in being able to quantify the potential risk that timing luck creates.

 


 

[1] In reality, we probably wouldn’t hire a different manager to implement the same strategy with different rebalance timing even if we could find such managers. A more feasible solution would be for a single manager to run different sleeves implementing each rebalance iteration.

 

Factor Investing & The Bets You Didn’t Mean to Make

This post is available as a PDF download here.

Summary­­

  • Factor investing seeks to balance specificity with generality: specific enough to have meaning, but general enough to be applied broadly.
  • Diversification is a key tool to managing risk in factor portfolios. Imprecision in the factor definitions means that unintended bets are necessarily introduced.
  • This is especially true as we apply factors across securities that share fewer and fewer common characteristics. Left unmonitored, these unintended bets have the potential to entirely swamp the factor itself.
  • By way of example, we explore a simple value-based country model.
  • While somewhat counter-intuitive, constraints have the potential to lead to more efficient factor exposures.

In quantitative investing, we seek a balance between generality and specificity.  When a model is too specific – designed to have meaning on too few securities or in too few scenarios – we lose our ability to diversify.  When a model is too generic, it loses meaning and forecasting power.

The big quant factors – value, momentum, defensive, carry, and trend – all appear to find this balance: generic enough to be applied broadly, but specific enough to maintain a meaningful signal.

As we argued in our past commentary A Case Against Overweighting International Equity, the imprecision of the factors is a feature, not a bug.  A characteristic like price-to-earnings may never fully capture the specific nuances of each firm, but it can provide a directionally accurate roadmap to relative firm valuations.  We can then leverage diversification to average out the noise.

Without diversification, we are highly subject to the imperfections of the model.  This is why, in the same piece, we argued that making a large regional tilt – e.g. away from U.S. towards foreign developed – may not be prudent: it is a single bet that can take decades to resolve.  If we are to sacrifice diversification in our portfolio, we’ll require a much more accurate model to justify the decision.

Diversification, however, is not just measured by the quantity of bets we take.  If diversification is too naively interpreted, the same imprecision that allows factors to be broadly applied can leave our portfolios subject to the returns of unintended bets.

Value Investing with Countries

If taking a single, large regional tilt is not prudent, perhaps value investing at a country level may better diversify our risks.

One popular way of measuring value is with the Shiller CAPE: a cyclically-smoothed price-to-earnings measure.  In the table below, we list the current CAPE and historical average CAPE for major developed countries.

CAPEMean CAPEEffective Weight
Australia18.517.22.42%
Belgium25.015.40.85%
Canada22.021.43.76%
Denmark36.524.50.73%
France20.921.94.85%
Germany20.620.64.36%
Hong Kong18.218.35.21%
Italy16.822.11.33%
Japan28.943.211.15%
Netherlands23.514.81.45%
Singapore13.922.11.09%
Spain13.418.31.58%
Sweden21.523.01.21%
Switzerland25.921.93.15%
United Kingdom16.515.36.55%
United States30.520.350.30%

Source: StarCapital.de.  Effective weight is market-capitalization weight of each country, normalized to sum to 100%.  Mean CAPE figures use data post-1979 to leverage a common dataset.

While evidence[1] suggests that valuation levels themselves are enough to determine relative valuation among countries, we will first normalize the CAPE ratio by its long-term average to try to account for structural differences in CAPE ratios (e.g. a high growth country may have a higher P/E, a high-risk country may have a lower P/E, et cetera).  Specifically, we will look at the log-difference between the mean CAPE and the current CAPE scores.

Note that we recognize there is plenty to criticize and improve upon here.  Using a normalized valuation metric will mean a country like Japan, which experienced a significant asset bubble, will necessarily look under-valued.  Please do not interpret our use of this model as our advocacy for it: we’re simply using it as an example.

Using this value score, we can compare how over and undervalued each country is relative to each other.  This allows us to focus on the relative cheapness of each investment.  We can then use these relative scores to tilt our market capitalization weights to arrive at a final portfolio.

 

Value ScoreRelative Z-ScoreScaled Z-ScoreScaled Weights
Australia-0.07-0.130.882.31%
Belgium-0.48-1.500.400.37%
Canada-0.030.021.024.15%
Denmark-0.40-1.220.450.36%
France0.050.271.276.65%
Germany0.000.111.115.24%
Hong Kong0.010.131.136.37%
Italy0.271.022.022.92%
Japan0.401.452.4529.59%
Netherlands-0.46-1.430.410.65%
Singapore0.461.652.653.14%
Spain0.311.152.153.68%
Sweden0.070.331.331.75%
Switzerland-0.17-0.450.692.36%
United Kingdom-0.08-0.140.886.22%
United States-0.41-1.250.4524.26%

Source: StarCapital.de.  Calculations by Newfound Research.  “Value Score” is the log-difference between the country’s Mean CAPE and its Current CAPE.  Relative Z-Score is the normalized value score of each country relative to peers.  Scaled Z-Score applies the following function to the Relative Z-Score: (1+x) if x > 0 and 1 / (1+x) if x < 0.  Scaled weights multiply the Scaled Z-Score against the Effective Weights of each country and normalize such that the total weights sum to 100%.

While the Scaled Weights represent a long-only portfolio, what they really capture is the Market Portfolio plus a dollar-neutral long/short factor tilt.

Market Weight+ Long / Short = Scaled Weights
Australia2.42%-0.11%2.31%
Belgium0.85%-0.48%0.37%
Canada3.76%0.39%4.15%
Denmark0.73%-0.37%0.36%
France4.85%1.80%6.65%
Germany4.36%0.88%5.24%
Hong Kong5.21%1.16%6.37%
Italy1.33%1.59%2.92%
Japan11.15%18.44%29.59%
Netherlands1.45%-0.80%0.65%
Singapore1.09%2.05%3.14%
Spain1.58%2.10%3.68%
Sweden1.21%0.54%1.75%
Switzerland3.15%-0.79%2.36%
United Kingdom6.55%-0.33%6.22%
United States50.30%-26.04%24.26%

To understand the characteristics of the tilt we are taking – i.e. the differences we have created from the market portfolio – we need only look at the long/short portfolio.

Unfortunately, this is where our model loses a bit of interpretability.  Since each country is being compared against its own long-term average, looking at the increase or decrease to the aggregate CAPE score is meaningless.  Indeed, it is possible to imagine a scenario whereby this process actually increases the top-level CAPE score of the portfolio, despite taking value tilts (if value, for example, is found in countries that have higher structural CAPE values).  We can, on the other hand, look at the weighted average change to value score: but knowing that we increased our value score by 0.21 has little interpretation.

One way of looking at this data, however, is by trying to translate value scores into return expectations.  For example, Research Affiliates expects CAPE levels to mean-revert to the average level over a 20-year period.[2]  We can use this model to translate our value scores into an annualized return term due to revaluation.  For example, with a current CAPE of 30.5 and a long-term average of 20.3, we would expect a -2.01% annualized drag from revaluation.

By multiplying these return expectations against our long/short portfolio weights, we find that our long/short tilt is expected to create an annualized revaluation premium of +1.05%.

The Unintended Bet

Unfortunately, re-valuation is not the only bet the long/short portfolio is taking.  The CAPE re-valuation is, after all, in local currency terms.  If we look at our long/short portfolio, we can see a very large weight towards Japan.  Not only will we be subject to the local currency returns of Japanese equities, but we will also be subject to fluctuations in the Yen / US Dollar exchange rate.

Therefore, to achieve the re-valuation premium of our long/short portfolio, we will either need to bear the currency risk or hedge it away.

In either case, we can use uncovered interest rate parity to develop an expected return for currency.  The notion behind uncovered interest rate parity is that investors should be indifferent to sovereign interest rates.  In theory, for example, we should expect the same return from investing in a 1-year U.S. Treasury bond that we expect from converting $1 to 1 euro, investing in the 1-year German Bund, and converting back after a year’s time.

Under uncovered interest rate parity, our expectation is that currency change should offset the differential in interest rates.  If a foreign country has a higher interest rate, we should expect that the U.S. dollar should appreciate against the foreign currency.

As a side note, please be aware that this is a highly, highly simplistic model for currency returns.  The historical efficacy of the carry trade clearly demonstrates the weakness of this model.  More complex models will take into account other factors such as relative purchasing power reversion and productivity differentials.

Using this simple model, we can forecast currency returns for each country we are investing in.

FX Rate1-Year RateExpected FX RateCurrency Return
Australia1.2269-0.47%1.2546-2.21%
Belgium1.2269-0.47%1.2546-2.21%
Canada0.80561.17%0.8105-0.60%
Denmark0.1647-0.55%0.1685-2.29%
France1.2269-0.47%1.2546-2.21%
Germany1.2269-0.47%1.2546-2.21%
Hong Kong0.12781.02%0.1288-0.75%
Italy1.2269-0.47%1.2546-2.21%
Japan0.0090-0.13%0.0092-1.88%
Netherlands1.2269-0.47%1.2546-2.21%
Singapore0.75651.35%0.7597-0.42%
Spain1.2269-0.47%1.2546-2.21%
Sweden0.12410.96%0.1251-0.81%
Switzerland1.0338-0.72%1.0598-2.46%
United Kingdom1.37950.43%1.3981-1.33%
United States1.00001.78%1.00000.00%

Source: Investing.com, XE.com.  Euro area yield curve employed for Eurozone countries on the Euro.

Multiplying our long/short weights against the expected currency returns, we find that we have created an expected annualized currency return of -0.45%.

In other words, we should expect that almost 50% of the value premium we intended to generate will be eroded by a currency bet we never intended to make.

One way of dealing with this problem is through portfolio optimization.  Instead of blindly value tilting, we could seek to maximize our value characteristics subject to currency exposure constraints.  With such constraints, what we would likely find is that more tilts would be made within the Eurozone since they share a currency.  Increasing weight to one Eurozone country while simultaneously reducing weight to another can capture their relative value spread while remaining currency neutral.

Of course, currency is not the only unintended bet we might be making.  Blindly tilting with value can lead to time varying betas, sector bets, growth bets, yield bets, and a variety of other factor exposures that we may not actually intend.  The assumption we make by looking at value alone is that these other factors will be independent from value, and that by diversifying both across assets and over time, we can average out their impact.

Left entirely unchecked, however, these unintended bets can lead to unexpected portfolio volatility, and perhaps even ruin.

Conclusion

In past commentaries, we’ve argued that investors should focus on achieving capital efficiency by employing active managers that provide more pure exposure to active views.  It would seem constraints, as we discussed at the end of the last section, might contradict this notion.

Why not simply blend a completely unconstrained, deep value manager with market beta exposure such that the overall deviations are constrained by position limits?

One answer why this might be less efficient is that not all bets are necessarily compensated.  Active risk for the sake of active risk is not the goal: we want to maximize compensated active risk.  As we showed above, a completely unconstrained value manager may introduce a significant amount of unintended tracking error.  While we are forced to bear this risk, we do not expect the manager’s process to actually create benefit from it.

Thus, a more constrained approach may actually provide more efficient exposure.

That is all not to say that unconstrained approaches do not have efficacy: there is plenty of evidence that the blind application of value at the country index level has historically worked.  Rather, the application of value at a global scale might be further enhanced with the management of unintended bets.

 


 

[1] For example, Predicting Stock Market Returns Using the Shiller CAPE (StarCapital Research, January 2016) and Value and Momentum Everywhere (Asness, Moskowitz, and Pedersen, June 2013)

[2] See Research Affiliate’s Equity Methodology for their Asset Allocation tool.

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