Category: Weekly Commentary Page 15 of 21

Diversifying the What, How, and When of Trend Following

On April 2, 2018

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

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.

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.

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.

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.

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.

**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:

Our signals identify no change and we remain invested; the market sells off dramatically over the next month.
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.

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 1^st week of the month, another on the 2^nd 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

By Corey Hoffstein

On March 26, 2018

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

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.

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.

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.

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.

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 500	14.4%	12.0%	-52.3%
12-1 TS Momentum	11.7%	12.3%	-10.9%
80/20	12.3%	9.4%	-42.5%
60/40	10.1%	6.9%	-32.0%
CBOE S&P 500 5% Put Protection Index	10.2%	10.1%	-36.6%
Salient Trend Index (Managed Futures)	1.2%	10.3%	-14.3%
Salient Risk Parity Index	6.6%	8.7%	-30.8%
HFRX Global Hedge Fund Index	1.5%	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

You Are Not a Monte-Carlo Simulation

By Corey Hoffstein

On March 19, 2018

In Sequence Risk, Weekly Commentary

This commentary is available as a PDF download here.

Summary

Even when an investment has a positive expected average growth rate, the experience of most individuals may be catastrophic.
By focusing on the compound average growth rate, we can see the median realizations – which account for risk – are often more crucial decision points than ensemble averages, which are the focal point of Monte Carlo analysis.
These arguments also provide a simple explanation for investor behavior that avoids the need for utility theory concepts that have been used for the past 200+ years.
Since we can neither average our results with other investors nor average our results with potential copies of ourselves in infinite states of the world, the best we can do is try to average over time.
Because we all live in a multi-period world where we have a single investment portfolio that compounds over time, managing risk can help us maximize our long-term growth rate even if it seems foolish in hindsight.

Pretend we come to you offering a new investment strategy. Each week, you earn 0.65% (such that over a year you earn 40%), but there is a 1-in-200 chance that you lose -95%. Would you invest?

If we simulate out a single trial, we can see that within a year, we may lose most of our money.

Of course, just because things went wrong in our singular example does not mean that this is necessarily a bad investment. In fact, if we evaluate the prospects of this investment by looking at the average experience, we end up with something far more attractive (the “Ensemble,” which is essentially a Monte-Carlo simulation of the strategy).

The math here is simple: 99.5% of the time we make 1.0065x our money and 0.5% of the time, we end up with 0.05x our money. On average, then, we end up with 1.0017x, or 1.092x annualized. While the average experience is not the 40% annualized we sought, the 9.2% return after a year is still nothing to scoff at.

Of course, the average is not actually achievable. There are not infinite variations of this investment strategy for you to allocate your capital across, nor, we suspect, do you have access to infinite versions of you living in parallel universes who can pool their risk.

Rather, you are forced to diversify your risk over time. Here we end up with a different picture.

Another series of unfortunate events?

Not so fast. You see, when we move to diversifying over time, we need to look at a time-weighted average. It is not the arithmetic mean we are after, but rather the geometric mean which will account for the effects of compounding. Calculating the geometric mean – 1.0065^99.5% x 0.05^0.5% – leaves us with a value of 0.9915, i.e. our wealth is expected to decay over time.

Wait.

How is it possible that on average the strategy is a winner if each and every path is expected to decay over time?

The simple answer: A few fortunate outliers make up for all decaying paths.

The slightly more complex answer: In this investment, our wealth can never go below $0 but we can theoretically make an infinite amount of money. Thus, over time, the average is dragged up.

The Misleading Mean

In many cases, the average experience can be entirely misleading for the experience you can expect. In the world of bell-curves and normal distributions, we typically expect experiences to be clustered around the average. For example, there are more people close to the average height than there are far away.

However, when other distributions apply, the average can be unlikely. Wealth distribution is a perfect example of this. In 2013 in the United States, the top 10% of families held 76% of the wealth while the bottom 50% held 1%. Using 2017 figures, if we divided net worth among the U.S. population – i.e. the “average” household wealth – it would come out to around $760,000 per family. The bottom 50%, however, have a net worth closer to $11,000 per family.

In other words, if you pick a random person off the street, their experience is likely much closer to $11,000 than $760,000. It’s the wealthy outliers that are pulling the average up.

A more applicable metric, in this case, might be the median, which will say, “50% of experiences are below this level and 50% are above.”

The Role of Risk

As it turns out, the median is important for those of us diversifying over time as well. If we consider our hypothetical investment strategy above, our intuition is that the median result is probably not great. Eventually, it feels like, everyone goes practically bankrupt. If we plot the median result, we see almost exactly that.

(As a side note, if you’re wondering why the median result exhibits a sawtooth pattern rather than the smoother results of the mean, the answer is the median is the actual result that sits at the 50^th percentile. Knowing that the probability of losing 95% of our wealth is 1-in-200, it takes time for enough individuals to experience a poor result for the median to drop.)

In fact, if we model investment wealth as a Geometric Brownian Motion (a commonly used stochastic process for modeling stock prices), then over the long run an investor’s compound growth rate approaches the median, not the mean.[1] The important difference between the two is that while volatility does not affect the expected level of wealth, it does drive the mean and median further apart. In fact, the median growth rate is the mean growth rate minus half the volatility squared (which you might recognize as being the common approximation for – drum roll please – the geometric growth rate).

In other words: volatility matters.

Most investors we speak with have an intuitive grasp of this concept. They know that when you lose 10% of your wealth, you need to gain 11.11% back to get to break even.

And when you lose 50%, and you need to earn 100% to get back to break even. Under compound results, feeling twice the pain from losses than the pleasure from gain makes complete sense. There are no individual and independent trials: results have consequences.

This is why taking less risk can actually lead to greater growth in wealth in the long run. If we take too little risk, we will will not participate, but too much risk can lead to ruin. For example, below we plot final wealth results after a 50% drop in market value and a 100% recovery depending on your capture ratio.

As an example of reading this graph, if we start with $1 and experience a 50% loss and a 100% gain, but are only 50% exposed to each of those movements (i.e. we lose 25% and then gain 50%), we end up with $1.125. At the far right of the graph, we can see that at 2x exposure, the first 50% move completely wipes out our capital.

Common Sense Utility Theory

What economists have found, however, is that even if we offer our investment as a one-off event – where the expected return is definitively positive – most would still forego it. To resolve this conundrum, economists have proposed utility theory.

The argument is that investors do not actually try to maximize their expected change in wealth, but rather try to maximize the expected utility of that change. The earliest formalization of this concept was in a paper written by Daniel Bernoulli in 1738, where he proposed a mathematical function that would correct the expected return to account for risk aversion.

Bernoulli’s originally proposed function was log-utility. And under log-utility, our investment strategy offering is no longer appealing: log(1.0065) x 99.5% + log(0.05) x 0.50% is a negative value. What’s interesting about log utility is that, due to the property of logarithms, it ends up creating the identical decision axiom as had we used our compound growth rate model.

log(1.0065) x 99.5% + log(0.05) x 0.50% = log(1.0065^99.5%) + log(0.05^0.5%) = log(1.0065^99.5% x 0.05^0.5%)

So while utility theory is supposed to correct for behavioral foibles like “risk aversion,” what it really does is take a single-period bet and turn it into a multi-period, compound bet.

Under the context of multi-period, compounding results, “risk aversion” is not so foolish. If we have our arm mauled off by a lion on the African veldt, we cannot simply “average” our experience with others in the tribe and end up with 97% of an arm. We cannot “average” our experience across the infinite universes of other potential outcomes where we were not necessarily mauled. Rather, our state is permanently altered for life.

Similarly, if we lose 50% of our money, we cannot just “average” our results with other investors. Nor can we average our results with all the potential infinite alternate universes where we did not lose 50%. The best we can do is try to average over time, which means that our compound growth rate matters. And, as we demonstrated above, so does risk.

Conclusion

Ex-post, managing risk can often feel foolish. Almost exactly 9 years after the bottom of the 2008-2009 bear market, the S&P 500 has returned more than 380%. Asset class, geographic, and process diversification largely proved foolish relative to simple buy-and-hold.

Ex-ante, however, few would forgo risk management. Ask yourself this: would you sell everything today to buy only U.S. large-cap stocks? If not, then there is little to regret about not having done it in the past. While the narratives we spin often make realized results seem obvious in hindsight, the reality is that our collective crystal balls were just as cloudy back then as they are today.

Few lament that their house did not burn down when they buy fire insurance. We buy insurance “in case,” not because we want the risk to materialize.

We all live in a multi-period world where we have a single investment portfolio that compounds over time. In such a world, risk matters tremendously. A single, large loss can take us permanently off plan. Even small losses can put us off course when compounded in a streak of bad luck. While a focus on risk aversion may seem foolish in hindsight when risk does not materialize, going forward we know that managing risk can help us maximize our long-term growth rate.

[1] Derivations for this result can be found in our commentary Growth Optimal Portfolios

Thinking in Long/Short Portfolios

By Corey Hoffstein

On March 5, 2018

In Risk & Style Premia, Risk Management, Weekly Commentary

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.

	Portfolio	Benchmark	Implied Long/Short
Stock A	25%	50%	-25%
Stock B	75%	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.

R_Portfolio – R_Benchmark = b x R_Long/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[R_Portfolio – R_Benchmark] = b x E[R_Long/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[R_Portfolio – R_Benchmark] = b x s[R_Long/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[R_Portfolio – R_Benchmark] / s[R_Portfolio – R_Benchmark]

Re-writing these terms, we have:

IR = E[R_Long/Short] / s[R_Long/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[R_Long/Short] > Fee_Portfolio – Fee_Benchmark

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.

Should You Dollar-Cost Average?

By Nathan Faber

On February 12, 2018

In Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary

Dollar-cost averaging (DCA) versus lump sum investing (LSI) is often a difficult decision fraught with emotion.
The historical and theoretical evidence contradicts the notion that DCA leads to better results from a return perspective, and only some measures of risk point to benefits in DCA.
Rather than holding cash while implementing DCA, employing a risk managed strategy can lead to better DCA performance even in a muted growth environment.
Ultimately, the best solution is the one that gets an investor into an appropriate portfolio, encourages them to stay on track for their long term financial goals, and appropriately manages any behavioral consequences along the way.

Dollar-cost averaging (DCA) is the process of investing equal amounts into an asset or a portfolio over a period of time at regular intervals. It is commonly thought of as a way to reduce the risk of investing at the worst possible time and seeing your investment immediately decline in value.

The most familiar form of dollar-cost averaging is regular investment directed toward retirement accounts. A fixed amount is deducted from each paycheck and typically invested within a 401(k) or IRA. When the securities in the account decline in value, more shares are purchased with the cash, and over the long run, the expectation is to invest at a favorable average price.

For this type of dollar-cost averaging, there is not a lot of input on the investor’s part; the cash is invested as it arrives. The process is involuntary once it is initiated.

A slightly different scenario for dollar-cost averaging happens when an investor has a lump sum to invest: the choice is to either invest it at once (“lump-sum investing”; LSI) or spread the investment over a specified time horizon using DCA.

In this case, the investor has options, and in this commentary we will explore some of the arguments for and against DCA with a lump sum with the intention of reducing timing risk in the market.

The Historical Case Against Dollar-Cost Averaging

Despite the conventional wisdom that DCA is a prudent idea, investors certainly have sacrificed a fair amount of return potential by doing it historically.

In their 2012 paper entitle Dollar-Cost Averaging Just Means Taking Risk Later[1], Vanguard looked at LSI versus DCA in the U.S., U.K., and Australia over rolling 10-year periods and found that for a 60/40 portfolio, LSI outperformed DCA about 2/3 of the time in each market.

If we assume that a lump sum is invested in the S&P 500 in equal monthly amounts over 12-months with the remaining balance held in cash earning the risk-free interest rate, we see a similar result over the period from 1926 to 2017.

Why does dollar-cost averaging look so bad?

In our previous commentary on Misattributing Bad Behavior[2], we discussed how the difference between investment return – equivalent to LSI – and investor return – equivalent to DCA – is partly due to the fact that investors are often making contributions in times of positive market returns. Over this 92 year period from 1926 to 2017, the market has had positive returns over 74% of the rolling 12-month periods. Holding cash and investing at a later date means forgoing some of these positive returns. From a theoretical basis, this opportunity cost is the equity risk premium: the expected excess return of equities over cash.

In our current example where investors voluntarily choose to dollar-cost average, the same effect is experienced.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The average outperformance of the LSI strategy was 4.1%, and as expected, there is a strong correlation between how well the market does over the year and the benefit of LSI.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

Surely DCA Worked Somewhere

If the high equity market returns in the U.S., and as the Vanguard piece showed in the U.K. and Australia, were the force behind the attractiveness of lump sum investing, let’s turn to a market where returns were not so strong: Japan. As of the end of 2017, the MSCI Japan index was nearing its high water mark set at the end of 1989: a drawdown of 38 years.

Under the same analysis, using the International Monetary Fund’s (IMF) Japanese discount rate as a proxy for the risk-free rate in Japan, DCA only outperforms LSI slightly more than half of the time over the period from 1970 to 2017.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

Truncating the time frame to begin in 1989 penalizes DCA even more – perhaps surprisingly, given the negligible average return – with it now outperforming slightly under 50% of the time.

Over the entire time period, there is a similar relationship to the outperformance of LSI versus the performance of the Japanese equity index.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The Truth About Dollar-Cost Averaging

Given this empirical evidence, why is dollar-cost averaging still frequently touted as a superior investing strategy?

The claims – many of which come from media outlets – that dollar-cost averaging is predominantly beneficial from a return perspective are false. It nearly always sacrifices returns, and many examples highlighted in these articles paint pictures of hypothetical scenarios that, while grim, are very isolated and/or unrealistic given the historical data.

Moving beyond the empirical evidence, dollar-cost averaging is theoretically sub-optimal to lump sum investing in terms of expected return.

This was shown to be the case in a mean-variance framework in 1979 by George Constantinides.[6]

His argument was that rather than committing to a set investment schedule based on the initial information in the market, adopting a more flexible approach that adjusts the investment amount based on subsequent market information will outperform DCA.

In the years since, many other hypotheses have been put forward for why DCA should be beneficial – different investor utility functions, prospect theory, and mean reversion in equity returns, among others – and most have been shown to be inadequate to justify DCA.

More recently, Hayley (2012)[7] explains the flaw in many of the DCA arguments based on a cognitive error in assuming that the purchase at a lower average price increases the expected returns.

His argument is that since purchasing at the average price requires buying equal share amounts each period, you can only invest the total capital at the true average price of a security or portfolio with perfect foreknowledge of how the price will move. This leads to a lower average purchase price for DCA compared to this equal share investing strategy.

But if you had perfect foreknowledge of the future prices, you would not choose to invest equal share amounts in the first place!

Thus, the equal share investing plan is a straw man comparison for DCA.

We can see this more clearly when we actually dive into examples that are similar to ones generally presented in favor of DCA.

We will call the equal share strategy that invests the entire capital amount, ES Hypothetical. This is the strategy that uses the knowledge of the price evolution. The more realistic equal share investing strategy assumes that prices will remain fixed and purchases the same shares in each period as the DCA strategy purchases in the first period. The strategy is called ES Actual. Any remaining capital is invested in the final period regardless of whether it purchases more or fewer shares than desired, but the results would still hold if this amount were considered to still be held as cash (possibly borrowed if need be) since the analysis ends at this time step.

The following tables show the final account values for 4 simple market scenarios:

Downtrend
Uptrend
Down then up
Up then down

In every scenario, the DCA strategy purchases shares at a lower average cost than the ES Hypothetical strategy and ends up better off, but the true comparison is less clear cut.

The ES Actual and LSI strategies’ average purchase prices and final values may be higher or lower than DCA.

A Comparison of DCA to Equal Share Investing and LSI

Calculations by Newfound Research. All examples are hypothetical.

A More General Comparison of LSI and DCA

In these examples, DCA does outperform LSI half the time, but these examples are extremely contrived.

We can turn to simulations to get a better feel for how often LSI will outperform DCA and by how much under more realistic assumptions of asset price movements.

Using Monte Carlo, we can see how often LSI outperforms DCA for a variety of expected excess returns and volatilities over 12-month periods. Using expected excess returns allows us to neglect the return on cash.

For any positive expected return, LSI is expected to outperform more frequently at all volatility levels. The frequency increases as volatility decreases for a given expected return.

If the expected annual return is negative, then DCA outperforms more frequently.

Calculations by Newfound Research. Results assume Geometric Brownian Motion using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

Turning now to the actual amount of outperformance, we see a worse picture for DCA.

For more volatile assets, the expected outperformance is in LSI’s favor even at negative expected returns. This is the case despite what we saw before about DCA outperforming more frequently for these scenarios.

As interest rates increase, DCA will benefit assuming that the expected return on equities remains the same (i.e. the expected excess return decreases). However, even if we assume that the cash account could generate an extra 200 bps, which is generous given that this would imply that cash rates were near 4%, for the 15% volatility and 5% expected excess return case, this would still mean that LSI would be expected to outperform DCA by 100 bps.

What About Risk?

It is clear that DCA does not generally outperform LSI from a pure return point-of-view, but what about when risk is factored in? After all, part of the reason DCA is so popular is because it is said to reduce the risk of investing at the worst possible time.

Under the same Monte Carlo setup, we can use the ulcer index to quantify this risk. The ulcer index measures the duration and severity of the drawdowns experienced in an investment, where a lower ulcer index value implies fewer and less severe drawdowns.

The chart below shows the median ratio of the LSI ulcer index and the DCA ulcer index. We plot the ratio to better compare the relative riskiness of each strategy.

As we would expect, since the DCA strategy linearly moves from cash to an investment, the LSI scheme takes on about twice the drawdown risk in many markets.

When the lump sum is invested, the whole investment is subject to the mercy of the market, but if DCA is used, the market exposure is only at its maximum in the last month.[8]

The illustration of this risk alone may be enough to convince investors that DCA meets its objective of smoothing out investment returns. However, at what cost?

Combining the expected outperformance and the risk embodied in the ulcer index shows that LSI is still expected to outperform on a risk adjusted basis between about 35% and 45% of the time.

While this is lower than it was from a pure return perspective, it should be taken with a grain of salt.

First, we know from the start that LSI will be more exposed to drawdowns. One possible solution would be treat a ratio of ulcer indices of 2 (instead of 1) as the base case.

Second, for an investor who is not checking their account monthly, the ulcer index may not mean much. If you only looked at the account value at the beginning and end of the year regardless of whether you did DCA or LSI, then LSI is generally expected to leave the account better off; the intermediate noise does not get “experienced.”

When Can DCA Work?

So now that we have shown that DCA is empirically and theoretically suboptimal to LSI , why might you still want to do it?

First, we believe there is still a risk reduction argument that makes sense when accounting for investor behavior. Most research has focused on risk in the form of volatility. We showed previously that focusing more on drawdown risk can lead to better risk-adjusted performance of DCA.

We could also look at the gain-to-pain ratio, defined here as the average outperformance divided by the average underperformance of the LSI strategy.

The following chart shows a sampling of asset classes expected returns and volatilities from Research Affiliates with indifference boundaries for different gain-to-pain ratios. Indifferences boundaries show the returns and volatilities with constant gain-to-pain ratios. For a given gain-to-pain ratio (e.g. 1.5 means that you will only accept the risk in LSI if its outperformance over DCA is 50% higher, on average), any asset class points that fall below that line are good candidates for DCA.

The table below shows which asset classes correspond to each region on the chart.

Source: Research Affiliates. Calculations by Newfound Research. Results assume Geometric Brownian Motion using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

As the indifference coefficient increases, the benefit of DCA from a gain-to-pain perspective becomes less. For volatile asset classes with lower expected returns (e.g. U.S. equities and long-term U.S. Treasuries), DCA may make sense. For less volatile assets like income focused funds and assets with higher expected growth like EM equities, LSI may be the route to pursue.

A second reason for using DCA is that there are also some market environments that are actually favorable to DCA. As we saw previously, down-trending markets lead to better absolute performance for DCA and volatility makes DCA more attractive from a drawdown risk perspective even in markets with positive expected returns.

Sideways markets are also good for DCA. So are markets that have a set final return.[9] The more volatility the better for DCA in these scenarios.

The chart below shows the return level below which DCA is favored. If you are convinced that the market will return less than -0.6% this year, then DCA is expected to outperform LSI.

Calculations by Newfound Research. Results assume Brownian Bridges using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

While a set final return may be an unrealistic hope – who knows where the market will be a year from now? – it allows us to translate beliefs for market returns into an investing plan with DCA or LSI.

However, even though the current high-valuation environment has historically low expected returns for stocks and bonds, the returns over the next year may vary widely. The appeal of DCA may be stronger in this environment even though it is sub-optimal to LSI.

Instead of using DCA on its own as a risk management tool – one that may sacrifice too much of the return to be had – we can pair it with other risk management techniques to improve its odds of outperforming LSI.

Finding a DCA Middle Ground

One of the primary drags on DCA performance is the fact that much of the capital is sitting in cash for most of the time.

Is there a way to reduce this cost of waiting to invest?

One initial alternative to cash is to hold the capital in bonds. This is in line with the intuitive notion of beginning in a low risk profile and moving gradually to a higher one. While this improves the frequency of outperformance of DCA historically, it does little to improve the expected outperformance.

Another option is to utilize a risk managed sleeve that is designed to protect capital during market declines and participate in market growth. Using a simple tactical strategy that holds stocks when they are above their 10-month SMA and bonds otherwise illustrates this point, boosting the frequency of outperformance for DCA from 32% to 71%.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The tactical strategy narrows the distribution of expected outperformance much more than bonds.

Since we know that the tactical strategy did well over this historical period with the benefit of hindsight, we can also look at how it would have done if returns on stocks and bonds were scaled down to match the current expectations from Research Affiliates.[10]

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The frequency of outperformance is still in favor of the tactical strategy, and the distribution of outperformance exhibits trends similar to using the actual historical data.

Going back to the Japanese market example, we also see improvement in DCA using the tactical strategy. The benefit was smaller than in the U.S, but it was enough to make both the frequency and expected outperformance swing in favor of DCA, even for the period from 1989 to 2017.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results. Data from 1970 to 2017.

Deploying cash immediately into a risk-managed solution does not destroy the risk of DCA underperforming if it uses cash. The cost of using this method is that a tactical strategy can be exposed to whipsaw.

One way to mitigate the cost of whipsaw is to use a more diversified (in terms of process and assets) risk management sleeve.

Conclusion

Dollar-cost averaging verses lump sum investing is often a difficult decision fraught with emotion. Losing 10% of an investment right off the bat can be a hard pill to swallow. However, the case against DCA is backed up by empirical evidence and many theoretical arguments.

If a portfolio is deemed optimal based on an investor’s risk preferences and tolerances, then anything else would be suboptimal. But what is optimal on paper is not always the best for an investor who cannot stick with the plan.

Because of this, there are times when DCA can be beneficial. Certain measures of risk that account for drawdowns or the asymmetric psychological impacts of gains and losses point to some benefits for DCA over LSI.

Given that even in this low expected return market environment, the expected return on cash is still less than that on equities and bonds, deploying cash in a risk-managed solution or a strategy that has higher expected returns for the amount of risk it takes may be a better holding place for cash while implementing a DCA scheme.

It is important to move beyond a myopic view, commonly witnessed in the market, that DCA is best for every situation. Even though LSI may feel like market timing, DCA is simply another form of market timing. With relatively small balances, DCA can also increase commission costs and possibly requires more oversight or leads to higher temptation to check in on a portfolio, resulting in rash decisions.

Ultimately, the best solution is the one that gets an investor into an appropriate portfolio, encourages them to stay on track for their long term financial goals, and appropriately manages any behavioral consequences along the way.

[1] https://personal.vanguard.com/pdf/s315.pdf

[2] https://blog.thinknewfound.com/2017/02/misattributing-bad-behavior/

[3] A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy, https://faculty.chicagobooth.edu/george.constantinides/documents/JFQA_1979.pdf

[4] Dollar-Cost Averaging: The Role of Cognitive Error, https://www.cass.city.ac.uk/__data/assets/pdf_file/0008/128384/Dollar-Cost-Averaging-09052012.pdf

[5] This is a form of sequence risk. In DCA, the initial returns on the investment do not have the same impact as the final period returns.

[6] Milevsky, Moshe A. and Posner, Steven E., A Continuous-Time Re-Examination of the Inefficiency of Dollar-Cost Averaging (January 1999). SSBFIN-9901. Available at SSRN: https://ssrn.com/abstract=148754

[7] Specifically, we use the “Yield & Growth” capital market assumptions from Research Affiliates. These capital market assumptions account assume that there is no valuation mean reversion (i.e. valuations stay the same going forward). The adjusted average nominal returns for U.S. equities and 10-year U.S. Treasuries are 5.3% and 3.3%, respectively.

Category: Weekly Commentary Page 15 of 21

Diversifying the What, How, and When of Trend Following

Summary

The What: Asset Diversification

The How: Process Diversification

One Signal to Rule Them All?

Identifying the Magic Parameter

The When: Timing Luck

Conclusion

Protect & Participate: Managing Drawdowns with Trend Following

Summary

What is Trend Following?

The Basic Trend Following Setup

Empirical Evidence: Trend Following in a Crisis

Ex-Ante Expectations About Participation

Pre-2008 versus Post-2008 Experience

Conclusion

You Are Not a Monte-Carlo Simulation

Summary­

The Misleading Mean

The Role of Risk

Common Sense Utility Theory

Conclusion

Thinking in Long/Short Portfolios

Summary­

Conclusion

Should You Dollar-Cost Average?

Summary­­

The Historical Case Against Dollar-Cost Averaging

Surely DCA Worked Somewhere

The Truth About Dollar-Cost Averaging

A More General Comparison of LSI and DCA

What About Risk?

When Can DCA Work?

Finding a DCA Middle Ground

Conclusion

**The What: Asset Diversification**

**The How: Process Diversification**

**The When: Timing Luck**

Summary

Summary

Summary