Flirting with Models

The Research Library of Newfound Research

Tag: trend equity Page 2 of 3

Three Applications of Trend Equity

By

On February 25, 2019

In Portfolio Construction, Risk & Style Premia, Trend, Weekly Commentary

This post is available as a PDF download here.

What is Trend Equity?

Trend equity strategies seek to meaningfully participate with equity market growth while side-stepping significant and prolonged drawdowns.  These strategies aim to achieve this goal by dynamically adjusting market exposure based upon trend-following signals.

A naïve example of such a strategy would be a portfolio that invests in U.S. equities when the prior 1-year return for U.S. equities is positive and divests entirely into short-term U.S. Treasuries when it is negative.

The Theory

This category of strategies relies upon the empirical evidence that performance tends to persist in the short-run: positive performance tends to beget further positive performance and negative performance tends to beget further negative performance. The theory behind the evidence is that behavioral biases exhibited by investors lead to the emergence of trends.

In an efficient market, changes in the underlying value of an investment should be met by an immediate, commensurate change in the price of that investment.  The empirical evidence of trends suggests that investors may not be entirely efficient at processing new information.  Behavioral theory (Figure I) suggests that investors anchor their views on prior beliefs, causing price to underreact to new information.  As price continues to drift towards fair value, herding behavior occurs, causing price to overreact and extend beyond fair value.  Combined, these effects cause a trend.

Trend equity strategies seek to capture this potential inefficiency by systematically investing in equities when they are exhibiting positively trending characteristics and divesting when they exhibit negative trends.  The potential benefit of this approach is that it can try to exploit two sources of return: (1) the expected long-term risk premium associated with equities, and (2) the convex payoff structure typically associated with trend-following strategies.

The Positive Convexity of Trend Following

As shown in Figure II, we can see that a hypothetical implementation of this strategy on large-cap U.S. equities has historically exhibited a convex return profile with respect to the underlying U.S. equity index, meaningfully participating in positive return years while reducing exposure to significant loss years.

“Risk Cannot Be Destroyed, Only Transformed.”

While the flexibility of trend equity strategies gives them the opportunity to both protect and participate, it also creates the potential for losses due to “whipsaw.”  Whipsaws occur when the strategy changes positioning due to what appears to be a change in trend, only to have the market rapidly reverse course.  Such a scenario can lead to ”buy high, sell low” and “sell low, buy high” scenarios.  These scenarios can be exacerbated by the fact that trend equity strategies may go several years without experiencing whipsaw to only then suddenly experience multiple back-to-back whipsaw events at once.

As Defensive Equity

The most obvious implementation of trend equity strategies is within a defensive equity sleeve.  In this approach, an allocation for the strategy is funded by selling strategic equity exposure (see Figure III).  Typically combined with other defensive styles (e.g. minimum volatility, quality, et cetera), the goal of a defensive equity sleeve is to provide meaningful upside exposure to equity market growth while reducing downside risk.

This implementation approach has the greatest potential to reduce a policy portfolio’s exposure to downside equity risk and therefore may be most appropriate for investors for whom ”failing fast” is a critical threat.  For example, pre-retirees, early retirees, and institutions making consistent withdrawals are highly subject to sequence risk and large drawdowns within their portfolios can create significant impacts on portfolio sustainability.

The drawback of a defensive equity implementation is that vanilla trend equity strategies can, at best, keep up with their underlying index during strong bull markets (see Figure IV).  Given the historical evidence that markets tend to be up more frequently than they are down, this can make this approach a frustrating one to stick with for investors.  Furthermore, up-capture during bull markets can be volatile on a year-to-year basis, with low up-capture during whipsaw periods and strong up-capture during years with strong trends.  Therefore, investors should only allocate in this manner if they plan to do so over a full market cycle.

Implementation within a Defensive Equity sleeve may also be a prudent approach with investors for whom their risk appetite is far below their risk capacity (or even need); i.e. investors who are chronically under-allocated to equity exposure.  Implementation of a strategy that has the ability to pro-actively de-risk may allow investors to feel more comfortable with a larger exposure.

Finally, this approach may also be useful for investors seeking to put a significant amount of capital to work at once.  While evidence suggests that lump-sum investing (“LSI”) almost always out-performs dollar cost averaging (”DCA”), investors may feel uncomfortable with the significant timing luck from LSI.  One potential solution is to utilize trend equity as a middle ground; for example, investors could DCA but hold trend equity rather than cash.

Pros

  • Maintains overall strategic allocation policy.
  • May help risk-averse investors more confidently maintain an appropriate risk profile.
  • May provide meaningful reduction in exposure to significant and prolonged equity losses.

Cons

  • High year-to-year tracking error relative to traditional equity benchmarks.
  • Typically under-performs equities during prolonged bull markets (see Figure IV).

As a Tactical Pivot

One creative way of implementing a trend equity strategy is as a tactical pivot within a portfolio.  In this implementation, an allocation to trend equity is funded by selling both stocks and bonds, typically in equal amounts (see Figure V).  By implementing in this manner, the investor’s portfolio will pivot around the policy benchmark, being more aggressively allocated when trend equity is fully invested, and more defensively allocated when trend equity de-risks.

This approach is often appealing because it offers a highly intuitive allocation sizing policy.  The size of the tactical pivot sleeve as well as the mixture of stocks and bonds used to fund the sleeve defines the tactical range around the strategic policy portfolio (see Figure VI).

One benefit of this implementation is that trend equity no longer needs to out-perform an equity benchmark to add value.  Rather, so long as the strategy outperforms the mixture of stocks and bonds used to fund the allocation (e.g. a 50/50 mix), the strategy can add value to the holistic portfolio design.  For example, assume a trend equity strategy only achieves an 80% upside capture to an equity benchmark during a given year.  Implemented as a defensive equity allocation, this up-capture would create a drag on portfolio returns relative to the policy benchmark.  If, however, trend equity is implemented as a tactical pivot – funded, for example, from a 50/50 mixture of stocks and bonds – then so long as it outperformed the funding mixture, the portfolio return is improved due to its tilt towards equities.

Implementation as a tactical pivot can also add potential value during environments where stocks and bonds exhibit positive correlations and negative returns (e.g. the 1970s).

One potential drawback of this approach is that the portfolio can be more aggressively allocated than the policy benchmark during periods of sudden and large declines.  How great a risk this represents will be dictated both by the size of the tactical pivot as well as the ratio of stocks and bonds in the funding mixture.  For example, the potential overweight towards equities is significantly lower using a 70/30 stock/bond funding mix than a 30/70 mixture.  A larger allocation to bonds in the funding mixture creates a higher downside hurdle rate for trend equity to add value during a negative equity market environment.

Pros

  • Lower hurdle rate for strategy to add value to portfolio during positive equity environments.
  • Intuitive allocation policy based on desired level of tactical tilts within the portfolio.
  • May provide cushion in environments where stocks and bonds are positively correlated.

Cons

  • Portfolio may be allocated above benchmark policy to risky assets during a sudden market decline.
  • Higher hurdle rate for strategy to add value to portfolio during negative equity environments.

As a Liquid Alternative

Due to its historically convex return profile and potentially high level of tracking error exhibited over short measurement horizons, trend equity may also be a natural fit within a portfolio’s alternative sleeve.  Indeed, when analyzed more thoroughly, trend equity shares many common traits with other traditionally alternative strategies.

For example, a vanilla trend equity implementation can be decomposed into two component sources of returns: a strategic portfolio and a long/short trend-following overlay.  Trend following can also be directly linked to the dynamic trading strategy required to replicate a long option position.

There are even strong correlations to traditional alternative categories.  For example, a significant driver of returns in equity hedge and long/short equity categories is dynamic market beta exposure, particularly during significant market declines (see Figure VII).  Trend equity strategies that are implemented with factor-based equity exposures or with the flexibility to make sector and geographic tilts may even more closely approximate these categories.

One potential benefit of this approach is that trend equity can be implemented in a highly liquid, highly transparent, and cost-effective manner when compared against many traditional alternatives.  Furthermore, by implementing trend equity within an alternatives sleeve, investors may give it a wider berth in their mental accounting of tracking error, allowing for a more sustainable allocation versus implementation as a defensive equity solution.

A drawback of this implementation, however, is that trend equity will increase a portfolio’s exposure to equity beta.  Therefore, more traditional alternatives may offer better correlation- and pay-off-based diversification, especially during sudden and large negative equity shocks.  Furthermore, trend equity may lead to overlapping exposures with existing alternative exposures such as equity long/short or managed futures.  Investors must therefore carefully consider how trend equity may fit into an already existing alternative sleeve.

Pros

  • Highly transparent, easy-to-understand investment process.
  • Implemented with highly liquid underlying exposures.
  • Investors often given alternatives a wider berth of allowable tracking error than more traditional allocations.

Cons

  • May be more highly correlated with existing portfolio exposures than other alternatives.
  • Potentially overlapping exposure with existing alternatives such as equity long/short or managed futures.

Tightening the Uncertain Payout of Trend-Following

By

On January 28, 2019

In Craftsmanship, Portfolio Construction, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Long/flat trend-following strategies have historically delivered payout profiles similar to those of call options, with positive payouts for larger positive underlying asset returns and slightly negative payouts for near-zero or negative underlying returns.
  • However, this functional relationship contains a fair amount of uncertainty for any given trend-following model and lookback period.
  • In portfolio construction, we tend to favor assets that have a combination of high expected returns or diversifying return profiles.
  • Since broad investor behavior provides a basis for systematic trend-following models to have positive expected returns, taking a multi-model approach to trend-following can be used to reduce the variance around the expected payout profile.

Introduction

Over the past few months, we have written much about model diversification as a tactic for managing specification risk, even with specific case studies. When we consider the three axes of diversification, model diversification pertains to the “how” axis, which focuses on strategies that have the same overarching objective but go about achieving it in different ways.

Long/flat trend-following, especially with equity investments, aims to protect capital on the downside while maintaining participation in positive markets. This leads to a payout profile that looks similar to that of a call option.1

However, while a call option offers a defined payout based on the price of an underlying asset and a specific maturity date, a trend-following strategy does not provide such a guarantee. There is a degree of uncertainty.

The good news is that uncertainty can potentially be diversified given the right combinations of assets or strategies.

In this commentary, we will dive into a number of trend-following strategies to see what has historically led to this benefit and the extent that diversification would reduce the uncertainty around the expected payoff.

Diversification in Trend-Following

The justification for a multi-model approach boils down to a simple diversification argument.

Say you would like to include trend-following in a portfolio as a way to manage risk (e.g. sequence risk for a retiree). There is academic and empirical evidence that trend-following works over a variety of time horizons, generally ranging from 3 to 12 months. And there are many ways to measure trends, such as moving average crossovers, trailing returns, deviations from moving averages, risk adjusted returns, etc.

The basis for deciding ex-ante which variant will be the best over our own investment horizon is tenuous at best. Backtests can show one iteration outperforming over a given time horizon, but most of the differences between strategies are either noise from a statistical point of view or realized over a longer time period than any investor has the lifespan (or mettle) to endure.

However, we expect each one to generate positive returns over a sufficiently long time horizon. Whether this is one year, three years, five years, 10 years, 50 years… we don’t know. What we do know is that out of the multitude the variations of trend-following, we are very likely to pick one that is not the best or even in the top segment of the pack in the short-term.

From a volatility standpoint, when the strategies are fully invested, they will have volatility equal to the underlying asset. Determining exactly when the diversification benefits will come in to play – that is, when some strategies are invested and others are not – is a fool’s errand.

Modern portfolio theory has done a disservice in making correlation seem like an inherent trait of an investment. It is not.

Looking at multiple trend-following strategies that can coincide precisely for stretches of time before behaving completely differently from each other, makes many portfolio construction techniques useless.  We do not expect correlation benefits to always be present.  These are nonlinear strategies, and fitting them into a linear world does not make sense.

If you have pinned up ReSolve Asset Management’s flow chart of portfolio choice above your desk (from Portfolio Optimization: A General Framework for Portfolio Choice), then the decision on this is easy.

Source: ReSolve Asset Management.  Reprinted with permission

From this simple framework, we can break the different performance regimes down as follows:

The Math Behind the Diversification

The expected value of a trend-following strategy can be thought of as a function of the underlying security return:

Where the subscript i is used to indicate that the function is dependent on the specific trend-following strategy.

If we combine multiple trend-following strategies into a portfolio, then the expectation is the average of these functions (assuming an equal weight portfolio per the ReSolve chart above):

What’s left to determine is the functional form of f.

Continuing in the vein of the call option payoff profile, we can use the Black-Scholes equation as the functional form (with the risk-free rate set to 0). This leaves three parameters with which to fit the formula to the data: the volatility (with the time to expiration term lumped in, i.e. sigma * sqrt(T-t)), the strike, and the initial cost of the option.

where d1 and d2 are defined in the standard fashion and N is the cumulative normal distribution function.

rK is the strike price in the option formula expressed as a percent relative to the current value of the underlying security.

In the following example, we will attempt to provide some meaning to the fitted parameters. However, keep in mind that any mapping is not necessarily one-to-one with the option parameters. The functional form may apply, but the parameters are not ones that were set in stone ex-ante.2

An Example: Trend-Following on the S&P 500

As an example, we will consider a trend-following model on the S&P 500 using monthly time-series momentum with lookback windows ranging from 4 to 16 months. The risk-free rate was used when the trends were negative.

The graph below shows an example of the option price fit to the data using a least-squares regression for the 15-month time series momentum strategy using rolling 3-year returns from 1927 to 2018.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The volatility parameter was 9.5%, the strike was 2.3%, and the cost was 1.7%.

What do these parameters mean?

As we said before this can be a bit tricky. Painting in broad strokes:

  • The volatility parameter describes how “elbowed” payoff profile is. Small values are akin to an option close to expiry where the payoff profile changes abruptly around the strike price. Larger values yield a more gentle change in slope.
  • The strike represents the point at which the payoff profile changes from participation to protection using trend-following lingo. In the example where the strike is 2.3%, this means that the strategy would be expected to start protecting capital when the S&P 500 return is less than 2.3%. There is some cost associated with this value being high.
  • The cost is the vertical shift of the payoff profile, but it is not good to think of it as the insurance premium of the trend-following strategy. It is only one piece. To see why this is the case, consider that the fitted volatility may be large and that the option price curve may be significantly above the final payout curve (i.e. if the time-scaled volatility went to zero).

So what is the actual “cost” of the strategy?

With trend-following, since whipsaw is generally the largest potential detractor, we will look at the expected return on the strategy when the S&P 500 is flat, that is, an absence of an average trend. It is possible for the cost to be negative, indicating a positive expected trend-following return when the market was flat.

Looking at the actual fit of the data from a statistical perspective, the largest deviations from the expected value (the residuals from the regression) are seen during large positive returns for the S&P 500, mainly coming out of the Great Depression. This characteristic of individual trend-following models is generally attributable to the delay in getting back into the market after a prolonged, severe drawdown due to the time it takes for a new positive trend to be established.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Part of the seemingly large number of outliers is simply due to the fact that these returns exhibit autocorrelation since the periods are rolling, which means that the data points have some overlap. If we filtered the data down into non-overlapping periods, some of these outliers would be removed.

The outliers that remain are a fact of trend-following strategies. While this fact of trend-following cannot be totally removed, some of the outliers may be managed using multiple lookback periods.

The following chart illustrates the expected values for the trend-following strategies over all the lookback periods.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The shorter-term lookback windows have the expected value curves that are less horizontal on the left side of the chart (higher volatility parameter).

As we said before the cost of the trend-following strategy can be represented by the strategy’s expected return when the S&P 500 is flat. This can be thought of as the premium for the insurance policy of the trend-following strategies.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions.  Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The blend does not have the lowest cost, but this cost is only one part of the picture. The parameters for the expected value functions do nothing to capture the distribution of the data around – either above or below – these curves.

The diversification benefits are best seen in the distribution of the rolling returns around the expected value functions.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Now with a more comprehensive picture of the potential outcomes, a cost difference of even 3% is less than one standard deviation, making the blended strategy much more robust to whipsaw for the potential range of S&P 500 returns.

As a side note, the cost of the short window (4 and 5 month) strategies is relatively high. However, since there are many rolling periods when these models are the best performing of the group, there can still be a benefit to including them. With them in the blend, we still see a reduction in the dispersion around the expected value function.

Expanding the Multitude of Models

To take the example even further down the multi-model path, we can look at the same analysis for varying lookback windows for a price-minus-moving-average model and an exponentially weighted moving average model.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

And finally, we can combine all three trend-following measurement style blends into a final composite blend.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

As with nearly every study on diversification, the overall blend is not the best by all metrics. In this case, its cost is higher than the EWMA blended model and its dispersion is higher than the TS blended model. But it exhibits the type of middle-of-the-road characteristics that lead to results that are robust to an uncertain future.

Conclusion

Long/flat trend-following strategies have payoff profiles similar to call options, with larger upsides and limited downsides. Unlike call options (and all derivative securities) that pay a deterministic amount based on the underlying securities prices, the payoff of a trend-following strategy is uncertain,

Using historical data, we can calculate the expected payoff profile and the dispersion around it. We find that by blending a variety of trend-following models, both in how they measure trend and the length of the lookback window, we can often reduce the implied cost of the call option and the dispersion of outcomes.

A backtest of an individual trend-following model can look the best over a given time period, but there are many factors that play into whether that performance will be valid going forward. The assets have to behave similarly, potentially both on an absolute and relative basis, and an investor has to hold the investment for a long enough time to weather short-term underperformance.

A multi-model approach can address both of these.

It will reduce the model specification risk that is present ex-ante. It will not pick the best model, but then again, it will not pick the worst.

From an investor perspective, this diversification reduces the spread of outcomes which can lead to an easier product to hold as a long-term investment. Diversification among the models may not always be present (i.e. when style risk dominates and all trend-following strategies do poorly), but when it is, it reduces the chance of taking on uncompensated risks.

Taking on compensated risks is a necessary part of investing, and in the case of trend-following, the style risk is something we desire. Removing as many uncompensated risks as possible leads to more pure forms of this style risk and strategies that are robust to unfavorable specifications.

When Simplicity Met Fragility

By

On October 29, 2018

In Craftsmanship, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Research suggests that simple heuristics are often far more robust than more complicated, theoretically optimal solutions.
  • Taken too far, we believe simplicity can actually introduce significant fragility into an investment process.
  • Using trend equity as an example, we demonstrate how using only a single signal to drive portfolio allocations can make a portfolio highly sensitive to the impact of randomness, clouding our ability to determine the difference between skill and luck.
  • We demonstrate that a slightly more complicated process that combines signals significantly reduces the portfolio’s sensitivity to randomness.
  • We believe that the optimal level of simplicity is found at the balance of diversification benefit and introduced estimation risk. When a more complicated process can introduce meaningful diversification gain into a strategy or portfolio with little estimation risk, it should be considered.

Introduction

In the world of finance, simple can be surprisingly robust.  DeMiguel, Garlappi, and Uppal (2005)1, for example, demonstrate that a naïve, equal-weight portfolio frequently delivers higher Sharpe ratios, higher certainty-equivalent returns, and lower turnover out-of-sample than competitive “optimal” allocation policies.  In one of our favorite papers, Haldane (2012)2demonstrates that simplified heuristics often outperform more complicated algorithms in a variety of fields.

Yet taken to an extreme, we believe that simplicity can have the opposite effect, introducing extreme fragility into an investment strategy.

As an absurd example, consider a highly simplified portfolio that is 100% allocated to U.S. equities.  Introducing bonds into the portfolio may not seem like a large mental leap but consider that this small change introduces an axis of decision making that brings with it a number of considerations.  The proportion we allocate between stocks and bonds requires, at the very least, estimates of an investor’s objectives, risk tolerances, market outlook, and confidence levels in these considerations.3

Despite this added complexity, few investors would consider an all-equity portfolio to be more “robust” by almost any reasonable definition of robustness.

Yet this is precisely the type of behavior we see all too often in tactical portfolios – and particularly in trend equity strategies – where investors follow a single signal to make dramatic allocation decisions.

So Close and Yet So Far

To demonstrate the potential fragility of simplicity, we will examine several trend-following signals applied to broad U.S. equities:

  • Price minus the 10-month moving average
  • 12-1 month total return
  • 13-minus-34-week exponential moving average cross-over

Below we plot over time the distance each of these signals is from turning off.  Whenever the line crosses over the 0% threshold, it means the signal has flipped direction, with negative values indicating a sell and positive values indicating a buy.

In orange we highlight those periods where the signal is within 1% of changing direction. We can see that for each signal there are numerous occasions where the signal was within this threshold but avoided flipping direction.  Similarly, we can see a number of scenarios where the signal just breaks the 0% threshold only to revert back shortly thereafter.  In the former case, the signal has often just managed to avoid whipsaw, while in the latter it has usually become unfortunately subject to it.

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

Is the avoidance of whipsaw representative of the “skill” of the signals while the realization of whipsaw is just bad luck?  Or might it be that the avoidance of whipsaw is often just as much luck as the realization of whipsaw is poor skill?  How can we determine what is skill and what is luck when there are so many “close calls” and “just hits”?

What is potentially confusing for investors new to this space is that academic literature and practitioner evidence finds that these highly simplified approaches are surprisingly robust across a variety of investment vehicles, geographies, and time periods.  What we must stress, however, is that evidence of general robustness is not evidence of specific robustness; i.e. there is little evidence suggesting that a single approach applied to a single instrument over a specific time horizon will be particularly robust.

What Randomness Tells Us About Fragility

To emphasize the potential fragility on utilizing a single in-or-out signal to drive our allocation decisions, we run a simple test:

  1. Begin with daily market returns
  2. Add a small amount of white noise (mean 0%; standard deviation 0.025%) to daily market returns
  3. Calculate a long/flat trend equity strategy using 12-1 month momentum signals4
  4. Calculate the rolling 12-month return of the strategy minus the alternate market history return.
  5. Repeat 1,000 times to generate 1,000 slightly alternate histories.

The design of this test aims to deduce how fragile a strategy is via the introduction of randomness.  By measuring 12-month rolling relative returns versus the modified benchmarks, we can compare the 1,000 slightly alternate histories to one another in an effort to determine the overall stability of the strategy itself.

Now bear with us, because while the next graph is a bit difficult to read, it succinctly captures the thrust of our entire thesis.  At each point in time, we first calculate the average 12-month relative return of all 1,000 strategies.  This average provides a baseline of expected relative strategy performance.

Next, we calculate the maximum and minimum relative 12-month relative performance and subtract the average.  This spread – which is plotted in the graph below – aims to capture the potential return differential around the expected strategy performance due to randomness. Or, put another way, the spread captures the potential impact of luck in strategy results due only to slight changes in market returns.

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

We can see that the spread frequently exceeds 5% and sometimes even exceeds 10. Thus, a tiny bit of injected randomness has a massive effect upon our realized results.  Using a single signal to drive our allocation appears particularly fragile and success or failure over the short run can largely be dictated by the direction the random winds blow.

A backtest based upon a single signal may look particularly good, but this evidence suggests we should dampen our confidence as the strategy may actually have just been the accidental beneficiary of good fortune.  In this situation, it is nearly impossible to identify skill from luck when in a slightly alternate universe we may have had substantially different results.  After all, good luck in the past can easily turn into misfortune in the future.

Now let us perform the same exercise again using the same random sequences we generated.  But rather than using a single signal to drive our allocation we will blend the three trend-following approaches above to determine the proportional amount of equities the portfolio should hold.5  We plot the results below using the same scale in the y-axis as the prior plot.

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

We can see that our more complicated approach actually exhibits a significant reduction in the effects of randomness, with outlier events significantly decreased and far more symmetry in both positive and negative impacts.

Below we plot the actual spreads themselves.  We can see that the spread from the combined signal approach is lower than the single signal approach on a fairly consistent basis.  In the cases where the spread is larger, it is usually because the sensitivity is arising from either the 10-month SMA or 13-minus-34-week EWMA signals.  Were spreads for single signal strategies based upon those approaches plotted, they would likely be larger during those time periods.

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

Conclusion

So, where is the balance?  How can we tell when simplicity creates robustness and simplicity introduces fragility? As we discussed in our article A Case Against Overweighting International Equity, we believe the answer is diversificationversus estimation risk.

In our case above, each trend signal is just a model: an estimate of what the underlying trend is.  As with all models, it is imprecise and our confidence level in any individual signal at any point in time being correct may actually be fairly low.  We can wrap this all together by simply saying that each signal is actually shrouded in a distribution of estimation risk.  But by combining multiple trend signals, we exploit the benefits of diversification in an effort to reduce our overall estimation risk.

Thus, while we may consider a multi-model approach less transparent and more complicated, that added layer of complication serves to increase internal diversification and reduce estimation risk.

It should not go overlooked that the manner in which the signals were blended represents a model with its own estimation risk.  Our choice to simply equally-weight the signals indicates a zero-confidence position in views about relative model accuracy and relative marginal diversification benefits among the models.  Had we chosen a more complicated method of combining signals, it is entirely possible that the realized estimation risk could overwhelm the diversification gain we aimed to benefit from in the first place.  Or, conversely, that very same added estimation risk could be entirely justified if we could continue to meaningfully improve diversification benefits.

If we return back to our original example of a 100% equity portfolio versus a blended stock-bond mix, the diversification versus estimation risk trade-off becomes obvious.  Introducing bonds into our portfolio creates such a significant diversification gain that the estimation risk is often an insignificant consideration.  The same might not be true, however, in a tactical equity portfolio.

Research and empirical evidence suggest that simplicity is surprisingly robust.  But we should be skeptical of simplicity for the sake of simplicity when it foregoes low-hanging diversification opportunities, lest we make our portfolios and strategies unintentionally fragile.

 

Decomposing Trend Equity

By

On September 24, 2018

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

This post is available as a PDF download here.

Summary­

  • We introduce the simple arithmetic of portfolio construction where a strategy can be broken into a strategic allocation and a self-financing trading strategy.
  • For long/flat trend equity strategies, we introduce two potential decompositions.
  • The first implementation is similar to equity exposure with a put option overlay. The second is similar to a 50% equity / 50% cash allocation with a 50% overlay to a straddle.
  • By evaluating the return profile of the active trading strategy in both decompositions, we can gain a better understanding for how we expect the strategy to perform in different environments.
  • In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.

The Simple Arithmetic of Portfolio Construction

In our commentary A Trend Equity Primer, we introduced the concept of trend equity, a category of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following.  In this brief follow-up piece, we aim to provide further transparency into the behavior of trend equity strategies by decomposing this category of strategies into component pieces.

First, what do we mean by “decompose”?

As it turns out, the arithmetic of portfolios is fairly straight forward.  Consider this simple scenario: we currently hold a portfolio consisting entirely of asset A and want to hold a portfolio that is 50% A and 50% of some asset B.  What do we do?

Figure 1

No, this is not a trick question.  The straightforward answer is that we sell 50% of our exposure in A and buy 50% of our exposure in B.  As it turns out, however, this is entirely equivalent to holding our portfolio constant and simply going short 50% exposure in A and using the proceeds to purchase 50% notional portfolio exposure in B (see Figure 2).  Operationally, of course, these are very different things.  Thinking about the portfolio in this way, however, can be constructive to truly understanding the implications of the trade.

The difference in performance between our new portfolio and our old portfolio will be entirely captured by the performance of this long/short overlay. This tells us, for example, that the new portfolio will outperform the old portfolio when asset B outperforms asset A, since the long/short portfolio effectively captures the spread in performance between asset B and asset A.

Figure 2: Portfolio Arithmetic – Long/Short Overlay

Relative to our original portfolio, the long/short represents our active bets.  A slightly more nuanced view of this arithmetic requires scaling our active bets such that each leg is equal to 100%, and then only implementing a portion of that overlay.  It is important to note that the overlay is “dollar-neutral”: in other words, the dollars allocated to the short leg and the long leg add up to zero.  This is also called “self-funding” because it is presumed that we would enter the short position and then use the cash generated to purchase our long exposure, allowing us to enter the trade without utilizing any capital.

Figure 3: Portfolio Arithmetic – Scaled Long/Short Overlay

In our prior example, a portfolio that is 50% long B and 50% short A is equivalent to 50% exposure to a portfolio that is 100% long B and 100% short A.  The benefit of taking this extra step is that it allows us to decompose our trade into two pieces: the active bets we are making and the sizing of these bets.

Decomposing Trend Equity

Trend equity strategies are those strategies that seek to combine structural exposure to equities with the potential benefits of an active trend-following trading strategy.  A simple example of such a strategy is a “long/flat” strategy that invests in large-cap U.S. equities when the measured trend in large-cap U.S. equities is positive and otherwise invests in short-term U.S. Treasuries (or any other defensive asset class).

An obvious question with a potentially non-obvious answer is, “how do we benchmark such a strategy?”  This is where we believe decomposition can be informative.  Our goal should be to decompose the portfolio into two pieces: the strategic benchmark allocation and a dollar-neutral long/short trading strategy that captures the manager’s active bets.

For long/flat trend equity strategies, we believe there are two obvious decompositions, which we outline in Figure 4.

Figure 4

Strategic Position

Trend Strategy

Decomposition

Positive Trend

Negative Trend

Strategic +
Flat/Short Trend Strategy

100% Equity

No Position

-100% Equity
100% ST US Treasuries

Strategic + 50% Long/Short Trend Strategy

50% Equity
50% ST US Treasuries

100% Equity
-100% ST US Treasuries

-100% Equity
+100% ST US Treasuries

Equity + Flat/Short

The first decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is allocated to U.S. equities.  This is complemented by a trading strategy that goes short large-cap U.S. equities when the trend is negative, investing the available cash in short-term U.S. Treasuries, and does nothing otherwise.

The net effect is that when trends are positive, the strategy remains fully invested in large-cap U.S. equities.  When trends are negative, the overlay nets out exposure to large-cap U.S. equities and leaves the portfolio exposed only to short-term U.S. Treasuries.

In Figures 5, we plot the return profile of a hypothetical flat/short large-cap U.S. equity strategy.

Figure 5: A Flat/Short U.S. Equity Strategy

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

The flat/short strategy has historically achieved a payoff structure that looks very much like a put option: positive returns during significantly negative return regimes, and (on average) slight losses otherwise.  Of course, unlike a put option where the premium paid is known upfront, the flat/short trading strategy pays its premium in the form of “whipsaw” resulting from trend reversals.  These head-fakes cause the strategy to “short low” and “cover high,” creating realized losses.

Our expectation for future returns, then, is a combination of the two underlying strategies:

  • 100% Strategic Equity: We should expect to earn, over the long run, the equity risk premium at the risk of large losses due to economic shocks.
  • 100% Flat/Short Equity: Empirical evidence suggests that we should expect a return profile similar to a put option, with negative returns in most environments and the potential for large, positive returns during periods where large-cap U.S. equities exhibit large losses.  Historically, the premium for the trend-following “put option” has been significantly less than the premium for buying actual put options.  As a result, hedging with trend-following has delivered higher risk-adjusted returns.  Note, however, that trend-following is rarely helpful in protecting against sudden losses (e.g. October 1987) like an actual put option would be.

Taken together, our long-term return expectation should be the equity risk premium minus the whipsaw costs of the flat/short strategy. The drag in return, however, is payment for the expectation that significant left-tail events will be meaningfully offset.  In many ways, this decomposition lends itself nicely to thinking of trend equity as a “defensive equity” allocation.

Figure 6: Combination of U.S. Large-Cap Equities and a Flat/Short Trend-Following Strategy

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a negative 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

50% Equity/50% Cash + 50% Long/Short

The second decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is 50% large-cap U.S. equities and 50% short-term U.S. Treasuries.  The overlaid trend strategy now goes both long and short U.S. equities depending upon the underlying trend signal, going short and long large-cap U.S. Treasuries to keep the dollar-neutral profile of the overlay.

One difference in this approach is that to achieve the desired long/flat return profile, only 50% exposure to the long/short strategy is required.  As before, the net effect is such that when trends are positive, the portfolio is invested entirely in large-cap U.S. equities (as the short-term U.S. Treasury positions cancel out), and when trends are negative, the portfolio is entirely invested in short-term U.S. Treasuries.

In Figures 7, we plot the return profile of a hypothetical long/short large-cap U.S. equity strategy.

Figure 7: A Long/Short Equity Trend-Following Strategy

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills.  When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

We can see the traditional “smile” associated with long/short trend-following strategies.  With options, this payoff profile is reminiscent of a straddle, a strategy that combines a position in a put and a call option to profit in both extremely positive and negative environments.  The premium paid to buy these options causes the strategy to lose money in more normal environments.  We see a similar result with the long/short trend-following approach.

As before, our expectation for future returns is a combination of the two underlying strategies:

  • 50% Equity / 50% Cash: We should expect to earn, over the long run, about half the equity risk premium, but only expect to suffer about half the losses associated with equities.
  • 50% Long/Short Equity: The “smile” payoff associated with trend following should increase exposure to equities in the positive tail and help offset losses in the negative tail, at the cost of whipsaw during periods of trend reversals.

Taken together, we should expect equity up-capture exceeding 50% in strongly trending years, a down-capture less than 50% in strongly negatively trending years, and a slight drag in more normal environments.  We believe that this form of decomposition is most useful when investors are planning to fund their trend equity from both stocks and bonds, effectively using it as a risk pivot within their portfolio.

In Figure 8, we plot the return combined return profile of the two component pieces. Note that it is identical to Figure 6.

Figure 8

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills.  When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Conclusion

In this commentary, we continued our exploration of trend equity strategies. To gain a better sense of how we should expect trend equity strategies to perform, we introduce the basic arithmetic of portfolio construction that we later use to decompose trend equity into a strategic allocation plus a self-funded trading strategy.

In the first decomposition, we break trend equity into a strategic, passive allocation in large-cap U.S. equities plus a self-funding flat/short trading strategy. The flat/short strategy sits in cash when trends in large-cap U.S. equities are positive and goes short large-cap U.S. equities when trends are negative.  In isolating the flat/short trading strategy, we see a return profile that is reminiscent of the payoff of a put option, exhibiting negative returns in positive market environments and large gains during negative market environments.

For investors planning on utilizing trend equity as a form of defensive equity, this decomposition is appropriate.  It clearly demonstrates that we should expect returns that are less than passive equity during almost all market environments, with the exception being extreme negative tail events, where the trading strategy aims to hedge against significant losses.  While we would expect to be able to measure manager skill by the amount of drag created to equities during positive markets (i.e. the “cost of the hedge”), we can see from the hypothetical example inn Figure 5 that there is considerable variation year-to-year, making short-term analysis difficult.

In our second decomposition, we break trend equity into a strategic portfolio that is 50% large-cap U.S. equity / 50% short-term U.S. Treasury plus a self-funding long/short trading strategy.  If the flat/short trading strategy was similar to a put option, the long/short trading strategy is similar to a straddle, exhibiting profit in the wings of the return distribution and losses near the middle.

This particular decomposition is most relevant to investors who plan on funding their trend equity exposure from both stocks and bonds, allowing the position to serve as a risk pivot within their overall allocation.  The strategic contribution provides partial exposure to the equity risk premium, but the trading strategy aims to add value in both tails, demonstrating that trend equity can potentially increase returns in both strongly positive and strongly negative environments.

In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.

In this sense, trend equity strategies help investors achieve capital efficiency.  Allocations to the alternative return premia, in this case trend, does not require allocating away from the strategic, long-only portfolio.  Rather, exposure to both the strategic holdings and the trend-following alternative strategy can be gained in the same package.

A Trend Equity Primer

By

On September 17, 2018

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

This post is available as a PDF download here.

Summary­

  • Trend-following strategies exploit the fact that investors exhibit behavioral biases that cause trends to persist.
  • While many investment strategies have a concave payoff profile that reaps small rewards at the risk of large losses, trend-following strategies exhibit a convex payoff profile, one that pays small premiums with the potential of a large reward.
  • By implementing a trend-following strategy on equities, investors can tap into both the long-term return premium from holding equities and the convex payoff profile associated with trend following.
  • There are multiple ways to include a trend-following equity strategy in a portfolio, and the method of incorporation will affect the overall risk and return expectations in different market environments.
  • As long as careful consideration is given to whipsaw, hedging ability, and implementation costs, trend-following equity can be a potentially useful diversifier in most traditionally allocated portfolios.

A Balance of Risks

Most investors – individual and institutional alike – live in the balance of two risks: failing slow and failing fast.  Most investors are familiar with the latter: the risk of large and sudden drawdowns that can permanently impair an investor’s lifestyle or ability to meet future liabilities.  Slow failure, on the other hand, occurs when an investor fails to grow their portfolio at a speed sufficient to offset inflation and withdrawals.

Investors have traditionally managed these risks through asset allocation, balancing exposure to growth-oriented asset classes (e.g. equities) with more conservative, risk-mitigating exposures (e.g. cash or bonds).  How these assets are balanced is typically governed by where an investor falls in their investment lifecycle and which risk has the greatest impact upon the probability of their future success.

For example, younger investors who have a large proportion of their future wealth tied up in human capital often have very little risk of failing fast, as they are not presently relying upon withdrawals from their investment capital. Evidence suggests that the risk of fast failure peaks for pre- and early-retirees, whose future lifestyle will be largely predicated upon the amount of capital they are able to maintain into early retirement.  Later-stage retirees, on the other hand, once again become subject to the risk of failing slow, as longer lifespans put greater pressure upon the initial retirement capital to last.

Trend equity strategies seek to address both risks simultaneously by maintaining equity exposure when trends are positive and de-risking the portfolio when trends are negative.  Empirical evidence suggests that such strategies may allow investors to harvest a significant proportion of the long-term equity risk premium while significantly reducing the impact of severe and prolonged drawdowns.

The Potential Hedging Properties of Trend Following

When investors buy stocks and bonds, they are exposing themselves to “systematic risk factors.”  These risk factors are the un-diversifiable uncertainties associated with any investment. For bearing these risks, investors expect to earn a reward.  For example, common equity is generally considered to be riskier than fixed income because it is subordinate in the capital structure, does not have a defined payout, and does not have a defined maturity date.  A rational investor would only elect to hold stocks over bonds, then, if they expected to earn a return premium for doing so.

Similarly, the historical premium associated with many active investment strategies are also assumed to be risk-based in nature.  For example, quantitatively cheap stocks have historically outperformed expensive ones, an anomaly called the “value factor.”  Cheap stocks may be trading cheaply for a reason, however, and the potential excess return earned from buying them may simply be the premium required by investors to bear the excess risk.

In many ways, an investor bearing risk can be thought of as an insurer, expecting to collect a premium over time for their willingness to carry risk that other investors are looking to offload.  The payoff profile for premiums generated from bearing risk, however, is concave in nature: the investor expects to collect a small premium over time but is exposed to potentially large losses (see Figure 1).  This approach is often called being “short volatility,” as the manifestation of risk often coincides with large (primarily negative) swings in asset values.

Even the process of rebalancing a strategic asset allocation can create a concave payoff structure.  By reallocating back to a fixed mixture of assets, an investor sells assets that have recently outperformed and buys assets that have recently underperformed, benefiting when the relative performance of investments mean-reverts over time.

When taken together, strategically allocated portfolios – even those with exposure to alternative risk premia – tend to combine a series of concave payoff structures. This implies that a correlation-based diversification scheme may not be sufficient for managing left-tail risk during bad times, as a collection of small premiums may not offset large losses.

In contrast, trend-following strategies “cut their losers short and let their winners run” by design, creating a convex payoff structure (see Figure 1).1  Whereas concave strategies can be thought of as collecting an expected return premium for bearing risk, a convex payoff can be thought of as expecting to pay an insurance premium in order to hedge risk.  This implies that while concave payoffs benefit from stability, convex payoffs benefit from instability, potentially helping hedge portfolios against large losses at the cost of smaller negative returns during normal market environments.

Figure 1: Example Concave and Convex Payoff Structures; Profit in Blue and Loss in Orange

Source: Newfound Research.  For illustrative purposes only and not representative of any Newfound Research product or investment.

What is Trend Equity?

Trend equity strategies rely upon the empirical evidence2 that performance tends to persist in the short-run: positive performance tends to beget further positive performance and negative performance tends to beget further negative performance.  The theory behind the evidence is that behavioral biases exhibited by investors lead to the emergence of trends.

In an efficient market, changes in the underlying value of an investment should be met by an immediate, commensurate change in the price of that investment. The empirical evidence of trends suggests that investors may not be entirely efficient at processing new information.  Behavioral theory suggests that investors anchor their views on prior beliefs, causing price to underreact to new information.  As price continues to drift towards fair value, herding behavior occurs, causing price to overreact and extend beyond fair value.  Combined, these effects cause a trend.

Trend equity strategies seek to capture this potential inefficiency by systematically investing in equities when they are exhibiting positively trending characteristics and divesting when they exhibit negative trends.  The potential benefit of this approach is that it can try to exploit two sources of return: (1) the expected long-term risk premium associated with equities, and (2) the convex payoff structure typically associated with trend-following strategies.

As shown in Figure 2, a hypothetical implementation of this strategy on large-cap U.S. equities has historically matched the long-term annualized return while significantly reducing exposure to both tails of the distribution.  This is quantified in Figure 3, which demonstrates a significant reduction in both the skew and kurtosis (“fat-tailedness”) of the return distribution.

Figure 2

Figure 3

U.S. Large-Cap EquitiesTrend Equity
Annualized Return11.1%11.6%
Volatility16.9%11.3%
Skewness-1.40.0
Excess Kurtosis2.2-1.0

 Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.  The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Implementing Trend Equity

With trend equity seeking to benefit from both the long-term equity risk premium and the convex payoff structure of trend-following, there are two obvious examples of how it can be implemented in the context of an existing strategic portfolio. The preference as to the approach taken will depend upon an investor’s goals.

Investors seeking to reduce risk in their portfolio may prefer to think of trend equity as a form of dynamically hedged equity, replacing a portion of their traditional equity exposure.  In this case, when trend equity is fully invested, the portfolio will match the original allocation profile; when the trend equity strategy is divested, the portfolio will be significantly underweight equity exposure.  The intent of this approach is to match the long-term return profile of equities with less realized risk.

On the other hand, investors seeking to increase their returns may prefer to treat trend equity as a pivot within their portfolio, funding the allocation by drawing upon both traditional stock and bond exposures.  In this case, when fully invested, trend equity will create an overweight to equity exposure within the portfolio; when divested, it will create an underweight.  The intent of this approach is to match the long-term realized risk profile of a blended stock/bond mix while enhancing long-term returns.

To explore these two options in the context of an investor’s lifecycle, we echo the work of Freccia, Rauseo, and Villalon (2017).  Specifically, we will begin with a naïve “own-your-age” glide path, which allocates a proportion of capital to bonds equivalent to the investor’s age.  We assume the split between domestic and international exposures is 60/40 and 70/30 respectively for stocks and bonds, selected to approximate the split between domestic and international exposures found in Vanguard’s Target Retirement Funds.

An investor seeking to reduce exposure to negative equity tail events could fund trend equity exposure entirely from their traditional equity allocation. Applying the own-your-age glide path over the horizon of June 1988 to June 2018, carving out 30% of U.S. equity exposure for trend equity (e.g. an 11.7% allocation for a 35 year old investor and an 8.1% allocation for a 55 year old investor) would have offered the same long-term return profile while reducing annualized volatility and the maximum drawdown experienced.

For an investor seeking to increase return, funding a position in trend equity from both U.S. equities and U.S. bonds may be a more applicable approach.  Again, applying the own-your-age glide-path from June 1988 to June 2018, we find that replacing 50% of existing U.S. equity exposure and 30% of existing U.S. bond exposure with trend equity would have offered a nearly identical long-term volatility profile while increasing long-term annualized returns.

Figure 4

Source: Newfound Research.  For illustrative purposes only and not representative of any Newfound Research product or investment.

 

Figure 5: Hypothetical Portfolio Statistics, June 1988 – June 2018

Original
Glidepath		Same Return,
Decrease Risk		Increase Return,
Same Risk
Annual Return8.20%8.25%8.60%
Volatility8.58%8.17%8.59%
Maximum Drawdown-28.55%-24.71%-23.80%
Sharpe Ratio0.610.640.65

 Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.  The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

 

Figure 6: Own-Your-Age Glide Paths Including Trend Equity

Source: Newfound Research.  For illustrative purposes only and not representative of any Newfound Research product or investment.  Allocation methodologies described in the preceding section.

A Discussion of Trade-Offs

At Newfound Research, we champion the philosophy that “risk cannot be destroyed, only transformed.”  While we believe that a convex payoff structure – like that empirically found in trend-following strategies – can introduce beneficial diversification into traditionally allocated portfolios, we believe any overview is incomplete without a discussion of the potential trade-offs of such an approach.

The perceived trade-offs will be largely dictated by how trend equity is implemented by an investor.  As in the last section, we will consider two cases: first the investor who replaces their traditional equity exposure, and second the investor that funds an allocation from both stocks and bonds.

In the first case, we believe that the convex payoff example displayed Figure 1 is important to keep in mind.  Traditionally, convex payoffs tend to pay a premium during stable environments.  When this payoff structure is combined with traditional long-only equity exposure to create a trend equity strategy, our expectation should be a return profile that is expected to lag behind traditional equity returns during calm market environments.

This is evident in Figure 7, which plots hypothetical rolling 3-year annualized returns for both large-cap U.S. equities and a hypothetical trend equity strategy. Figure 8 also demonstrates this effect, plotting rolling 1-year returns of a hypothetical trend equity strategy against large-cap U.S. equities, highlighting in orange those years when trend equity underperformed.

For the investor looking to employ trend equity as a means of enhancing return by funding exposure from both stocks and bonds, long-term risk statistics may be misleading.  It is important to keep in mind that at any given time, trend equity can be fully invested in equity exposure.  While evidence suggests that trend-following strategies may be able to act as an efficient hedge when market downturns are gradual, they are typically inefficient when prices collapse suddenly.

In both cases, it is important to keep in mind that convex payoff premium associated with trend equity strategies is not consistent, nor is the payoff guaranteed. In practice, the premium arises from losses that arrive during periods of trend reversals, an effect popularly referred to as “whipsaw.”  A trend equity strategy may go several years without experiencing whipsaw, seemingly avoiding paying any premium, then suddenly experience multiple back-to-back whipsaw events at once.  Investors who allocate immediately before a series of whipsaw events may be dismayed, but we believe that these are the costs necessary to access the convex payoff opportunity and should be considered on a multi-year, annualized basis.

Finally, it is important to consider that trend-following is an active strategy. Beyond management fees, it is important to consider the impact of transaction costs and taxes.

Figure 7Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.   The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Figure 8

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.   The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Conclusion

In this primer, we have introduced trend equity, an active strategy that seeks to provide investors with exposure to the equity risk premium while mitigating the impacts of severe and prolonged drawdowns.  The strategy aims to achieve this objective by blending exposure to equities with the convex payoff structure traditionally exhibited by trend-following strategies.

We believe that such a strategy can be a particularly useful diversifier for most strategically allocated portfolios, which tend to be exposed to the concave payoff profile of traditional risk factors.  While relying upon correlation may be sufficient in normal market environments, we believe that the potential premiums collected can be insufficient to offset large losses generated during bad times.  It is during these occasions that we believe a convex payoff structure, like that empirically found in trend equity, can be a particularly useful diversifier.

We explored two ways in which investors can incorporate trend equity into a traditional profile depending upon their objective.  Investors looking to reduce realized risk without necessarily sacrificing long-term return can fund their trend equity exposure with their traditional equity allocation.  Investors looking to enhance returns while maintaining the same realized risk profile may be better off funding exposure from both traditional stock and bond allocations.

Finally, we discussed the trade-offs associated with incorporating trend equity into an investor’s portfolio, including (1) the lumpy and potentially large nature of whipsaw events, (2) the inability to hedge against sudden losses, and (3) the costs associated with managing an active strategy.  Despite these potential drawbacks, we believe that trend-following equity can be a potentially useful diversifier in most traditionally allocated portfolios.

Bibliography

Freccia, Maxwell, and Rauseo, Matthew, and Villalon, Daniel, DC Solutions Series: Defensive Equity, Part 2.  Available at https://www.aqr.com/Insights/Research/DC-Solutions/DC-Solutions-Series-Defensive-Equity-Part-2.  Accessed September 2018.

Hsieh, David A. and Fung, William, The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers. The Review of Financial Studies, Vol. 14, No. 2, Summer 2001. Available at SSRN: https://ssrn.com/abstract=250542

Hurst, Brian and Ooi, Yao Hua and Pedersen, Lasse Heje, A Century of Evidence on Trend-Following Investing (June 27, 2017). Available at SSRN: https://ssrn.com/abstract=2993026 or http://dx.doi.org/10.2139/ssrn.2993026

Lempérière, Yves, and Deremble, Cyril and Seager, Philip and Potters, Marc, and Bouchaud, Jean-Phillippe. (April, 2014), Two Centuries of Trend Following, Journal of Investment Strategies, 3(3), pp. 41-61.

Page 2 of 3

Previous

Next

Powered by WordPress & Theme by Anders Norén