A L-U-V-Wy Recovery

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Summary

• There has been considerable speculation as to the shape of the market’s recovery.
• Practitioners have taken to using letters as short hand for the recovery they forecast. Whether the market makes a fast V-shaped recovery, a slower U-based formation, a W-style double-bottom, or an L-shaped reset is heavily debated.
• As a path dependent strategy, trend following will behave differently in each of these types of outcomes. More specifically, a given trend specification may or may not be successful for a given drawdown depth, speed, and shape.
• In this commentary, we use Brownian Bridges to simulate out different market recovery paths. Over these paths we run different trend following models, summarizing their performance.
• We find that success is highly outcome specific. For investors with a particular view (or probability-weighted set of views) as to how recoveries will play out, these results may help guide their choice of trend-following model.
• For investors without strongly held views, we believe these results continue to reinforce the importance of a diversified approach.
  

The extreme nature of the recent equity market sell-off means that your mileage with trend-following will have varied dramatically depending upon the models you employed, the assets you traded, and even when you rebalanced your portfolio.

In this commentary we want to ask a bit of a different question: how might we expect different trend-following strategies to perform going forward?  What happens, for example, if we really did hit market bottom already and we experience a rapid V-shaped recovery?  Or, conversely, what happens if we drift lower into a perpetual market malaise?

In this commentary, we aim to explore some of these questions by simulating different drawdown and recovery scenarios.  Specifically, for a given drawdown depth and speed we will trace out four distinct market patterns:

• V: The market reaches its max drawdown and then rallies back to peak value.
• U: The market reaches its max drawdown, meanders sideways for a bit, and then rallies back to its peak value.
• W: The market reaches its max drawdown, retreats up to 75% of the peak value, falls back to the max drawdown, and then rallies back to the peak.
• L: The market reaches its max drawdown after and then meanders sideways.

For each scenario (i.e. drawdown depth, speed, and shape) we simulate 25,000 market paths.  We attach these paths to the S&P 500’s returns prior to April 3^rd, 2020.  We then run a number of different long/flat trend-following strategies and report the median forward performance achieved over the simulations.

Drawdown levels are assumed to be total drawdown from all-time highs (measured as of market close).  At close on April 3^rd, 2020, the market was at a -26.2% drawdown.

Note that forward performance is based upon market levels as of market close on April 3^rd, 2020.  From that point, the market would need to rally 35.5% to return to all-time highs.

A Bit More Detail

If you’re interested in a bit more of the technical detail, read on.  Otherwise, feel free to skip to the next section for the results.

To achieve our desired market shapes, we employ Brownian Bridges, assuming zero drift and constant volatility of 25%.  This is somewhat unrealistic, as markets exhibit jumps and stochastic volatility, but we’re looking for “directionally correct” not “perfectly precise” with this analysis.

For a given N-day drawdown, we draw each pattern as:

• V: The market reaches its max drawdown after N days and then rallies back to peak value after N+33 days.
• U: The market reaches its max drawdown after N days, meanders sideways for N days, and then rallies back to its peak value in N+33 days.
• W: The market reaches its max drawdown after N days, retreats up to 75% of the peak value after N/2 days, falls back to the max drawdown after N/2 days, and then rallies back to the peak after N+33 days.
• L: The market reaches its max drawdown after N days and then meanders sideways for N days.

Note that the extra +33 days are to account that market peak occurred 33 trading days ago.

As an example, if we have a V-shaped recovery with a 40% drawdown over a 21-day period, we assume the market falls from 2481.9 to 2017.6 over a 21-day period, and then recovers from 2017.6 to 3362.7 over a 54-day period.

Using these assumptions, we plot example paths for each shape below.

Source: Tiingo.  Calculations by Newfound Research.

Note that, by construction, all the paths seem to converge at the same drawdown level at t=751.  While this point represents the drawdown target (in this case, 40% from the S&P 500 peak), it does not represent the maximum drawdown that is possible for a given path.  Clearly, the generated V, U, and L paths all hit much lower levels.

The Results

The tables below are sorted by target drawdown level.  For a given max drawdown, we then have tables for V-, U-, W-, and L-shaped recoveries.

Each row of the table reflects the speed of the recovery in trading days.  We range the speed from 7- to 378-days (approximately 1.5 years).  Please note that this speed does not reflect the span of the entire recovery.  For example, for a U-shaped recovery taking 126 days, we assume 126 more days of losses, 126 days of sideways performance, and 159 days for the recovery (please see technical section above for more specific details).

Before reviewing the results, we cannot stress enough that the precision of decimal places should not be mistaken for accuracy.  The goal of this exercise is to develop a broad-based, directional comprehension of how trend signals might behave under given market patterns.  There is no reason to believe the market will necessarily follow any of these patterns.  Furthermore, we report only a median performance number, when in reality there are 25,000 simulations with distinct – and sometimes quite wide ranging – outcomes.

Nor do these tables capture drawdown avoided, which is often an important consideration of those using trend models.

(Note that we use moving-average-crossover signals here rather than time-series momentum or price-minus-moving-average models.  There was no particular reason for this choice other than we already had some code written up that made this analysis easier!  While there is not a direct 1-for-1 mapping between these signals, a 12-month time-series momentum signal would likely be similar to the 20×100 or 50×150 results).

Nevertheless, with that out of the way, let’s dive into the results.

30% Drawdown

40% Drawdown

50% Drawdown

60% Drawdown

Some broad thoughts:

• When reviewing these tables, it is important to recognize that not all of the outcomes are necessarily high probability events. For example, the 200×400 system would have a further -40% loss if the market hits a total drawdown of 60% over the next 7-63 days.  Similarly, the 10×30 system would have a 100%+ return if the market fell to a 60% drawdown and then completely recovered in a fast V- or U-shaped recovery.  We’ll leave to the reader to assign their own probabilities to these types of outcomes.
• For a shallow and fast V-shaped recovery, both very fast and very slow signals appear to work. Very fast signals have already turned off and will turn on quickly enough; very slow signals are still on and therefore won’t ever turn off!  Intermediate signals, however, risk flipping off near the lows and staying off during the subsequent rally.
• If a V or U persists for too long, however, the latent volatility (here assumed to be a static 25%) can cause issues for fast-moving models, as the long-term trend is too shallow compared to the short-term noise. We do not show it hear, but the more drawn-out the drawdown and the higher the latent volatility, the more likely that the short-term models will be whipsawed.
• In deeper, U-shaped recoveries, intermediate-term models (e.g. 20×100 or 50×150) shine. The depth of the drawdown gives them enough time to turn off and the bottoming process gives them enough time to normalize and re-enter as the market turns back up.  Short-term signals also seem to do quite well, but obviously require much more trading and we do not explicitly account for transaction costs here.
• Instead of the usual gradient, the tables for W-shaped recoveries exhibit many more “islands” where a given model and speed will either really work, or really fail, compared to peers around it. This style of recovery is where a model risks being double whipsawed or, conversely, missing both drawdowns and catching both upsides and therefore capturing more than just the recovery back to all-time highs.
• L’s are pretty much a loser for everyone across the board, which is no real surprise. Without shorting, the best we can do is try to protect.  Here the results are all about, “how quickly did you get out” and “were you able to avoid whipsaw as the market went sideways along the bottom.”  Fast models, which are already out, will likely protect more on the immediate downside, but risk being whipsawed in a prolonged sideways market.  Slower signals, on the other hand, may do better at avoiding whipsaw in such a scenario.
• For the horizons we’re looking at, super long-term trends don’t seem to add much value unless the drawdown is very deep and prolonged. This aligns with all the research we’ve done in the past that demonstrates that the convexity of a trend following system must be measured over a horizon that is similar to the model speed.  Put rhetorically: why would we ever expect a slow-moving trend system to react to the fastest equity sell-off in U.S. history?

Conclusion

In this note, we explored the potential outcomes for simple long/flat equity trend models given potential V-, U-, W-, and L-shaped market recoveries.

The results come as no surprise: as a path dependent strategy, the depth of the market drawdown, time horizon, and recovery shape all play a critical role in determining the success or failure of a given model.

For investors with a view as to how a recovery may play out, these tables might provide some guidance as to the types of trend following models they might look to employ.  Even a probabilistic view could be used as a weighting mechanism for several systems (being careful to consider correlation among those systems, however).

For investors who do not hold a strong view, however, we believe these tables continue to reinforce the importance of a diversified approach.

Corey Hoffstein

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.