Introduction
In previous posts, we’ve explored how massive diversification serves as a crucial tool for outlier hunters—not only to provide correlation benefits in chaotic regimes but also to increase our chances of capturing rare market events. It’s the frequency of these outliers in our trade distribution that significantly enhances our long-term performance.
In this post, we’ll delve into a classic trend follower’s equity curve to see this ‘lifting power’ in action. At first glance, the equity curve of a highly diversified trend follower might appear stable and devoid of substantial volatility. However, a closer look reveals that the true lifting power resides in the outliers.
Unveiling the Power of Outliers
Before we start, I must emphasize that the results shown are derived from a massively diversified trend-following backtest, not from real trading. This theoretical model portfolio aims to convey the powerful messages of this post.
The model portfolio comprises 35 markets. While ideally, we aim to diversify across hundreds of uncorrelated markets, this example with 35 markets will still illustrate the magic of outliers. Each market is traded using 10 uncorrelated trend-following models each following the Golden Rules of “cutting losses short and letting profits run”, but specifically designed with different entries and exits to spread the benefits of outliers across the time series and reduce clustering effects of Outliers.
A Superficial Glance at the Portfolio Result Over 24 Years
Refer to Figure 1, which displays the uncompounded portfolio result for the 35-market portfolio using a standard $500 risk per trade. There were 11,252 trades made with 10 trend-following systems across 35 markets.
The red line represents the daily equity reading of the portfolio, and the blue line indicates the realized balance of the portfolio. The blue line, our capital line, is preserved at all times to limit drawdowns. In a positively skewed trade distribution, the red line tends to sit above the blue line, signifying unrealized equity.
Figure 1: 35 Market Equity Curve using 10 Systems Per Market
If you examine Figure 2, which is the last few years of the equity curve presented in Figure 1, you will see that at the end of the test period, where the red line reaches its peak, we were managing approximately $600K in unrealized equity. This substantial figure was predominantly driven by a successful trade in Cocoa. This example vividly illustrates the essence of trend following: the ability to let profits run and allow unrealized equity to grow to extreme levels when capturing significant market movements, often referred to as ‘riding the tsunamis of the seas.’
Figure 2: Zooming into the end of the Equity Curve of Figure 1
In trend following, the strategy focuses on identifying and capitalizing on significant market trends. The approach involves taking positions in the direction of the trend and holding these positions as long as the trend persists. This method inherently results in the accumulation of unrealized equity, particularly during periods of strong and sustained market movements.
The $600K in unrealized equity observed at the peak of the red line in Figure 2 demonstrates the power of this approach. It shows how, by not cutting profits short and allowing trades to run their course, trend followers can achieve substantial gains from a single market event. In this case, the Cocoa trade exemplifies a classic outlier event—a rare, significant market move that generates disproportionate returns relative to other trades.
This concept of unrealized equity is crucial for understanding the long-term success of trend following. Unlike realized profits, which are booked and can no longer contribute to future growth, unrealized equity continues to provide potential for further gains. It allows the portfolio to benefit fully from ongoing trends without the premature constraints imposed by closing positions too early.
Moreover, the presence of such significant unrealized equity highlights the importance of risk management in trend following. While the strategy allows for substantial gains during favorable market conditions, it also requires robust mechanisms to protect the accumulated equity (Realised Balance) from sharp reversals. Remember we are fanatics in preserving our hard earned realised capital. This is typically achieved through the use of trailing stops and other risk management tools that enable traders to lock in profits while still allowing for potential upside as the trend continues.
The example of the Cocoa trade and the $600K in unrealized equity at the end of the test period underscores the core philosophy of trend following: capturing and riding outliers to their full potential. It also reflects the inherent volatility and unpredictability of financial markets, where such outlier events can arise unexpectedly and contribute significantly to overall portfolio performance.
By zooming into the end of the equity curve and examining the role of unrealized equity, we gain a deeper appreciation of the mechanics and advantages of trend following. This strategy leverages the power of significant market trends, maximizing returns through disciplined risk management and the ability to stay invested in winning trades for as long as possible. This approach not only enhances long-term performance but also positions the portfolio to benefit from the inherent non-linear dynamics of financial markets.
Before moving on, let’s revisit the equity curve with additional context. In Figure 3, we add a regression line and a comparative benchmark—an equivalent-sized portfolio applied to a buy-and-hold strategy in the S&P SPY ETF over the same period.
Figure 3: Revisiting the Portfolio Equity Curve with a few Additions
At first glance, you might think it’s a standard equity curve seen in many backtests: a linear, ascending curve with minimal volatility. However, a deeper look reveals more. Notice how the portfolio result deviated from the regression line post-GFC (Global Financial Crisis) and only recently returned to it. This deviation underscores the impact of the “decade-long winter” for trend followers. Despite this, heavy system diversification minimized this impact, allowing the realized balance to continue growing. In fact, the realized balance stagnated for only 269 days, as marked on the chart.
The most crucial observation here is the lifting power of the portfolio when compared to the benchmark. The equity curve dwarfs the performance of the benchmark with significantly lower adverse volatility. This is the essence of the ‘magic of classic trend following.’
The acceleration of this lifting power is driven by the ensemble of trading models used in the example. Each model is designed to produce uncorrelated results per market, enhancing our chances of extracting an edge from outliers. This approach allows us to trade more correlated markets because the uncorrelated system suite breaks down the existing market correlations, amplifying the benefits of diversification.
Note to Readers: Many ask me why I don’t consider allocating a sizeable portion of capital to mean reversion rather than simply focussing on 100% trend following. This graph holds the reason. Why would I invest in a smooth equity curve that sits in line with or slightly above the benchmark comparison, simply to seek the best of all worlds (Trend Following plus Mean Reversion)? Given my understanding of what 100% Trend Following Portfolios can deliver under maximal diversification, why would I allocate a sizeable portion of that capital to a strategy that would dilute returns to keep things smoother? I would simply be compromising the ‘lifting power’ of my Trend Following Portfolio. The optimal deployment of your precious capital should always be towards further diversification in your hunt for Outliers.
Diving Under the Hood to See How Smooth it All Is
To truly understand the lifting power within our portfolio, we need to deconstruct the results observed in Figure 3 and examine the contributions of each of the 35 markets. Figure 4 provides a detailed view of the individual contributions to the total portfolio result, highlighting approximately nine significant outliers that have massively influenced the overall performance.
Figure 4: Examining the Portfolio Constituents and their Contribution
It’s important to emphasize that while this example focuses on 35 markets, there are many more outliers within the portfolio composition than those featured here. In this sample, there are over 20 material contributions that drive performance, as illustrated by a histogram of trade results. If we expanded this to 300 markets using our models, the frequency of outliers would remain approximately 5-10% of our trade results, demonstrating the immense potential impact from expanded market diversification.
Returning to Figure 4, we see that when peering under the hood, the equity curve is actually far from smooth. The apparent smoothness in the compiled portfolio result arises from the way these contributions aggregate due to their uncorrelated properties. The significant lifting power in the portfolio comes from the non-linear contributions of these outliers, massively amplifying the long-term wealth of the portfolio.
Peering Into Significant Outliers
Now, let’s dive deeper into the significant outliers within the series, focusing on seven illustrative examples. Each of these anomalies is unique and explosive in character.
In Figure 5, we observe the performance of Cocoa over the past 24 years using 10 trend-following models. Below the equity curve, a price chart shows how price movements correlate with performance results. For 23 years, Cocoa hardly contributed to portfolio growth, but then, like a tsunami, we see the mother of all outliers, amplified by our 10 trend-following models.
Figure 5: The Mother of Outliers: Cocoa
Next, in Figure 6, we see an extraordinary contribution from Copper between 2004 and 2006, driven by a perfectly formed trending price series with limited whipsaws. Since then, the market has been relatively dormant.
Figure 6: The Copper Bonanza: High Grade Copper
In Figure 7, we examine an explosive outlier in Corn between 2021 and 2022, with additional lesser outliers in 2011/2012 and 2008/2009. Our systems were able to extract more value from the outlier in 2021 and 2022 than from previous outlier regimes.
Figure 7: The Power of Corn: Corn
Figure 8 showcases a massive outlier in Crude Oil between 2021 and 2023, associated with the bull run following its sharp price drop into negative territory in 2020.
Figure 8: The Crude Elephant: Crude Oil WTI
We can’t forget Cotton, as seen in Figure 9, which highlights a massive outlier event in 2011.
Figure 9: We Can’t Forget Cotton: Cotton #2
Soybean Oil experienced two large outliers over its time series, with the most significant contribution in 2021/2022 and a lesser contribution in 2007/2008, as shown in Figure 10.
Figure 10: Soybean Oil
Finally, Figure 11 presents the famous Orange Juice (OJ) outlier, which continues to run today with many models capturing its trends.
Figure 11: The OJ Squeeze: Orange Juice
These massive contributions highlight the unpredictable nature of outliers. They can arise at any moment without warning, driven mostly by endogenous factors within the financial markets themselves. While we can often rationalize their occurrence in hindsight, predicting these events in foresight is nearly impossible. Yet, these material events significantly contribute to overall portfolio performance.
By examining these figures, it becomes clear that the lifting power of outliers is a fundamental component of successful trend-following strategies. Understanding and embracing this non-linear dynamic is crucial for achieving robust, long-term investment performance.
Stripping Out the Material Contributions from Outlier Events
Now that we understand what drives the lifting power of our portfolio results—namely, the non-linear outliers arising in the tails of the return distribution—let’s examine what happens when we tame these contributions.
To do this, we’ll compare and contrast a portfolio of 28 markets (excluding the major outlier contributors Cocoa, Copper, Corn, Crude Oil, Cotton #2, Soybean Oil, and Orange Juice) against the full 35-market portfolio. Refer to Figure 12 for the portfolio equity curve comparison.
Figure 12: Portfolio Equity Curve Comparison (35 Mkts Vs 28 Mkts Stripped of dominant Contributors)
In Figure 12, you’ll notice that portfolio performance increases by a whopping 65% due to the inclusion of 7 markets with massive outliers. Now of course we would expect a reduction of total performance of the 28 Market portfolio given that it is seven markets short. We would expect at least a 25% increase in the 35 market portfolio, but the 60% increase is testament to the non linear impacts that have been thrown away in this process. We not only have lost significant lifting power, but we have also smoothed the result in the process. The 28-market equity curve appears far smoother, with a Sharpe Ratio of 2.66, suggesting to the naive reader that it might be a better portfolio for compounding. However, this is misleading. The raw 35-market portfolio achieves a far higher uncompounded equity result despite having a lower Sharpe Ratio of 1.80. This discrepancy arises because the Sharpe Ratio penalizes beneficial volatility.
Note: This is not to say the Outliers don’t exist in the 28 Market Portfolio. They still do (Refer to Figure 12A), but these Outliers are of lesser material positive impact to the overall portfolio. The result is that the overall portfolio exhibits a far smoother result with higher Sharpe. Not surprising really considering that we have removed a substantial portion of the beneficial volatility in this process.
Figure 12A: Contributing Equity Curves of 28 Market Portfolio
We won’t delve into the shortcomings of the Sharpe Ratio here, as this has been discussed in previous blog posts. Instead, let’s focus on a critical aspect of trend following: the debate between letting profits run unbridled, as done in classic trend following, versus approaches that aim to tame volatility through volatility targeting or correlation management, continuously adjusting the portfolio to optimally allocate capital.
This is the core issue: markets do not offer opportunities at all times. The dominant drivers of performance are unpredictable anomalies that are not always present. By continuously adjusting portfolio volatility through dynamic position adjustments based on volatility targets or correlation analysis, you risk tampering with the outliers that are key to a trend follower’s success. The analysis here makes it clear that tampering with unrealized equity can significantly hinder long-term wealth prospects.
The central message is straightforward: do not tamper with your unrealized equity. It drives your betting system and concentrates your efforts towards capturing outliers.
To further illustrate this point, let’s look at the power of histograms. Figure 13 demonstrates the impact on the portfolio’s positive skew when we remove the major outlier contributors.
Figure 13: Histogram of Results for 35 Market Portfolio Vs 28 Market Portfolio
Figure 13 supports the argument that tampering with unrealized profits can drastically reduce long-term wealth prospects and diminish the positive skew of your portfolio—a hallmark of classic trend following and a significant reason for its effectiveness as a diversifier in traditional portfolios.
By examining these histograms, it becomes evident that maintaining the integrity of your unrealized equity is crucial. Any attempt to manage or tame it can erode the lifting power that outliers provide, ultimately weakening the overall performance of your portfolio.
This detailed analysis underscores the importance of embracing the non-linear dynamics that outliers bring to a trend-following strategy. By doing so, you harness their full potential, driving robust long-term investment performance and achieving superior diversification benefits.
Conclusion
The central message is clear: outliers are the driving force behind the lifting power of trend-following portfolios. By maintaining a diversified portfolio and allowing profits to run unbridled, we can capitalize on these rare but significant events. Tampering with unrealized profits through continuous adjustments based on volatility or correlation can diminish the portfolio’s long-term performance. The key to success lies in embracing the non-linear contributions of outliers, which significantly amplify long-term wealth and offer a unique diversification benefit to traditional portfolios.
Reflect on the histograms in Figure 13, which illustrate the positive skew of the 35-market portfolio compared to the 28-market portfolio. This analysis underscores the profound impact of outliers and reinforces the value of classic trend following in achieving robust, long-term investment performance.
Addendum
I received feedback on this post from a good friend suggesting that the outliers seemed to dominate in the long direction. To illustrate this effect, I prepared the histograms in Figure 14 below.
A question that might arise is whether we should only consider trading this portfolio in the long direction.
As Figure 14 shows, there are still outliers in the short trades, though they are not as pronounced as those in the long trades. It might be tempting to trade long only, but I don’t recommend this due to the significant correlation benefits that short trades provide to the overall portfolio. While short trades are generally harder to capitalize on with symmetrical systems, enduring trends often present more manageable trades with significant extensions.
Additionally, markets do not always rise; they can also decline sharply. Excluding short trades could increase the warehoused risk in your portfolio, as many return streams may suddenly become positively correlated at the worst times. This can lead to an increase in negative skew, even with the application of regime filters.
Figure 14: Histogram of Long Versus Short Trades for the 35 Market Portfolio