The Lifting Power of Outliers

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

The Many Paths of Uncertainty

As a trend follower, a key aspect of our approach lies in the way we approach risk. In fact we prefer to call ourselves risk managers as opposed to speculative traders.

We view risk as being far wider than what has been reflected by the historical record and treat risk as comprising two aspects.

The risk that resides in the historical record which we can see reflected in our backtests and the risk associated with the many possible paths that reside outside this single historic path which is absent from our backtests.

We understand that the possible risks that lie ahead of us in the many possible future paths, exceed the known risks that we have experienced from our limited past track record. We therefore adopt the premise that our worst drawdown is always ahead of us.

The following diagram provided by @waitnutwhy from Twitter Sphere illustrates this notion.

If we consider our history, there has been a single path taken to where we are today and a single risk sequence along that path…but from where we are today looking into the void of the future there is no such guiding sequential record. The future is one of many possible paths.

Now most traders focus on what history has revealed to us through their back-tests and adopt such principles that the future is influenced by events of the past, such as a prior equilibrium level, a prior support level, a past mean value or an historic intrinsic value. They therefore adopt a ‘convergent premise’ that price is likely to revert to that historic value….but as we can see in this braided possible view of future paths, a replication of the single historic path is exceedingly unlikely over the longer term. You see in a complex adaptive system, the only real guarantee that we have is that over an extended future, the far more likely proposition is that the future will be significantly different from the past.

This ubiquitous feature of a different future from the past is common to all complex adaptive systems where the agents that make up that complex system adapt and the system itself develops new efficiencies based on emergent structures that unfold through a systems evolution. The notion of system stationarity, or a repeated history, in the context of probabilities assigned across an almost infinite array of possible future paths, highlight the fruitlessness of trading systems that assume history will repeat or that capitalising on repeating patterns will lead to long term wealth.

By far the greatest degree of change to an unfolding system lies in the ‘improbable events’ associated with future paths that have never been experienced in the past. These ‘fat tailed events’ are the real game changers and where the fates of traders are determined by single ‘windfalls’ or ‘crushing defeats’.

As a diversified systematic trend follower, we treat this alternative array of possible risk sequences found in the infinite array of possible future paths very seriously. It is within these unforeseen events where our outliers reside that make our game so worth it, but to experience them, we have to survive the battering received from an almost infinite array of unfavourable events found in our future path.

In fact, we totally disregard the historical sequence of a particular market as being significant to our trading models. We do not undertake backtests to develop any opinion of expectation regarding the future, but rather we undertake backtests to ‘stress test’ our assumptions using a known historic data stream.

You see we treat all markets equally through our method and in our bet size allocation towards each market. Our method simply cuts losses short at all times, uses ATR based stop, trailing stop and position size calculation to normalize our approach to every market and we treat them all equally in terms of their possible risk contribution for the future.

What this actually means is that our method is configured to address a far greater possible array of future risk paths than alternative methods which simply configure their systems to what has been presented in the past.

Now many traders fall under the illusion that what history has demonstrated over their lifetimes is reflective of all possible risks….however the following excellent walk-through of the Dow Jones over the past 125 years demonstrates that the past 50 years or so of our memory is only a small sliver of a far greater representative sample of risk paths that have been delivered by our historical record alone.

So that video gives you a broader appreciation of the risks that lie in an extended scope of our single historic path.  So just imagine the virtually unlimited possibilities that the many paths of ‘uncertainty’ will bring for the future.

How confident are you now about the future longevity of your convergent trading models?

Trend Followers may be accused of having simple models….but where we shine is in our very serious treatment of risk which is found wanting with alternative approaches.

Trade well and prosper.

Challenging the Conventional Wisdom of Statistics in Complex Adaptive Systems – Beware of Idealised Models

In the ever-evolving landscape of financial markets, the application of traditional statistical models, such as the Central Limit Theorem (CLT), often proves to be inadequate for capturing the complexities of complex adaptive systems (CAS). These systems, which are a hallmark of financial markets, defy the conventional assumptions of linearity, independence, identical distribution, and stationarity, which underpin many statistical theories. This incongruence arises from the unpredictable and open-ended nature of CAS, which stands in stark contrast to the idealized conditions assumed in these models.

A prominent manifestation of this discordance is observed in the behavior of tail events within financial markets. These critical events, crucial in the realm of risk management, challenge the norms established by traditional statistical approaches. The CLT, a cornerstone in understanding data distribution and guiding diversification strategies, presupposes a normal distribution across large data sets. This presumption, however, is not reflective of numerous real-world systems that do not conform to the criteria of being closed or enduring systems.

The Cauchy distribution exemplifies the divergence from traditional statistical expectations. Characterized as a continuous probability distribution without a defined mean or variance, it demonstrates non-normal, heavy-tailed features that contradict the assumptions of the Central Limit Theorem (CLT). When variables conforming to the Cauchy distribution are accumulated, the result is not a normal distribution, but rather a preservation of the Cauchy distribution’s distinctive heavy-tailed nature. It’s important to note that this example does not imply a precise understanding of the ideal distribution model for capturing the tail characteristics of liquid financial markets. Instead, it highlights that certain distribution types prevalent in chaotic environments do not align with the expectations of a normal distribution, particularly when considering large sample sizes.

Complex adaptive systems, characterized by their non-linear interactions, interdependence, varied distributions, non-stationarity, and emergent behaviors, further accentuate the inapplicability of the CLT in comprehending or forecasting their dynamics. This mismatch necessitates a critical reevaluation, if not an outright revision, of the theoretical frameworks commonly employed in developing diversification strategies for investment portfolios.

While traditional statistical theorems like the CLT have their place, their application must be contextualized and scrutinized, particularly in financial markets where exceptions to these rules are not uncommon. A risk manager must remain vigilant and aware of these exceptions when applying these theoretical principles. This article contends that the relevance of the CLT is more pronounced in scenarios involving stable, predictable distributions. However, its applicability diminishes in situations characterized by tail events. For instance, in the context of Classic Trend Following strategies, which primarily target trends located in the tail regions of distributions, the decision to diversify should not be overly reliant on theorems that may not be pertinent to the inherently chaotic nature of these markets.

The unpredictability of the future is magnified in complex adaptive systems, which are not closed systems with a static population of data points. Instead, these systems are dynamic, with their populations continuously evolving, rendering traditional benchmarks like mean and variance as fluid, not fixed, parameters. Different market regimes may necessitate varying degrees of diversification. To presume an optimal level of diversification is to fall into the trap of overgeneralization and potentially risky assumptions. For risk managers, adhering to these assumptions without considering the unique nature of their operational environment can be detrimental to the success of their strategies. The overarching conclusion is that during periods of regime change, conventional statistical wisdom might not only be inadequate but could also lead to misguided decisions in risk management, particularly for portfolios that are not adequately diversified.

Trade well and prosper.

Let’s Consider Skew

As diversified systematic trend followers, we just love the positive skew of our trade results….but to explain why, we need to dig quite deeply into what skewness means exactly.

It is defined as a measure of asymmetry of a trade distribution about its mean and is expressed by the following formula.

Now it is important to note that the formula above assumes that a particular distribution can be categorized as having a single mean and a single standard  deviation around this mean, which is an inherently Gaussian assumption. We ‘as realists’ however understand that over large data samples, ‘real markets’ and ‘real trade results’ are more complex than that, and may frequently comprise multiple means and varying standard deviations that reflect different market conditions. However, despite this failing of the skewness formula when being applied to real distributions of complex adaptive systems such as these financial markets, we can simplify skewness to refer to the asymmetry between the magnitude of average wins and the average losses of the distribution of trade results.

Just don’t get too prescriptive in your use of these damned single measure statistics of theoretical distributions.

For example where our average winners are far greater than our average losers, our trade distribution histogram plots as a distribution with clear positive skew. If our average winners were far smaller than our average losers, then our trade distribution would plot with clear negative skew. The direction of the tails of these asymmetric distributions signify their ability to address the risk arising when real markets start to display exotic fat tailed behaviour.

What we mean is that the extremal value of a skewed distribution such as the maximum loss or the maximum win signifies where bias in the trade lies when exposed to the Power Laws found in ‘fat tailed’ environments. When conditions extend beyond the Gaussian envelope into the exotic tails of a distribution, events considered to be far less frequent actually become far more frequent than what a Normal distribution would imply. So for negative skewed systems, large losses are far more frequent than anticipated and for positive skewed systems, large wins are far more frequent than anticipated.

Chart 1 below reflects a trade distribution with positive skew. There is a long right tail to the distribution of trade results. While the vast proportion of trades are small losses, you can see that the exceptional winners result in the average win being far higher than the average loss. This feature creates a positive skew to the distribution of trade returns in this example.

Chart 1: Histogram of Trade Results of a Trend Following System with Positive Skew

The distribution of trade results in Chart 1 above applies to a trend following system comprising 237 trades undertaken between 1st January 2000 to today with an equity curve that is displayed in Chart 2 below.

Chart 2: Equity Curve of a Trend Following System comprising 237 trades 

Now the reason that we like positive skew of our trade results is that under non-linear market conditions, the beneficial outlier can exponentially outweigh all the small losses associated with our trend following technique that cuts losses short at all times but lets profits run. This can be attributed to the Power Laws that reside in ‘Fat Tailed market environments. Trade events in the tails of the distribution can be many orders of magnitude greater than the trade events that lie within more ‘normal’ bounds of the trade distribution’.

Whether a system has positive or negative skew is important when considering the unforeseen risks associated with ‘fat tailed’ environments.  A system with negative skew provides a ‘risk signature of weakness’ where the occasional large loss, under ‘fat tailed’ non-Gaussian market conditions can turn into exponentially larger losses than expected, particular when large losses become consecutive in nature.

Positively skewed systems on the other hand demonstrate through their risk signature that they are ‘robust’ and do not leave themselves open to the possibility of large losses. By always cutting losses short there is no exponential increase in losses when conditions become unfavorable as all adverse tail events are excluded from the trade history. There may be more small losses, but these events are not exponential in nature. Of course, by letting profits run, the trend follower leaves themselves open to the possibility of ‘exponential profits’ associated with favorable tail events.

Now that we understand the significance of skewness to non-linear risk events,  lets now turn to the question of how we accurately measure skewness? As skewness is often incorrectly applied by the statistician.

How to Measure Skewness

The first point we need to understand when assessing the skewness arising from trend following systems is that we need to eliminate effects in the distribution that may arise from money management methods deployed by the system.

For example the trade results of the trend following system described in Charts 1 and 2 display compounded effects. In this system we applied a 1% trade risk of equity for each trade. This means that the trade results include the impacts of compounding in their signature. So we cannot use $ profit or $ loss per trade as a basis to calculate skew as these raw results will include effects of compounding. Rather we need to apply a method that normalises the trade results to exclude the impacts of money management method to ‘truly see’ the real skew in the system results.

So in the following examples we will be using a % of equity as a method to normalise the trade results. We could also apply an ATR or R multiple for each trade as well to achieve the same outcome.

The following table displays the skew of various methods applied to the trade results.

Now the question we need to ask when referring to the skew, is which result is ‘correct’?

Well we need to understand that all these different interpretations of skew arise from the same system result. The only difference is in how these results are consolidated.

The ‘correct’ result is actually represented by the ‘Trade Results’ column of 1.32. This skew calculation reflects the actual asymmetry of all trade results.

The Daily results and the Monthly Results column compound the skew by virtue of the fact that these methods consolidate trade results into a daily or monthly record. The consolidation process actually compounds the skew of positively skewed systems. The reason for this compounded nature through consolidation is that we are altering the skew of the distribution through consolidation. With classic trend following models outside periods of ‘Outlier’, most of our trades are losses. As we consolidate these losses the relative disparity between our Outliers and linear sequence of losses becomes more extreme leading to higher overall skew in the distribution. This effect compounds the asymmetry in the series.

We therefore need to be particularly careful in how we use skew to compare between alternatives. Ensure that you choose a particular method and stick with it. Unfortunately when assessing the skew between different Fund Managers based on available data, you sometimes only have monthly return data to work with and cannot determine the ‘real skew’ of the method….but it helps to be aware of these issues arising from the way we measure skew.

Anyway….enough of the rambling. Let’s hope you just don’t skew things up the next time you use it.

Trade well and prosper.

Navigating the Unpredictable Seas of Financial Markets

In the world of financial markets, where unpredictability and volatility are the norms, achieving long-term success is a major challenge. These markets are filled with potential risks and opportunities, making the ability to navigate through uncertainty an essential skill for investors and traders aiming for growth and stability.

Diversified systematic trend followers are a group of skilled market participants who have mastered the art of dealing with this uncertainty. They’ve developed strategies that turn the often erratic behaviour of the markets into opportunities for consistent long-term wealth growth. Their approach is methodical and disciplined, relying on thorough analysis and a strong commitment to their trading process.

This post aims to break down the strategies and core principles behind the success of these trend followers. We’ll take a close look at their methods, understanding why they stand out in the competitive world of investing. The process of diversified systematic trend following is about not just surviving but thriving in the ever-changing financial markets.

The Core Principles of Trend Following

 

Understanding Market Dynamics

At the heart of a trend follower’s strategy is a deep understanding of market dynamics. Trend followers understand that financial markets are far more than mere aggregations of numbers and trends; they are intricate adaptive systems, continuously evolving and responding to a variety of influences. These systems are influenced by a myriad of factors – economic, political, psychological, and more – each contributing to the market’s behaviour in unique and often unpredictable ways.

One key aspect that trend followers are particularly attuned to is the presence of fat tails in market data distributions. Unlike a Gaussian (or normal) distribution, which predicts a certain range of outcomes with a high probability, fat tails indicate a higher likelihood of extreme outcomes, both positive and negative. This means that significant market events, such as crashes or booms, are not just rare anomalies but are more common than traditional financial theories would suggest.

This understanding of fat tails is a pivotal element in the strategy of trend followers. It enlightens them to the fact that markets are capable of moving in more extreme ways than what is typically predicted by standard financial models. Unlike the average investor who might view market movements as a steady and predictable rhythm, trend followers are keenly aware of the inherent uncertainty and the irregular pulse of the markets. They recognize that it’s this unpredictability, rather than a consistent pattern, that often gives rise to significant risk events.

Traders who neglect the fat tail risks inherent in financial markets risk severe consequences due to underestimating the likelihood and magnitude of extreme market movements. Leveraging positions without considering these outliers can lead to amplified losses. This, coupled with potential liquidity issues and psychological impacts, can result in substantial, sometimes irreversible, losses. The compounded effect of these risks over a series of trades deplete capital reserves significantly. Moreover, standard hedging strategies might prove inadequate against these extreme events, leaving traders vulnerable and unprepared for market volatility. Such oversight can lead to a risk of ruin, where traders find themselves unable to recover from heavy losses.

For individuals aspiring to a long and successful trading career, spanning thousands of trades, the elimination of irrecoverable events from their trading record is imperative. The adage ‘cut losses short and let profits run’ transcends being merely a well-known trading maxim; it embodies the very foundation of a sustainable long-term investment strategy. This principle emphasizes the critical importance of prioritizing survival over mere performance. It’s about striking a balance between prudent risk management and the pursuit of growth, ensuring that each trade contributes positively to a robust and enduring trading journey. This approach isn’t just a tactic, but a strategic mindset essential for anyone committed to navigating the complex and often unforgiving realm of financial markets with resilience and success.

Trend followers perceive market irregularities and extreme movements not as inevitable setbacks, but as opportunities ripe for strategic exploitation. They employ specific tactics designed to mitigate the likelihood of adverse trading outcomes, effectively neutralizing potential negative consequences. With the downside risk addressed, they are then poised to capitalize on the financial markets’ tail events, seizing the substantial upside potential they offer. These rare but powerful market shifts are seen as valuable chances for significant gains. Their approach to both risk management and seizing opportunities is distinct and forward-thinking. Rather than confining their strategies to average market conditions, trend followers expand their focus to encompass and proactively prepare for market extremes. This comprehensive preparation allows them to navigate through market volatility, transforming potential risks into rewarding opportunities.

By adopting this approach, trend followers develop strategies that are not just robust but are also adaptable to sudden and significant market shifts. These strategies are designed to do more than just withstand the shock of extreme market events; they aim to exploit these occurrences. The goal is to position their portfolios in a way that not only mitigates potential losses in volatile times but also capitalizes on the opportunities these times may present.

In essence, trend followers transform what many see as market chaos and unpredictability into a landscape ripe with potential. They navigate the markets with a perspective that views uncertainty not as a deterrent but as an integral and valuable aspect of the financial ecosystem. This perspective allows them to identify and seize opportunities that others, constrained by conventional models and the fear of volatility, might overlook or avoid.

When it comes to managing risk, trend followers treat the inherent uncertainty of financial markets as a call to go beyond traditional risk assessment methods that simply tackle the bulk of the market distribution of returns. They utilize risk management tools and techniques that are specifically designed to handle the potential of extreme events .

In seeking opportunities, the knowledge of fat tails equips trend followers to strategically align themselves to benefit from significant market movements. They maintain a vigilant eye for indications of markets trending toward an extreme. These signs are not seen as warnings, but as potential gateways to profitable positions, aligning perfectly with the trend following strategy. By doing so, they turn the uncertainty and irregularities of market behavior into profitable opportunities, effectively riding the waves of market extremes.

The recognition that financial markets are complex adaptive systems with fat tails is a cornerstone of the trend follower’s worldview. It shapes their entire approach to trading, from the way they manage risk to how they identify potential opportunities, setting them apart from traditional investors who might rely on more conventional market models.

Embracing Non-Ergodicity

Trend followers are acutely aware that financial markets exhibit a non-ergodic nature. This concept signifies that while the markets, on average, may suggest a certain level of stability and predictability, the experience of individual market participants can vary dramatically. In essence, the aggregated outcomes across many participants or over a long period might show one trend, but any single participant’s experience might be starkly different, and often more volatile.

This critical understanding of non-ergodicity fundamentally shapes the way trend followers approach the markets. It informs them that the aggregate performance metrics of the market do not necessarily apply to individual portfolios. Therefore, they do not get swayed by the illusion of stability painted by average returns. Instead, they focus on the potential for extreme deviations that these averages can mask.

Non-ergodic processes in financial markets are characterized by the presence of irreversible events that can have a lasting impact on a trader’s career. These events, such as a substantial loss leading to risk of ruin, act as definitive full stops in a trader’s journey. In a trading career that ideally spans thousands of trades over many years, even a single irreversible event can abruptly end the possibility of future trading, thereby nullifying the potential benefits of compounding gains over time.

Compounding is a powerful force in finance, where small, consistent gains can accumulate into substantial wealth over an extended period. However, this only holds true if the trader remains active in the market and can continue to make trades. An irreversible event like a total capital loss breaks this chain of compounding, effectively preventing the trader from capitalizing on future opportunities.

The harsh reality of financial markets is that they are replete with such non-ergodic characteristics. A stark consequence of this is that only a small percentage of market participants manage to survive over the long term. The markets are indeed strewn with the metaphorical “corpses” of traders who failed to prioritize survival over performance. Many traders, lured by the prospect of high returns, overlook the critical importance of managing risks and protecting their capital. In doing so, they expose themselves to the possibility of catastrophic losses, which can abruptly end their trading careers.

This phenomenon underlines a crucial principle in trading: survival must take precedence over performance. Without survival, there is no platform for performance or the realization of compounded returns. Successful traders are those who not only seek profit but also rigorously manage risk to avoid the pitfalls that lead to irreversible consequences. By doing so, they ensure their longevity in the market, which is the true foundation for building compounded wealth over time.

Acknowledging this disparity, trend followers prioritize risk management as a core component of their strategy. They know that focusing solely on chasing high returns without considering the individual risk can lead to significant, and sometimes irreparable, financial damage. By concentrating on risk management, they aim to ensure their survival through various market conditions, especially during periods of high volatility or downturns.

This emphasis on risk management over mere return chasing does not mean that trend followers avoid seeking profits. Rather, they approach profit generation with a lens that always considers the risk involved. They strive to create a balance where the pursuit of returns does not expose them to disproportionate risk, particularly the kind of risk that could lead to significant losses or even the total erosion of their capital.

In practice, this approach often involves deploying strategies that are resilient in the face of market shocks and capable of adapting to changing market conditions. Trend followers diversify their investments across various asset classes, deploy system diversification to force uncorrelated properties into their portfolio and typically deploy small bets and stop-loss orders to limit potential losses and prevent any return stream compromising their ambitions of long term wealth. They also tend to be cautious with the use of leverage, understanding that while it can amplify gains, it can also magnify losses, especially in non-ergodic environments.

By embracing the non-ergodic nature of the markets, trend followers adopt a holistic and realistic view of market dynamics. They recognize that what works on average for the market does not necessarily work for the individual investor, especially in the short term. This insight drives them to craft strategies that prioritize the longevity and stability of their investments, ensuring they can weather the market’s ups and downs and emerge profitable over the long term.

The Dualistic Nature of Trades

In the world of trend following, every trade is inherently seen as having two faces: the potential for profit and the risk of loss. This dualistic nature is a fundamental concept that trend followers rigorously apply to every trading decision. Unlike traditional trading methods that might overly focus on the potential returns, trend followers adopt a more balanced view, giving equal importance to the risks involved.

This balanced approach is rooted in the understanding that every trade, regardless of its apparent promise, carries with it an inherent risk. Trend followers, therefore, meticulously analyze both the upside and downside potential of each trade. They employ conditional probabilities to project not just the potential gains, but also to calculate the likelihood and extent of potential losses over thousands of trades.

For instance, a trend follower might consider a trade with a high potential return. Rather than diving in based solely on the attractive profit margin, they will also assess the probability and impact of a loss. If a trade has, say, a 60% chance of delivering a significant profit but a 40% risk of incurring a substantial loss, a trend follower will calculate the expected value of the trade over many iterations. This helps them understand not just the potential gain from one successful trade, but the cumulative impact of such a trade over time, considering both winning and losing scenarios.

By applying this methodology, trend followers aim to avoid the pitfalls of myopic or short term decision-making. Their goal is to ensure that their trading strategy remains profitable over the long term. They understand that a single trade’s success or failure is less important than the overall trend of their trading outcomes. As such, they strategize to ensure that the cumulative effect of their trades maintains a positive trajectory.  Furthermore, this dualistic approach to trading compels trend followers to implement strict risk management protocols.

In essence, by recognizing and respecting the dualistic nature of trades, trend followers can create a disciplined and measured trading framework. This framework helps them navigate the complexities of the market, making informed decisions that account for both the potential rewards and risks, thereby enhancing their chances of long-term success in the volatile world of trading.

In the practice of trend following, when risk and return are examined over the long term—spanning thousands of trades—the cumulative impact can be markedly different from what might be expected from a single trade. This is a critical distinction that trend followers make: the outcome of any individual trade is less significant compared to the aggregated result of many trades over time.

When a single trade is considered, the focus might be on its potential return and the associated risk. However, this view is quite narrow and doesn’t capture the full picture of a trading strategy’s effectiveness. Trend followers understand that the true test of a strategy’s robustness is how it performs over a vast number of trades, encompassing various market conditions.

By plotting risk and return conditionally across thousands of trades, trend followers can observe patterns and trends that are not apparent in shorter time frames or smaller sample sizes. This long-term perspective allows them to discern the true nature of their strategy’s risk-return profile. It’s akin to seeing a mosaic—each individual tile (or trade) may not reveal much, but when viewed together, they form a clear and coherent picture.

This approach also highlights the power of compounding effects, both positive and negative. For instance, a strategy that consistently yields small returns with controlled risks can lead to substantial growth over time, thanks to the compounding effect. Conversely, even a strategy with high returns can be detrimental if it’s coupled with high risks, as the negative compounding effect of losses can quickly erode gains.

Moreover, when risk and return are considered over thousands of trades, trend followers can better appreciate the importance of consistency and risk management. It becomes clear that avoiding large losses is as crucial, if not more, than capturing large gains. A few significant losses can have a disproportionate impact on the overall portfolio, underscoring the need for a disciplined approach to risk management.

By extending the analysis of risk and return over thousands of trades, trend followers gain a more comprehensive and realistic understanding of their strategy’s performance. This long-term perspective helps them develop and refine trading approaches that are sustainable, profitable, and resilient against market volatility. It shifts the focus from the success or failure of individual trades to the overall health and growth of the trading portfolio over time.

Surviving Outlier Events

Trend followers pay special attention to the leptokurtic nature of market behaviours, characterized by pronounced fat tails on both ends of the distribution curve. This observation is critical as it indicates a higher likelihood of encountering outlier events – extreme market movements that can either lead to substantial gains (right tail) or severe losses (left tail).

Understanding this characteristic of markets, trend followers craft their strategies to specifically address these potential outlier events. The primary goal is to construct a trading approach that robustly guards against the adverse impacts of left tail events while simultaneously positioning to take full advantage of the opportunities presented by right tail events. This dual focus is essential for their long-term survival and success in the markets.

Trend followers are known for their positively skewed performance profiles. This method is all about striking a balance between risk and reward, aiming to achieve long-term success. To do this, they meticulously limit their exposure to substantial losses, while positioning themselves to fully exploit the market’s rare but significant upward trends.

Conversely, trend followers also embrace the market’s potential for exceptional gains. They let winning positions run, occasionally increasing their stakes in profitable trends, thereby boosting their chances of reaping significant returns during robust market movements.  A key element of their approach involves the Anti-Martingale strategy, which contrasts sharply with the traditional Martingale system of increasing bets on losing positions. The Anti-Martingale strategy calls for increasing position sizes during winning streaks and maintaining or reducing them during downturns. This approach aligns with their goal of achieving a positively skewed performance, where the focus is on maximizing gains when successful and minimizing losses during less favorable times.

To mitigate the risks associated with left tail events, trend followers implement stringent risk management protocols. This often involves setting tight stop-loss orders, diversifying across various asset classes and markets, and employing strategies that are responsive to changing market conditions. The idea is to limit the potential damage from any single adverse event. By doing so, they ensure that even when the market takes an unexpected downturn, their overall portfolio remains resilient, preventing catastrophic losses that could end their trading journey.

Conversely, when it comes to the right tail opportunities – those rare but highly lucrative market movements – trend followers position themselves to capitalize on these events. They understand that such opportunities can significantly enhance their returns and are often the key drivers of long-term wealth creation in trading. To capture these right tail events, their strategies often include maintaining positions that could benefit from large market moves, using leverage judiciously, and patiently waiting for the right conditions to enter or escalate a trade.

This balanced approach to handling both sides of the market’s fat tail distribution is what enables trend followers to stay in the game over the long haul. They are not just surviving the market’s unpredictability; they are strategically positioned to thrive from it. By effectively managing the risks of catastrophic losses and being ready to seize the extraordinary gains, they ensure their presence in the market during times when the most significant wealth-building opportunities arise. In essence, their strategies are designed not just for endurance but for excellence, turning the challenges of leptokurtic market behaviour into a wellspring of potential success.

Strategies for Long-Term Success

In the strategy playbook of trend followers, diversification stands out not just as a risk management tool, but as a fundamental approach to trading. This goes beyond the conventional wisdom of not putting all one’s eggs in one basket. For trend followers, massive diversification is about creating a robust framework that can withstand and capitalize on the unpredictable nature of financial markets.

The essence of massive diversification lies in spreading investments across a wide range of assets, instruments and trend following strategies. This means not just diversifying across different stock sectors or geographical regions, but also considering various asset classes such as commodities, currencies, bonds, and potentially even alternative investments. Diversification also extends to the nature of trend following strategies used to deliberaly inject uncorrelated properties into the trend following portfolio and allow for system ensembles to navigate uncertain trending regimes. The rationale behind this extensive diversification is twofold.

Firstly, by allocating capital across a broad spectrum of assets, trend followers significantly reduce the impact of any single trade on their overall portfolio. In a diversified portfolio, the underperformance or loss in one area can be offset by gains in another. This balance helps in stabilizing the portfolio against market volatility and reduces the probability of substantial aggregate losses.

Secondly, massive diversification places trend followers in a prime position to capitalize on rare but impactful market movements, irrespective of where they occur. In a highly diversified portfolio, there’s a greater chance that some part of the portfolio is well-positioned to take advantage of these rare market events. Whether it’s a sudden surge in a particular commodity price or a sharp movement in a currency pair, a diversified portfolio means having a stake in various markets, increasing the likelihood of capturing these profitable movements.

Furthermore, diversification is not just about having a presence across different assets but also about the timing and strategy of entry and exit in these markets. Trend followers often employ systematic approaches, using algorithms and models to determine the optimal allocation and rebalancing of assets. This methodical approach ensures that diversification is not random but strategically aligned with market trends and potential opportunities.

In essence, massive diversification for trend followers is a deliberate strategy that seeks to balance the portfolio across various dimensions – assets, geographies, timeframes and systems. This comprehensive diversification strategy enhances their resilience against market downturns and positions them to benefit from the sporadic yet significant opportunities that arise in various market segments. It’s a cornerstone of their approach, enabling them to navigate the complexities of financial markets with a greater degree of confidence and efficacy.

The Barbell Approach – A Trick up the Sleeve for the Classic Trend Followers

The barbell approach is a strategic method employed by some trend followers (notably the Classic Trend Followers) to manage their capital with an eye towards both preservation and aggressive growth. This approach is named for its resemblance to a barbell, where weight is concentrated at two ends with a connection in the middle. In financial terms, the ‘weights’ are the two types of capital: realized capital and unrealized equity.

Realized Capital: This represents the core of a trend follower’s portfolio – the principal amount or the initial capital that has been invested. The primary objective with realized capital is preservation and protection. This portion of the portfolio is managed conservatively to ensure it remains secure and intact. The risk taken with this capital is calculated and controlled, with a focus on steady, reliable growth. It’s the ‘safe end’ of the barbell, where the risk of significant losses is minimized. Trend followers understand that protecting their realized capital is crucial for long-term survival in the markets.

Unrealized Equity: This represents the gains or profits that have been generated from successful trades but have not yet been cashed out. Unlike the realized capital, unrealized equity is where trend followers can afford to be more aggressive and take larger risks. This portion of the portfolio is used to pursue higher returns, often by reinvesting into potentially more lucrative but riskier trades. It’s the ‘risk end’ of the barbell, where the potential for higher returns is explored.

The beauty of the barbell approach lies in its dual focus. On one end, the trend follower secures their foundational capital, ensuring that even in the worst market scenarios, their base investment remains protected. On the other end, they leverage the gains they’ve made to chase opportunities for higher returns.

This strategy inherently acknowledges the unpredictable nature of the markets. While the realized capital provides a safety net against market downturns, the unrealized equity offers the flexibility and opportunity to capitalize on favourable market movements.

Moreover, this approach aligns with the principles of risk management and non-ergodicity in markets. By safeguarding their realized capital, trend followers ensure they don’t fall prey to the irreversible losses that can occur in volatile markets. Simultaneously, by using their unrealized equity for higher-risk, higher-reward trades, they position themselves to take advantage of the market’s leptokurtic nature, where the real opportunities for significant wealth generation often lie in the fat tails.

The barbell approach in trend following is a method of capital allocation that carefully balances the need for risk management with the desire for aggressive growth. It allows trend followers to maintain a steady base while actively pursuing the outsized gains that can come from the more unpredictable movements of the financial markets.

Process Over Prediction

The ethos of trend following is deeply rooted in the principle of prioritizing process over prediction. This fundamental approach differentiates trend followers from many other market participants who often rely on forecasting market movements. Trend followers understand that the financial markets are inherently complex and unpredictable, and that attempting to forecast their directions can be a futile and risky endeavor. Instead, they focus on developing and rigorously adhering to a robust, systematic process that guides their trading decisions.

The success of trend followers is largely attributed to their disciplined adherence to a structured, process-driven approach. This approach prioritizes managing risk, ensuring consistency, and maintaining adaptability, which are key to navigating the complexities and uncertainties of the financial markets. By focusing on process over prediction, trend followers position themselves to capitalize on market trends and movements, regardless of the direction, while protecting their capital from the inherent risks of trading.

Risk Management as a Foundation

In the world of trend following, risk management is not just a component of the strategy; it is the bedrock upon which all decisions are built. This deep-seated commitment to managing risk effectively differentiates trend followers from many other market participants. Understanding that the unpredictable nature of financial markets can swiftly erode gains, trend followers place a high priority on strategies that safeguard their capital. This focus on risk management is crucial for their long-term survival and success in the markets.

Risk management is the cornerstone of the trend following approach. By consistently applying risk-averse strategies, trend followers are able to protect their capital, navigate through market volatility, and position themselves for sustainable growth. This unwavering commitment to risk management is what allows them to thrive in the ever-changing landscape of the financial markets.

The Track Record of Success

The success of the trend following community is a well-documented and empirically validated fact in the world of finance. This isn’t based on a few isolated cases or anecdotal evidence, but rather on the long-term track records of numerous investors who have embraced this approach. The consistent performance of diversified systematic trend followers over various market cycles and conditions underscores the effectiveness of their methodology.

The track record of success among diversified systematic trend followers is well-established and supported by both empirical evidence and the long-term performance of numerous practitioners. This success is rooted in their disciplined, process-oriented approach, robust risk management practices, and ability to adapt to changing market conditions. The consistent application of these principles has enabled them to extract a sustainable edge in the market, making them some of the most successful long-term investors in the financial world.

Conclusion

Diversified systematic trend following is more than just a trading strategy; it’s a comprehensive framework for achieving sustained success in the ever-shifting landscape of the financial markets. This approach, characterized by its emphasis on risk management, its embrace of market unpredictability, and its unwavering commitment to a disciplined process, stands as a paradigm of how to turn the subtle nuances of market trends into a formidable mechanism for wealth accumulation.

Diversified systematic trend following is not merely a set of techniques for trading; it is a comprehensive philosophy for engaging with the financial markets. By prioritizing risk management, embracing the inherent unpredictability of markets, and adhering to a rigorous and disciplined process, trend followers have charted a course that allows them to navigate the turbulent waters of financial investing with confidence and achieve sustained success. Their approach stands as a beacon for anyone aspiring to build and preserve wealth in the complex world of financial markets.

Trade well and prosper.

Why it is So Hard to Exceed Performance Benchmarks?

In the world of the financial markets, consistently outperforming established benchmarks such as the S&P 500 is a monumental task that eludes many. This is exemplified by the SPIVA report, which evaluates the performance of actively managed funds against their benchmarks worldwide, revealing that a staggering 75% to 90% of funds fall short over extended periods. This prevalent underachievement raises critical inquiries about the inherent difficulties in surpassing market benchmarks. Despite possessing advanced skills and knowledge, even seasoned Fund Managers often struggle to eclipse these benchmarks. The reasons behind this phenomenon warrant a deeper exploration.

To understand this conundrum, it’s essential to delve into the mechanics of how averages operate within the context of financial indices and the performance of individual Fund Managers over time. Consider the S&P 500 index, a barometer of the total value and market capitalization of its constituent companies. At first glance, it might appear feasible for a well-informed fund manager to outmanoeuvre this average through strategic investment choices. However, the situation is significantly more complex.

The value of an index at any given moment is a snapshot that encapsulates the collective decisions of all market participants at that time, analogous to how the market price of a commodity, such as cocoa, is determined by the aggregate of buying and selling activities. It’s said that the benchmark or price serves as a “fossilized record” of a specific moment, capturing the essence of those who have endured, rather than those who have faltered.

Drawing a parallel to a vast marathon with thousands of participants, if averages are calculated based on the entrants present at various checkpoints, these figures won’t accurately reflect the overall average across the event’s duration. Instead, they merely document those who have managed to persevere at that particular juncture. Numerous participants will inevitably fall by the wayside due to insurmountable challenges, causing the average to deviate progressively from the initial average and ultimately represent only those who have survived to that point.

This distinction between the average performance of all participants at a single moment, as depicted by an index, and the average performance of an individual participant over time is a key factor in the difficulty Fund Managers face in outperforming benchmarks. To fully grasp this concept, it’s necessary to consider multiple temporal snapshots. These averages evolve, reflecting varying levels of market participation and the influence of traders’ decisions (to buy or sell) at those times. Financial markets are dynamic, characterized by phases of predictability, randomness, and uncertainty, all of which profoundly affect the averages at any given moment. It’s crucial to acknowledge that market participation is fluid, with new entrants and exits reshaping the landscape over time.

The non-ergodic nature of financial markets plays a pivotal role in this context. In such environments, the long-term experiences of an individual investor do not align with the collective experiences of many participants at a single point in time. Market conditions are subject to wide-ranging fluctuations over time, diverging from the static snapshot presented by an index at any given moment.

For example, a trader who excels in the market for a decade represents a small minority; the vast majority of traders (approximately 90%) withdraw within such time frames, leaving a mere 10% to influence current market prices. This high turnover rate implies that the average performance observed at any given moment does not encapsulate the long-term experiences of those who have exited the market.

Additionally, traders who remain active and navigate the “risk of ruin” successfully can see their returns compound over time, assuming they adapt to evolving market conditions. Conversely, a trader who exits the market ceases to affect future market dynamics and forfeits the opportunity for potential returns.

The challenge of consistently exceeding market benchmarks lies in the fundamental difference between the aggregated market performance at any instant and the sustained individual performance of market participants over time. This discrepancy, coupled with the dynamic and unpredictable nature of financial markets, renders the task of outperforming these benchmarks a formidable endeavour for traders and fund managers alike.

Confronted with the persistent issue of underperformance, even among adept market participants, one might wonder how it is possible to outdo these industry standards. The essence of achieving superior returns over an extended period is encapsulated in the principle of ‘survival.’ A trader who weathers the market’s fluctuations and remains active is better positioned to leverage advantageous moments that arise.

The focus should shift from the relentless pursuit of higher yields to the strategic avoidance of severe losses that could compromise long-term investment objectives. Hence, the key lies in emphasizing endurance over the pursuit of extraordinary gains. Higher returns are invariably linked with higher risks, particularly when magnified by the use of leverage. To ensure a lasting presence in the market, it is imperative to balance expectations of returns with the use of leverage judiciously.

The irony resides in the fact that enduring through numerous transactions necessitates prudent risk management, which might lead to reduced leverage and modest gains per transaction. Yet, over the span of thousands of transactions, these conservative gains, when compounded, can culminate in returns that surpass market benchmarks.

Suffering a significant loss or encountering a profound market downturn can severely impede the compounding of wealth over time, rendering such setbacks almost insurmountable. These unrecoverable losses not only eliminate the possibility of further market engagement but also arrest any prospects for future financial growth. Therefore, in the realm of investing, the art of survival through calculated risk management and the judicious use of leverage becomes the cornerstone for achieving long-term success and outpacing market benchmarks.

When we delve into strategies for enduring success in financial markets, the concept of the geometric average, particularly illustrated by the Compound Average Growth Rate (CAGR), becomes pivotal. Unlike simple averages, the geometric average accounts for the cumulative effect of compounding returns over time, highlighting the importance of the return sequence. This path-dependent nature of the geometric average underscores how the order and magnitude of returns can significantly influence the overall growth of an investment.

This approach to averaging underscores the importance of a disciplined strategy in managing and mitigating risks within a portfolio, while simultaneously nurturing the growth of profits. Such a method can carve a trajectory of returns that substantially amplifies the power of compounding. It’s about creating a favourable environment where the positive effects of compounding are not just maintained but actively enhanced through strategic decisions.

Investors and traders who adopt methodologies focused on swiftly mitigating losses, broad diversification to lessen the blow from any singular setback, and seizing opportunities that present substantial growth potential, can foster a series of returns with beneficial geometric qualities. By prioritizing these strategies, they can harness the full potential of compounding, which is instrumental in achieving superior long-term growth.

Trend-following traders serve as a prime example of this approach in action. They implement strategies that capitalize on the long-term trends in the market, allowing them to remain engaged over extended periods. This sustained participation, coupled with the strategic use of compounding, enables them to generate returns that not only outstrip traditional benchmarks but also eclipse the general market performance. This method underscores the synergy between strategic risk management, the exploitation of market trends, and the judicious use of compounding, illustrating a comprehensive blueprint for long-term financial prosperity in the unpredictable terrain of the market.

The TTU TF Index distinguishes itself remarkably in terms of performance when juxtaposed with benchmarks such as the S&P 500 TR Index and the SG Trend Index, by delivering substantially higher returns (Refer to Figure 1). This notable outperformance can be attributed to its unique selection criteria, which necessitates a minimum track record of 15 years for inclusion. This contrasts sharply with indices like the SG Trend Index, where the emphasis is on the size of the Fund Manager (FM) rather than the durability of their performance history.

Figure 1: Comparative Performance of TTU TF Index, SG Trend Index and S&P500TR Index

Note: For more information about the TTU TF Index, refer to the monthly Trend Following Performance Reports prepared on Top Traders Unplugged in the Blog posts. https://www.toptradersunplugged.com/blog

The exceptional performance of the TTU TF Index is primarily a result of the compounding benefits accrued by its constituents, who have remained consistently active over the prolonged period. In contrast to other indices, which may experience performance dilution due to the inclusion and subsequent removal of underperforming entities, the TTU TF Index benefits from a consistent and stable lineup of constituents. For example, the SG Trend Index, which ranks the top ten trend followers based on assets under management, undergoes constituent changes driven by fluctuating performance levels, which in turn negatively impacts its long-term performance through a compounding effect.

The members of the TTU TF Index have demonstrated remarkable resilience across various market conditions, including those that are typically challenging for trend-following strategies. By minimizing losses, these trend followers have not only managed to persevere through tough times but have also secured a higher long-term average return compared to other indices.

This achievement highlights the significance of geometric returns associated with enduring market presence. The ability to consistently leverage favourable market conditions while maintaining a competitive advantage is crucial for harnessing the profound effects of compounding over time. Thus, the TTU TF Index serves as a testament to the strategic advantage of prioritizing long-term track record and stability, showcasing how such an approach can lead to superior long-term performance in the complex landscape of financial markets.

Emphasizing endurance in the realms of trading and investing invariably involves accepting certain compromises, particularly with respect to potential gains. To secure a lasting presence in the market, it’s crucial to exercise restraint in the use of leverage and to eschew the pursuit of high returns through aggressive strategies. This prudence stems from an acknowledgment of the financial markets’ volatile nature, marked by unpredictable cycles or regimes whose timing and characteristics are not foreseeable. The unpredictability and variability of these market phases demand a resilient strategy capable of enduring diverse market conditions over extended periods.

The non-ergodic nature of financial markets is a fundamental concept to grasp, signifying that the patterns and outcomes witnessed over time do not consistently mirror the conditions and results observed at any specific point. This divergence results from the evolving mix and behaviours of market participants. Unlike ergodic systems, which presuppose uniformity in market conditions and participant actions, the actual market landscape is in constant flux, with participants entering and exiting, thereby altering market dynamics and introducing both challenges and opportunities.

Against this backdrop, the relevance of time-based averaging becomes apparent. The market encompasses a broader array and diversity of participants over time than is apparent at any single instance. An ‘absorbing barrier,’ such as a significant loss compelling a participant’s exit from the market, can preclude future participation, thus impacting the market’s long-term structure and dynamics. This underscores the necessity of adapting to shifting regimes and managing the risks tied to a mutable market landscape.

Trend Followers exemplify the ethos of valuing longevity. Their foremost aim is to maintain an active market presence, which positions them to leverage forthcoming opportunities and harness the power of compounded returns over time. Their strategy is intrinsically oriented towards the long-term, adopting a ‘barbell’ tactic that meticulously mitigates risk on one end to avert devastating losses, while on the other end, aiming to seize significant profits from clear market movements. This equilibrium enables Trend Followers to traverse a spectrum of market conditions, safeguarding their ongoing engagement and the prospect of achieving returns that exceed the average over time.

In summary, financial markets defy the ergodic hypothesis, where the aggregate long-term outcomes would reflect the individual experience of an investor or Fund Manager. Instead, markets are defined by their conditional probabilities and the influence of extreme, or ‘fat-tailed,’ events that can markedly alter outcomes from the average, leading to trajectories that significantly diverge from the anticipated average return.

Trade well and Prosper

Let’s Get Attracted to the Notion of Path Dependence

Understanding Non-Ergodic Processes and Its Implication in Various Fields

“Non ergodic” is a pivotal, yet often overlooked scientific term. To grasp its essence, one must first understand its counterpart: “ergodicity.” An “ergodic” system is one that eventually visits all its conceivable states. Think of a gas that is released into a controlled laboratory setting such as a glass box. When the system reaches equilibrium it is diffused throughout the box. Gas molecules are uniformly distributed at all points in space. An alternative way to view this experiment is to think in terms of time. Given enough time, the gas will be uniformly distributed throughout the glass box. Under conditions of equilibrium we can say that the distribution across time is aligned to the distribution across space. This allows us to adopt a simplified formula which can conveniently only consider the expectation value without worrying about the time dimension.

Rooted in Statistical Mechanics, this concept revolves around the “ergodic hypothesis,” a mathematical alternative to integrating Newton’s equations of motion for a system. Interestingly, ergodic systems don’t possess a deep-seated sense of “history.”

On the other hand, non-ergodic systems are quite the opposite. They don’t transition through every possible state. This difference carries profound implications.

Delving into the realm of biology, the evolution of life on Earth is undeniably non-ergodic and rich in history. Not every imaginable life form will emerge in our universe. This reality, combined with the phenomenon of heritable variation, sets the groundwork for Darwinian theory. While Darwin didn’t specify the exact methods of heritable variation, it’s pivotal to note that non-ergodicity shapes our historical narrative.

In equilibrium statistical mechanics, the ergodic hypothesis is invaluable. It predicates that the time average and the expectation value of an observable align. This hypothesis allows for complex dynamic descriptions to be simplified into probabilistic models, effectively side-lining the role of time. However, the scenarios where this assumption holds are limited, especially when dealing with systems that aren’t in equilibrium. This typically is found in many real world scenarios where systems evolve in time.

Surprisingly, economics, which frequently delves into non-equilibrium systems and growth models, has deeply entrenched itself in the ergodic assumption. Prevailing economic theories, such as expected utility theory and its successors, often make undiscriminating assumptions of ergodicity. The origins of this discrepancy trace back to the 17th-century when foundational ideas about risk and randomness in economics were formed. These concepts predated the introduction of ergodicity in 19th-century physics by a considerable margin.

Ole Peters and the Unveiling of Non-Ergodic Systems in Economics

Ole Peters is a luminary in highlighting the unique properties of non-ergodic systems, often challenging traditional views. His ground-breaking simulation involving a “gambling” game offers profound insights. Imagine starting with a bankroll of $100: every time you flip a coin and it lands on heads, you increase your bankroll by 50%. Conversely, flipping tails reduces it by 40%. To the casual observer, or someone steeped in traditional, ergodic thinking, this bet seems like a reasonable gamble. When one calculates expectations using a spatially weighted model, it does seem like a game with a small yet positive edge, especially as the game theoretically visits all states over countless trials.

 

 

The Famous Ole Peters Gambling Scenario¹

However, Peters’ simulation dismantled this perception. As he carried out his trials, a startling pattern emerged: regardless of the promising start, every wealth trajectory was plagued by an eventual risk of ruin. An unexpected force seemed to be at play, redirecting these trajectories. This force introduced the critical role of history or ‘time’ into determining the outcomes of his experiments.

The key to understanding this non-ergodic problem is to understand that the problem is an iterative problem dealing with non-linear (conditional) relations.

Imagine starting with a stake of $100. To accurately forecast its growth or decline, it’s essential to factor in this initial state when assigning probabilities. Say you hit a win, boosting your $100 to $150. However, if the next round results in a loss, your calculations shouldn’t merely deduct a fixed sum. Instead, they should reference the updated $150, resulting in a new total of $150 minus 40% of $150, which is $90.

This continuous consideration of the system’s preceding state, known as path dependence, is at the heart of the non-ergodic problem. It introduces cause and effect into the analysis of future paths. Ole Peters’ experiment illustrates this beautifully: by consistently referencing the system’s preceding state, we align with his outcomes. Those who overlook this pivotal step might mistakenly assume the game offers an advantageous edge.

Embracing path dependence reveals a startling insight: a system’s evolution isn’t bound to explore every conceivable state. Its trajectory is shaped, even dictated, by its historical states, making the past a powerful influencer of the future.

This particular experiment is now widely referenced as the “Ole Peters Gambling scenario.” It stands testament to the surprises non-ergodic systems can throw our way, challenging deeply-held beliefs in the financial and statistical worlds.

Given the intriguing results observed in certain simulations, it becomes pertinent to ask: what analytical tools are we employing to scrutinize financial markets? If these markets exhibit non-ergodic behaviours, are our tools adept enough? Are we inadvertently leaning on heuristic ergodic models that compute averages in a certain manner or models that assume results are independent to preceding causes? Or, are we embracing non-ergodic models that rightly acknowledge the crucial role of path dependence in determining outcomes?

The Enigma of Strange Attractors in Complex Adaptive Systems

Complex adaptive systems unlike simple games of chance also reveal peculiar path dependent properties when scrutinized over time. Specifically, in computer simulations that chart trajectories within a state space, not all potential states are reached. Instead, a peculiar entity, known as an “attractor,” emerges, influencing these trajectories and guiding them into a distinct geometry.

Lorentz stumbled upon this unique property while delving into chaos theory and studying the intertwining of periodicity with fractal geometry. The core mathematics involves the use of calculus to grasp properties of nonlinear differential equations.

The term “nonlinear” is paramount in this context. It describes systems in which inputs and outputs do not change proportionately. Financial markets, replete with numerous interconnected dependencies, are prime examples of such systems. The emotional response of humans offers a more intuitive example: winning $10 million in a lottery doesn’t generate ten times the excitement of winning $1 million.

Plotting trajectories of a set of nonlinear systems produces an unusual structure over time that restricts trajectories from exploring all possible states. These trajectories exhibit periods of predictability before making abrupt shifts to a different trajectory path with its own periodicity. Notably, the trajectory never circles back to its initiation point – a characteristic of non-ergodic systems, not ergodic ones. This emergent structure dominates the trajectory’s direction.

Unfolding of the Lorentz Attractor²

A parallel can be drawn with nonlinear systems like gravitational fields. For instance, an electron’s trajectory informs space on curving, but spacetime guides the electron’s motion. It’s a dance between micro and macro elements.

Regardless of the starting point in these simulations, trajectories eventually align, but never repeat, with a peculiar, dual-lobed shape. This spatial geometry, which asserts constraints on trajectory paths, is the “attractor.” They are ubiquitous in complex adaptive systems.

Continued simulations unravel the full splendor of this structure, reminiscent of a butterfly. This ignites curiosity: what might the symbolism or significance of this ‘butterfly shape’ truly be?

The Lorentz Attractor in all its Glory²

Let’s now take a glimpse at how these attractors change our estimates about the predictability of a system. You may be able to see how endogenous events of uncertainty emerge dependent on where your path is located on this attractor. The path dependent structure influences the uncertainty of our trajectory dependent on not only the initial state, but also where it is located on the path of allowable states.

From Predictability to Chaos²

Top Left Scenario: If the initial ring of uncertainty remains unchanged, it means our initial uncertainty about the system’s state has not grown. Essentially, our initial guess about the system’s state remains as uncertain (or certain) as before.

Top Right Scenario: Here, the ring becomes a “banana/boomerang” shape. This indicates that as the system evolved, the uncertainty regarding its state has changed in a specific manner. The transformation into a thin shape suggests that we’re not sure if the system will transition from one state (represented by the left-hand lobe) to another (the right-hand lobe).

Bottom Figure: In this scenario, there’s a high degree of uncertainty regarding the future state of the system. The position on the attractor is very uncertain, meaning it’s hard to predict where the system will end up over time.

Complex adaptive systems underscore the profound significance of their historical trajectories in influencing our capability to anticipate future outcomes. These systems, with their intricate and sometimes elusive characteristics, vacillate between predictability and unpredictability throughout their existence. We can’t merely rely on straightforward ergodic statistics in such contexts. For price followers and others navigating these systems, the path taken is not just a record of the past but a crucial determinant of future possibilities. It is essential to recognize and respect the inherent complexities and path dependence of such systems when making decisions about risk. Expectations are for those who like to assume ergodicity. Be non-ergodic my friends and capitalise on this weakness.

Trade well and Prosper.

Footnotes:

  1. The Ergodicity Problem in Economics, Ole Peters, Nature Physics Published 02 December 2019
  2. The Primacy of Doubt, Tim Palmer, Oxford University Press, Published in 2022

 

Russian Roulette, Formula 1 and Market Trends: Navigating the High Stakes of Uncertainty

In a world rife with unpredictability, the principle of survival takes precedence over the quest for immediate success. This tenet holds true across various high-stakes domains—from the capricious nature of financial markets to the competitive fervour of Formula 1 racing, even extending to the life-or-death randomness of Russian Roulette. This blog post explores the critical importance of prioritizing longevity over short-term gains, employing the concept of ergodicity, and drawing insightful parallels from extreme examples to the nuanced strategies of Diversified Systematic Trend Following (DSTF) in finance, particularly focusing on its unique approach to tail events.

The Paramount Importance of Survival

Survival, the act of enduring through adversity, is a strategy often overshadowed in the relentless pursuit of performance. Yet, in realms where uncertainty prevails, survival isn’t merely one strategy among many—it’s the foundation upon which all other successes are built.

In the relentless pursuit of peak performance and immediate gratification, the fundamental principle of survival often recedes into the background, overshadowed by more glamorous ambitions. Yet, in environments marked by profound uncertainty and constant flux, survival transcends being merely one strategy among a repertoire—it becomes the bedrock upon which the edifice of long-term success is constructed. This foundational aspect of survival is especially pertinent in domains fraught with unpredictability, where the ability to endure, adapt, and persevere is paramount.

Survival, in its essence, is the art of navigating through adversity, of remaining steadfast in the face of challenges that threaten existence, performance, or progress. It’s about the strategic conservation of resources, the prudent management of risks, and the wisdom to recognize that not every battle is worth fighting. In the grand tapestry of endeavours, whether in the natural world, in the high-octane arenas of sports, or within the labyrinthine complexities of financial markets, the principle of survival serves as a guiding star, a reminder that the first step toward triumph is to ensure one remains in the game.

The significance of survival becomes starkly evident when we consider the alternative—failure, cessation, or ruin. In environments where the stakes are high and the margins for error are slim, the cost of non-survival can be catastrophic, not just nullifying past achievements but also foreclosing future possibilities. Thus, survival is not just about avoiding failure; it’s about preserving the potential for future success, about keeping the doors to opportunity ajar.

Survival in any context, especially in finance, is a strategic endeavour that involves a thorough evaluation of the environment, an assessment of one’s strengths and weaknesses, and a careful management of risks. It’s about making well-informed decisions on when to advance or retreat and when to be assertive or accommodating, all aimed at ensuring ongoing viability. In finance, this strategy is reflected in the careful handling of investments, diversifying portfolios to minimize risk, and implementing protective measures like stop-loss orders to prevent significant losses. The goal is to balance the pursuit of profit with the fundamental need to maintain stability and solvency.

Central to the concept of survival is the recognition of time as a crucial element. The focus shifts from short-term gains to long-term viability, from immediate victories to sustained progress. This long view fosters resilience, encouraging strategies that can weather temporary setbacks in anticipation of future rewards. It’s about playing the long game, understanding that endurance through periods of adversity can position one favourably for when the tides turn.

Russian Roulette: A Stark Illustration

Russian Roulette serves as a poignant example of the delicate balance between survival and danger, each trigger pull bringing with it a stark contrast of life and death. This harrowing game highlights the inherent non-ergodicity in certain systems, where outcomes from a series of actions don’t simply average out but instead accumulate risk with every attempt. It underscores the critical importance of persevering in the face of existential threats.

In a typical game of Russian Roulette, a standard six-chamber revolver is used, loaded with a single bullet. Before each player’s turn, the cylinder is spun, ensuring the position of the loaded chamber is random. Players then take turns, each placing the revolver to their head and pulling the trigger.

For the first player, the chance of the revolver firing is 1 in 6, or about 16.67%. While this presents a significant risk, the odds are more skewed towards survival. The initial participant survives their turn as the revolver clicks empty. As the game progresses, each trigger pull doesn’t reset the odds but instead incrementally leads to an unavoidable lethal outcome. The risk doesn’t even out over time but grows with each successive attempt. This defines the essence of a non-ergodic system, where the long-term result for an individual diverges from the collective average, inevitably leading to catastrophe in this context.

In such a precarious system, the overriding lesson is the supreme value of survival. Participating in an endeavor where the threat of total loss mounts with each action is fundamentally unsustainable. The only foolproof method to “win” in such a scenario is to abstain entirely—to value survival above the allure of chance. This metaphor extends beyond this extreme example, applying to any situation where risks accumulate over time, emphasizing the imperative to judiciously manage risks and make decisions geared towards ensuring ongoing safety and avoiding ultimate ruin.

Risk of ruin is a fundamental concept that refers to the likelihood of reaching a point in a series of risks where recovery is impossible, effectively ending the game, venture, or career. This concept is particularly relevant in fields where decision-making is pivotal, such as investing, entrepreneurship, or any career path fraught with high-stakes choices. In these contexts, each decision carries a certain probability of success or failure, and the cumulative effect of these decisions can significantly impact one’s ability to generate future profits and, by extension, create wealth.

The risk of ruin compromises long-term survival by depleting the resources or opportunities necessary to continue participating in profit-generating activities. Once the point of ruin is reached, not only are current holdings lost, but the capacity to leverage future opportunities is also obliterated. In careers or ventures involving thousands of decisions, the interplay of contingent probabilities means that the impact of each choice is interconnected. A single catastrophic loss can set off a domino effect, jeopardizing future decisions and their potential gains. Therefore, managing risk to avoid ruin is paramount, as it ensures the preservation of capital and the ability to continue making decisions that could lead to profit.

Russian Roulette serves as an extreme yet illustrative example of the risk of ruin concept, where the stakes are not financial but life itself. In this harrowing game, participants face a literal survival scenario with each pull of the trigger. The game starkly highlights the ultimate risk of ruin—death, from which there is no recovery or chance of future participation. The analogy to career and wealth creation is profound: just as a single bullet can end the game of Russian Roulette, a single reckless decision can lead to financial ruin, eliminating any future prospects for wealth creation.

In Russian Roulette, the risk of ruin is immediate and irreversible, making the consequences of each decision glaringly evident. In the realm of career and financial decisions, the risk may not always be as immediate or catastrophic, but the principle remains the same. Ensuring long-term survival by carefully managing risk is crucial for ongoing participation in opportunities that lead to wealth creation. This underscores the importance of strategic decision-making and risk management in any high-stakes endeavor, where the preservation of the ability to continue making decisions is key to long-term success and wealth accumulation.

Formula 1 Racing: A Lesson in Strategy

Expanding on the analogy of Russian Roulette, we delve into how the non-ergodic nature of repeated high-stakes events, like individual races in an F1 season or any high-risk sporting event, underscores the critical importance of survival and strategic risk management.

In F1 racing, each race can be likened to an individual pull of the trigger in Russian Roulette, where the stakes are exceedingly high, and the outcomes of each event are unpredictable. However, unlike Russian Roulette, where the risk escalates towards an inevitable negative outcome, F1 offers opportunities for recalibration and strategic adjustments between races.

The allure of speed and the pursuit of victory in each race present a palpable risk, akin to the temptation of taking a chance in Russian Roulette. The immediate glory of winning a race can sometimes overshadow the overarching objective of winning the championship. The most successful F1 drivers and teams understand that each race, with its inherent risks, is part of a larger, season-long campaign where consistency, reliability, and strategic foresight are paramount.

Just as each pull of the trigger in Russian Roulette does not reset the odds but rather brings the player closer to an eventual negative outcome, each F1 race presents unique challenges and risks that do not simply reset after each event. The wear on the car, the physical and mental strain on the driver, and the dynamic nature of team strategies contribute to a compounding effect over the season. However, unlike the fatalistic trajectory of Russian Roulette, F1 teams have the opportunity to learn, adapt, and evolve their strategies between races to mitigate risks and enhance their chances of success.

The key to long-term triumph in F1 is the prioritization of survival and strategic risk management. This involves a calculated approach to racing, where sometimes securing points through a second or third-place finish is more valuable in the championship race than risking everything for a win in every race. It’s about knowing when to push the car to its limits and when to adopt a more conservative strategy to ensure a finish, accumulating valuable points towards the championship.

Successful F1 teams and drivers continually assess their performance, the reliability of their cars, and the strategies of their competitors. They make strategic adjustments based on a myriad of factors, including track conditions, weather, and the performance of rival teams. This adaptability is crucial in a non-ergodic system where past outcomes do not guarantee future results, and each race is an independent event with its own set of variables.

Like the stark choices presented in Russian Roulette, F1 requires a delicate balance between the pursuit of immediate glory and the overarching goal of championship success. The most successful participants in this high-stakes arena are those who, through strategic foresight and consistent performance, manage to navigate the uncertainties of each race while keeping their eyes on the ultimate prize.

Understanding Ergodicity in Financial Markets

In financial markets, like in the game of Russian Roulette and the series of races in an F1 season, each investment decision, much like each pull of the trigger or each race, carries its own set of risks and outcomes. The critical difference, however, lies in the ability of investors to influence their odds over time through strategic decisions, unlike the fixed and escalating odds in Russian Roulette.

Financial markets do not conform to ergodic principles, where the long-term average outcomes of the market would mirror the potential experience of an individual investor. Instead, markets are characterized by their contingent probabilities and the impact of extreme, or “fat-tailed,” events that can significantly skew outcomes away from the average, leading to paths that deviate substantially from the mean expected return.

In such a non-ergodic environment, the focus on minimizing negative risks becomes crucial. Similar to how a Formula 1 team balances speed with safety for season-long competition, investors need to adopt protective strategies to shield their capital from severe losses. This involves diversifying across different asset types to spread risk, setting stop-loss orders to curb losses, and constantly reassessing investment positions based on market feedback.

Risk in this context goes beyond the mere prospect of total loss, encompassing any significant setback that could jeopardize the long-term goal of wealth accumulation. Analogous to how a single error in Russian Roulette can be game-ending, or a significant mishap in Formula 1 could ruin a season, substantial market downturns can severely disrupt an investor’s wealth-building path.

The journey to growing wealth exponentially is not straightforward; it’s compounded, meaning that losses detract not just from current wealth but also from future growth potential. A notable loss reduces the capital base, setting back the process of wealth accumulation. This effect is like being pushed several steps back, requiring even more effort to return to the initial path.

The compounding effect means that recovering from a major loss demands disproportionately higher gains. For example, recuperating from a 20% loss requires a 25% gain, while a 50% loss demands a 100% gain to return to the original capital level. The deeper the loss, the more monumental the effort needed to regain ground, emphasizing the importance of avoiding significant losses in the pursuit of compounded wealth.

For investors, this underscores the need for a strategic focus on risk management and capital conservation. It’s not solely about chasing the highest returns but about ensuring consistent, sustainable growth with minimal risk of catastrophic losses. Strategies could involve diversifying across non-correlated assets, implementing stop-loss strategies, and adopting a conservative stance during volatile market periods.

Navigating the path to compounded wealth is like moving through a complex maze, where each misstep can lead further from the goal. Investors must proceed with caution, aware of potential pitfalls that could hinder progress. The emphasis should be on steady gains and preventing substantial losses that could interrupt the compounding journey. In essence, the path to building wealth is as much about the gains made as it is about the losses avoided.

Financial markets are prone to fat-tailed distributions, where extreme events, although statistically uncommon, occur more frequently than normal distribution would suggest. These events can significantly impact an investor’s portfolio, akin to a critical failure in an F1 race or an unfortunate outcome in Russian Roulette.

Investors need to anticipate and prepare for these fat-tailed occurrences, realizing that the market’s future isn’t simply an extension of its past average behaviour. This means guarding against downside risks while also positioning to capitalize on the opportunities presented by market volatility.

Sustained success and participation in financial markets hinge on the ability to navigate through inherent unpredictability and the occurrence of extreme events. This demands a disciplined, strategic investment approach that places a premium on preserving capital and managing risk meticulously.

Diversified Systematic Trend Following: Tailoring Strategies for Non-Ergodic Markets

Diversified Systematic Trend Following (DSTF) presents an advanced framework for mastering the intricacies of unpredictable, non-ergodic financial environments. This strategy breaks away from conventional investment approaches that typically aim to capture average market trends. Instead, DSTF probes into the market’s extreme behaviours, concentrating on rare but impactful tail events that have the power to significantly shift an investor’s path toward growing their wealth.

These tail events are the anomalies within market dynamics—instances that starkly contrast with typical market patterns. They could manifest as abrupt financial downturns, unexpected geopolitical shifts, or any unexpected market irregularities causing significant price swings. Despite their rarity, the effects of these events can be dramatic, resulting in either notable gains or losses. DSTF strategies are meticulously designed to detect and adapt to such drastic market changes, utilizing systematic approaches to either leverage these opportunities for gain or implement protective measures to prevent substantial losses, thus preserving the investor’s capital.

The ‘Inside-Out’ Approach: Responding to Tail Properties of the Markets

The inward-focused strategy of DSTF marks a significant departure from traditional investment methodologies. It entails an in-depth exploration of market intricacies, with an emphasis on identifying the potential for outlier events instead of merely concentrating on the most probable or average scenarios. This strategy recognizes the presence of ‘fat tails’ in financial market distributions, an acknowledgment of the heightened frequency of extreme events beyond what a normal distribution would suggest.

By strategically gearing up for these extreme occurrences, DSTF approaches ensure they are never blindsided by abrupt market fluctuations. This forward-thinking posture combines a safeguarding mechanism aimed at averting disastrous financial losses with a proactive component designed to capitalize on extraordinary market dynamics for notable returns. The core of this strategy lies not in the mere prediction of these outlier events but in establishing a resilient infrastructure that withstands varying market conditions.

Tailoring Strategies to Market Dynamics

DSTF strategies are continuously refined and adapted to align with evolving market conditions. This dynamic adjustment is crucial in non-ergodic environments where past performance is not always indicative of future results. DSTF practitioners employ sophisticated models and algorithms that are regularly updated based on new market data and insights. This ensures that the strategy remains responsive to the latest market dynamics, capable of identifying emerging trends, and adapting to shifts in market volatility.

Adapting to the ever-changing landscape of financial markets is a cornerstone of Diversified Systematic Trend Following (DSTF) strategies, mirroring the dynamic adjustments seen in Formula 1 racing where teams constantly tweak their approaches based on the latest developments on and off the track. This agility in DSTF is crucial for maintaining the strategy’s edge in an environment characterized by its unpredictability and rapid shifts.

In DSTF, continuous strategy refinement is akin to a Formula 1 team analysing data post-race to enhance their car’s performance for future races. Market conditions, much like racing conditions, can change dramatically due to economic reports, geopolitical events, or shifts in market sentiment. DSTF strategies employ advanced analytics, leveraging real-time data and sophisticated models to identify emerging trends and potential inflection points in the market.

This process involves re-evaluating existing positions, assessing the efficacy of current trading signals, and adjusting entry and exit criteria as necessary. Just as a racing team might adjust their car’s aerodynamics or tire strategy in response to track conditions, DSTF practitioners tweak their algorithms to better align with the current market environment, ensuring that the strategy remains optimally positioned to capture trends and mitigate risks.

Risk Management and Diversification

A cornerstone of the DSTF approach is its emphasis on risk management and diversification. By spreading investments across a wide array of assets and employing systematic risk controls, DSTF strategies aim to mitigate the impact of negative tail events. This diversification extends beyond traditional asset classes, exploring various markets and instruments to reduce correlation and enhance the strategy’s resilience to market downturns.

The Barbell Strategy: Balancing Risk and Reward

The Barbell Strategy, when integrated into Diversified Systematic Trend Following (DSTF) approaches, introduces a sophisticated method to strike a balance between risk and potential rewards. Echoing the careful equilibrium between velocity and safety seen in Formula 1, this strategy adopts a bifocal investment stance that aims to ensure stability while also seeking out opportunities for significant gains.

Envision a metaphorical barbell: at one end, the strategy is grounded in stringent risk control measures, aiming to systematically minimize losses in each transaction. This side of the strategy serves as a protective barrier, ensuring that no single loss can critically impact the overall portfolio, effectively averting any severe, left-tail outcomes that might compromise the investment path.

With this foundation of risk control, ensuring that losses are contained and their impact on the portfolio minimized, the strategy then pivots to the barbell’s other end. This is where the focus shifts to maximizing gains from successful ventures, allowing profits to flourish without restraint. This dual-pronged approach empowers DSTF to adeptly manoeuvre through the financial markets, carefully managing downside risks while being ready to capitalize on the positive potential of market trends.

This barbell tactic deeply embodies the DSTF’s ‘inside-out’ philosophy, specifically crafted to thrive in and exploit the unpredictable nature of financial markets, with a particular emphasis on the critical role of tail events.

Distinct from traditional investment strategies that typically look outward in, concentrating on average or expected outcomes, the ‘inside-out’ strategy probes the potential extremes of market behaviour. The barbell model complements this by organizing the portfolio to confront both the risks and opportunities these extreme or tail events present.

On the conservative side of the barbell, stringent risk management practices are in place to shield against negative tail events. This involves promptly curtailing losses on individual trades to protect the portfolio from severe market downturns, exemplifying the proactive risk management at the heart of the ‘inside-out’ approach.

Conversely, on the barbell’s aggressive end, the strategy aims to exploit positive tail events or right-tail opportunities with significant profit potential. By allowing profits to run in favourable conditions, DSTF seeks to harness the exceptional returns these rare events can offer, aligning with the ‘inside-out’ philosophy by focusing on the outliers rather than the mean.

Given the non-ergodic nature of financial markets, where the long-term outcomes for an investor may not mirror the average market performance, the barbell strategy is designed to prepare for a broad spectrum of outcomes, including those significantly deviating from the norm.

The conservative end of the barbell underscores the importance of survival by safeguarding against devastating losses, crucial in a non-ergodic environment where ongoing market participation is key. This mirrors the strategy in Russian Roulette, where the goal is to endure each round.

At the aggressive end, the strategy acknowledges that the journey to substantial wealth in a non-ergodic system may be marked by seizing rare, highly advantageous market conditions. By positioning for these right-tail events, the DSTF approach accepts the reality that extraordinary gains can profoundly influence an investor’s path to wealth.

Conclusion: Embracing the Art of Survival

The fundamental principle of survival, illuminated through the stark lens of Russian Roulette, the meticulous strategies of Formula 1 racing, and the intricate world of financial markets, holds a universal truth that transcends diverse contexts and challenges. This enduring principle is vividly embodied in Diversified Systematic Trend Following (DSTF) strategies, which navigate the unpredictable waters of financial markets with a keen focus on tail events and a strategic ‘inside-out’ approach.

DSTF stands out as a beacon of endurance and resilience, prioritizing long-term viability over the ephemeral allure of short-term gains. By concentrating on the extremities of market behaviour—the tail events—DSTF strategies prepare for the most significant risks and rewards, ensuring that the portfolio is robust enough to withstand market shocks while positioned to capture extraordinary opportunities. This careful balance between defence and offense, risk management, and growth potential is the essence of the art of survival in the financial domain.

The ‘inside-out’ approach of DSTF, which focuses on the potential for extreme outcomes rather than the average or expected returns, is particularly adept at navigating the non-ergodic nature of financial markets. In a realm where the future cannot simply be extrapolated from the past, this approach ensures that strategies remain flexible and responsive to the ever-changing market landscape, capable of adapting to unforeseen challenges and seizing emergent opportunities.

The principle of survival, while critical in the context of financial markets, extends its relevance far beyond, offering valuable insights into various facets of life and decision-making. Whether facing professional challenges, personal adversities, or strategic dilemmas, the wisdom of prioritizing long-term resilience, adapting to evolving circumstances, and preparing for a range of outcomes can guide individuals and organizations towards sustainable success.

In mastering the art of survival, whether in finance, sports, or life’s myriad challenges, there lies the promise of new beginnings. With each storm weathered and each adversity overcome, the path clears for the emergence of new opportunities, the potential for growth, and the realization of aspirations. DSTF, with its foundational emphasis on survival, serves as a paradigm for navigating uncertainty, not just to endure but to thrive and transform challenges into catalysts for innovation and progress.

The art of survival, as exemplified by DSTF in the financial markets, is a testament to the power of strategic foresight, adaptability, and resilience. It underscores the importance of preparing for the extremes, managing risks judiciously, and embracing change as a constant. By internalizing these principles, investors, professionals, and individuals alike can navigate the complexities of their respective fields, not merely surviving but flourishing, ready to welcome the dawn of new opportunities that lie ahead.