#### Diversification for Trend Following Models: The Small Variations Matter

#### Introduction

In the realm of trend following, one prevailing assumption is that highly correlated assets should not be traded together, as they are unlikely to provide diverse opportunities. However, this article will challenge this notion by delving into the nuances of trade correlations versus price correlations. By examining the behavior of different trend following systems applied to highly correlated assets, we will uncover why system diversification is crucial and how it can significantly impact the performance of a trend following portfolio.

#### Understanding the Importance of Trade Correlations

At first glance, the price series of Brent and Crude Oil appear nearly identical, leading many to believe that trading both is redundant (see Figure 1). This superficial analysis overlooks the critical distinction between price correlations and trade correlations, which are essential for outlier hunters.

**Source: Finvis**

**Figure 1: Comparison between the price series of Brent and Crude**

The assumption that highly correlated price series yield redundant trading opportunities fails to recognize the intricate dynamics of trend following systems. The real magic happens when we examine **trade correlations**—the return streams generated by applying trend following models to these assets.

#### The Misconception of Diversification Limits

A common belief in portfolio management is that diversification benefits diminish after a certain point, often cited as around 60 uncorrelated assets, based on the Central Limit Theorem. This theorem suggests that as sample sizes grow, they approximate a normal distribution, implying an optimal level of diversification. However, this theory falters when applied to non-linear distributions dominated by outliers.

The Central Limit Theorem implies that the benefits of diversification follow the square root law, where the reduction in portfolio risk is proportional to the square root of the number of assets. This relationship suggests that the risk reduction benefit diminishes as more assets are added. For example, the incremental risk reduction from adding the 50th asset to a portfolio is less than from adding the 5th asset.

**Note: **A common mistake by some experts is assuming that diversification limits apply the same way to all investment strategies. This assumption often comes from methods that don’t take advantage of beneficial volatility, like mean reversion strategies, which are known for their negative skew. In mean reversion, small profits are frequent but rarely turn into big gains, while occasional large losses can occur. This negative skew means diversification is less effective because smooth return streams quickly become correlated, and the uncorrelated large losses significantly harm the portfolio. However, in trend following, we seek beneficial outliers—those rare, large price moves that positively impact the portfolio. These beneficial outliers as we will see later in this article are less correlated with each other, allowing for greater diversification and potentially higher returns. In trend following, there’s no limit to how much diversification can benefit the portfolio.

In the world of trend following, outliers defy the constraints of normal distributions, rendering the notion of a theoretical diversification limit obsolete. Trend following strategies often thrive on capturing significant, unexpected price moves in various assets—events that fall outside the expectations of normal distributions.

For an outlier hunter, more diversification means better chances of capturing those rare, impactful events that drive portfolio returns. Here’s why:

**Non-Normal Distributions:**Financial markets often exhibit fat tails and skewed distributions, where extreme events occur more frequently than predicted by normal distribution models. In such environments, the benefits of diversification extend beyond the limits suggested by the Central Limit Theorem.**Increased Opportunity Set:**By diversifying across a larger number of assets, trend followers increase their opportunity set to capture outliers. The more diverse the portfolio, the higher the likelihood of encountering assets experiencing significant trends.**Risk Mitigation:**Diversification helps spread risk across various uncorrelated assets, reducing the impact of any single asset’s poor performance. This is particularly important in volatile markets where individual asset performance can be unpredictable.**Capitalizing on Uncertainty:**Outlier hunters thrive on uncertainty and the unexpected. Diversification across a broad array of markets enhances the probability of benefiting from unexpected events, which are the cornerstone of trend-following profitability.

The traditional view of diversification limits, rooted in the Central Limit Theorem and the square root law, does not hold in the context of trend following. For outlier hunters, there is no practical limit to diversification. The broader and more diversified the portfolio, the greater the chances of capturing those rare, high-impact events that can significantly drive returns. Embracing a wide array of uncorrelated assets allows trend followers to harness the true power of diversification in an unpredictable market landscape.

#### Exploring System Dispersion and Outliers

To illustrate this, we applied ten identical hypothetical trend following models with the same parameter settings to both Brent and Crude over a 24-year period. You would think that the application of the same models to a highly correlated pair of price series would lead to a highly correlated trade result. Not so fast intrepid explorer.

The models used (both long and short) were popular trend following models with medium to long term parameter sets such as:

- the Donchian Breakout System (DON);
- moving average crossover system (MAT);
- regression line breakout system (REG);
- Darvis Box breakout system (BOX);
- the Bollinger Band Retracement Entry into Trend system; and
- the Bollinger Band Breakout system (BBB).

**Figure 2: 10 Identical Trend Following Models applied to Brent and Crude**

When we look at the performance of these models on Brent:

**Figure 3: 10 Trend Following Models applied to Brent**

The returns in Figure 3 exhibit significant dispersion, ranging from poor to excellent performance. This variance is due to the unique interactions between each system and the price series, leading to different outcomes. For example each system is not in the market all the time. They only participate when trends become material in nature. Furthermore the small differences in price and the way they respond to system variables means many different disparate outcomes.

**Note:** For the backtesters out there who thought they would choose the best system from their backtest in 2010, they would be sorely disappointed to know that the best performer was a mid range performer by 2020 and a mid range performer as at 2010 was the best performer by 2020. Such is the nature of cherry picking best performers from a backtest, and why an ensemble approach is a far better method to deploy where all systems are used as opposed to the “Cherry picked One”.

Let’s move on. Now in particular we want to see the influence that Outliers have in creating the dispersion in results, so let us revisit the prior Figure with some added detail.

**Figure 4: 10 Trend Following Models applied to Brent: The Impact of Outliers**

The major ‘jump up’ steps in Figure 4 highlight the outliers—those rare but significant events that certain systems capture while others miss. These outliers are critical drivers of performance and the dominant drivers that splay the results and reduce correlation properties. Furthermore they demonstrate the importance of using an ensemble of systems to avoid the dreaded Type 2 error—missing out on these key opportunities. If all your systems missed the Outlier, they would all converge together with a less dispersed result.

#### Comparing Brent and Crude Systems

Consolidating the ten return streams into a sub-portfolio for Brent yields a robust equity curve with offset drawdowns and a strong overall return:

**Figure 5: 10 Trend Following Models applied to Brent: Sub Portfolio Result**

However, applying the same systems to Crude reveals stark differences (refer to Figure 6):

**Figure 6: 10 Trend Following Models applied to Crude: The Impact of Outliers**

Despite the high price correlation between Brent and Crude, the outliers in each return series and resulting performance are markedly different. This discrepancy underscores the impact of small variations in price series on outlier events—a phenomenon akin to the butterfly effect in non-linear systems.

#### Subportfolio Comparison: Brent vs. Crude

When comparing the sub-portfolios of Brent and Crude using the same systems, the results therefore diverge significantly:

**Figure 7: Subportfolio Comparison Between Brent and Crude**

Previously when comparing price correlations, both Brent and Crude were almost identical. Now when comparing return distributions between Brent and Crude we see how different they actually are. The differences are substantial, driven by the unique outlier events in each market. This highlights that trading both Brent and Crude with the same trend following models is not redundant but rather beneficial, as their trade results are uncorrelated despite their price correlations.

**Note:** For those that like a bit of further detail, notice how both subportfolios were quite highly correlated at their inception. This is because they were yet to latch onto an Outlier. The dispersion started diverging in January 2003 where Brent latched hold of an Outlier and Crude didn’t.

#### Conclusion

This analysis challenges the traditional wisdom regarding diversification limits in trend following portfolios. In a world dominated by outliers, diversification is a powerful tool that cannot be overstated. The more diversified a portfolio, the better equipped it is to capture those rare, impactful events that drive performance.

For outlier hunters, there is no theoretical limit to diversification. Embracing maximal diversification enhances correlation offsets and harnesses the lifting power of outliers, ultimately leading to more robust and resilient trend following portfolios.

**Trade well, my friends.**