# Trend Following Primer Series – A Risk Adjusted Approach to Maximise Geometric Returns – Part 9

## Primer Series Contents

- An Introduction- Part 1
- Care Less about Trend Form and More about the Bias within it- Part 2
- Divergence, Convergence and Noise – Part 3
- Revealing Non-Randomness through the Market Distribution of Returns – Part 4
- Characteristics of Complex Adaptive Markets – Part 5
- The Search for Sustainable Trading Models – Part 6
- The Need for an Enduring Edge – Part 7
- Compounding, Path Dependence and Positive Skew – Part 8
- A Risk Adjusted Approach to Maximise Geometric Returns – Part 9
- Diversification is Never Enough…for Trend Followers – Part 10
- Correlation Between Return Streams – Where all the Wiggling Matters – Part 11
- The Pain Arbitrage of Trend Following – Part 12
- Building a Diversified, Systematic, Trend Following Model – Part 13
- A Systematic Workflow Process Applied to Data Mining – Part 14
- Put Your Helmets On, It’s Time to Go Mining – Part 15
- The Robustness Phase – T’is But a Scratch – Part 16
- There is no Permanence, Only Change – Part 17
- Compiling a Sub Portfolio: A First Glimpse of our Creation – Part 18
- The Court Verdict: A Lesson In Hubris – Part 19
- Conclusion: All Things Come to an End, Even Trends – Part 20

# A Risk Adjusted Approach to Maximise Geometric Returns

In our prior Primer, we discussed that while an edge is an essential prerequisite for a trend following portfolio, the real game changer that is responsible for long term net wealth is the principle of compounding over the long-term.

Having this understanding, we then demonstrated how the path of returns delivered by a portfolio, is responsible for the degree of compounding (aka the geometric return) that can be achieved over a time series.

Better geometric returns are achieved when **adverse volatility is mitigated, **and **beneficial volatility is embraced**. Trend followers place a great deal of emphasis on managing risk in the portfolio to ensure that adverse drawdowns do not materially and detrimentally compromise wealth building objectives but they also leave their profit potential open (both long and short) to allow for unbridled step-ups in our equity curve through targeting outliers that lie in the tails of the market distribution of returns. It is this latter perspective that most of us don’t pay enough attention to.

In fact, when compared to alternative trading methods, the classic equity curve of a trend following global portfolio over the long-term is configured to generate superior wealth building returns. This is because the path of returns generated from trend following methods offers superior **risk-adjusted metrics **to alternative approaches.

Notice how I have focused on two separate aspects of a trend followers modus operandi when discussing how a trend follower’s process naturally produces a path of returns suited to compounding.

Most traders only consider the adverse volatility side of this statement and not the positive volatility side, and believe that a nice straight ascending equity curve (popular with convergent systems that possess negative skew) is what is required to produce the best path. But this is a problem that applies to traders with a linear mindset. We are non-linear guys who recognise that the ‘when and where’ non-linear things happen in a time series such as outliers, have exponential effects on the overall end result of that series.

Trend followers target the outlier (a non linear feature), and manage adverse tail risk at all times to produce a superior ‘stepped’ path to their cousins. In fact, as we will see in this Primer, we use diversification of non-correlated trend following return streams to further enhance the path of returns. We understand that, unlike traditional mantra suggests that “there are limits to the benefits that can be achieved by diversification”, there actually are no such limits for trend followers who trade the fat tails.

You see once again the devil is in the details. We are not simply using diversification as a method to manage adverse risk. If so, then we could agree with conventional wisdom that there was a point where no further marginal benefit would be received by additional diversification. However, this is not the case for trend followers as they use diversification to achieve **two objectives**:

- To mitigate adverse volatility which detracts from the benefits of compounding;
**AND** - To target the tails of the distribution of returns where the unpredictable outlier resides. This additional nugget
**vastly accelerates the compounding effect**over a time series.

It is the latter point that makes us understand that there are** no limits to the benefits of diversification when trading the fat tails**. Given that outliers are an unpredictable event, then the more diversified you are in targeting them, the greater the chance you have of ‘riding them’. When playing convergence on the other hand, by restricting the ability for your solution to capture outliers by using profit targets, you vastly underestime what compounding can achieve though its heavy lifting potential.

You see, through our method of collating diversified return streams into a global portfolio, we deliberately select return streams that when collated, provide offsets to reduce adverse excursions of the portfolio equity curve **AND** then we pile in as many uncorrelated return streams into the portfolio as we can muster, to target outliers and receive correlation benefits which accelerate the compounding effect.

Let us provide an example of what we mean by a risk-adjusted approach.

Below in Table 7 are performance metrics and non-compounded equity curves for the currency pairs AUDJPY and EURUSD that adopt a trend following system using a classic trend following approach.

Notice that the Maximum Drawdown of AUDJPY is 56.15%, the CAGR is 7.65% and the MAR ratio (which is the CAGR/Max Draw%) is 0.14. By visual reference you will notice periods of time where significant step ups in the equity curve were experienced. For example, at around 1986, 2009, 2014, 2017 and 2021 (refer to yellow ellipses)

Also notice that the Maximum Drawdown of EURUSD is 28.27%, the CAGR is 7.40% and the MAR ratio (which is the CAGR%/Max Draw%) is 0.26. By visual reference you will also notice periods of time where significant step ups in the equity curve were experienced by this market. For example, 1981, 1988, 1998, 2001, 2009 and 2015.

Both return streams have volatile signatures, however adverse volatility (expressed by Drawdowns) are relatively slow to build and not material in nature, but outlier impacts are steep, fast and major in extent.

**Table 7: Non-Compounded Return Streams of AUDJPY and EURUSD using a Trend Following System 1 ^{st} Jan 1980 to 25 Mar 2021**

Now let us compound these trend following results to see what can be produced in isolation and then as a composite.

Let us start this process by looking at compounding in isolation, where we apply a trade risk percentage of equity as opposed to a single lot per trade starting for AUDJPY only. We are simply looking at how each of these non-compounded path’s fare when we allow compounding to have a say in the matter.

**Table 8: Non-Compounded Vs Compounded Return Streams of AUDJPY and EURUSD using a Trend Following System 1 ^{st} Jan 1980 to 25 Mar 2021**

Table 8 above demonstrates several points of note.

- The uncompounded solution produces a CAGR of 7.65% and a Maximum Drawdown of 56.15%. The relationship between the return and the adverse drawdown is a MAR ratio of 0.14. With a Max Draw of 56.15% it is unlikely that many traders would possess this risk appetite when returns on offer are low.
- The compounded solution using low leverage of 1% trade equity using the same underlying non-compounded return stream produces a comparable CAGR of 7.79% but with a far lower drawdown of 31.28% and a far higher MAR of 0.25. Given the lower ulcers delivered by this compounded solution for the trader, it is far more likely that this strategy would be preferred to the non-compounded solution….and yet the fundamental basis for both return streams are the same?

This is what we mean by path dependency when dealing with compounded solutions. The shape of the return series created by classic trend following solutions is configured to allow for compounding to do heavy lifting in accelerating returns and reducing adverse volatility.

The third compounded solution, using high leverage of 5% trade equity is just used to demonstrate what these trend following systems are capable of if we unleash the tiger in them. In this extreme example, the solution delivered a powerful CAGR of 18.37% but you would have had to tolerate a maximum drawdown that nearly wiped the entire account of 87.64%. Now I am not saying any of us would tolerate this, but this is what a trend following return stream can generate if we want them to.

However, note the following with this ‘adrenalin pumping Formula One Grand Prix tiger’, despite the higher returns, look at what has happened to the MAR ratio. It has declined to 0.21. This is what happens under compounding where volatility of the return stream starts to compromise the compounding effect.

What we are therefore actually after, is the most efficient balance between risk and return expressed by the MAR ratio. Unlike other risk metrics such as Sharpe and Sortino, the MAR ratio (or for the advanced, the Serenity Ratio) is our preferred metric as it is a path dependent ratio that tells us the most efficient balance we can achieve for compounding to then do its heavy lifting. It is not about the risk inherent in the return stream itself that matters to us. We actually like volatile equity curves provided that the volatility is capped on the downside but left unhindered for the upside.

**Note to readers: The Serenity Ratio is a complex path dependent risk adjusted metric that only marginally outperforms the MAR ratio. For purposes of simplicity, we only discuss the MAR ratio in this series. For interested readers, the following article from KeyQuant provides an excellent introduction into this powerful path dependent metric. **

In fact, when you look at conventional wisdom, it is suggested that statistical practice should exclude the impact of outliers in any assessment, as their ‘magnitude’ overwhelms the average volatility of the every day return series. We of course beg to differ. When it is the extreme non-linear anomaly that is responsible for the greatest overall change across a time series, then it is essential that we pay specific attention to them.

Worrying about the ‘average’ drawdown of a series, or the average volatility of a series is simply not paying justice to the material effect that outliers play in determining a traders future successes or failures.

What really matters to us is the path or returns that are generated by our systems that gives us greatest bang for risk buck when we apply compounding to the series.

This is why we treat single measure ‘exotic’ points in the time series seriously such as the **maximum drawdown,** or the impact of **a few beneficial outliers** in that series. We pay close attention to the maximum favorable and maximum unfavorable excursion of a time series which is pivotal to path dependent outcomes. Water down the impact of these non-linear monsters at your peril. You will achieve at best moderate absolute returns over your lifetime, or at worst an account blow up, if you don’t take heed of this warning. Trend followers know this stuff and we strive for exceptional absolute risk-adjusted returns.

What importance is an average to the following string series of returns?

0.5, 1,-2,3,0.7,4,3,8,10,5,4,7,9,**105,0000**

The average of a series like this is inconsequential to us. What really matters to us is the impact of the 105,0000 in that series….or the anomaly that resides in the series. If you don’t want anomalies, then don’t trade the tails. Focus on the predictive game that resides in the peak of the distribution of returns….but we won’t be holding our breath that we will see you alive and well in the future.

Now to get back on track, rather than look at all the compounding options for our next example of EURUSD, I will simply show you the 1% compounded solution when compared against the non-compounded solution. This will once again ram home the point that path dependency really matters in our pursuit of absolute return over the long haul.

**Table 9: Non-Compounded Vs Compounded return Streams of EURUSD using a Trend Following System 1 ^{st} Jan 1980 to 25 Mar 2021**

The MAR of the compounded return stream exceeds the MAR of the non-compounded return stream in Table 9, simply due to the path dependence of the series. Once again trend following comes to the rescue and optimally configures a return path that allows compounding to work its magic. This is exactly what you need for the long road to wealth building.

We have not had to incorporate tail risk hedges into the portfolio return stream through clever option practices, as the trend following systematic processes have already embedded these principles within the technique.

So now let’s see what happens when we adopt an additional layer of secret sauce to this recipe through adding principles of diversification. We are not simply satisfied that the trend following method itself incorporates the fruits of path dependence into the return series. We then stretch this logic further and go to another new level of risk-adjusted magic by incorporating different non-correlated return streams into the process. This injects further long term wealth into the process.

So now we combine the 1% compounded AUDJPY and EURUSD series together at the global portfolio level, as we know that the location of drawdowns and the location of beneficial outliers in the series are not likely to exist at the same points in time for each separate return stream.

Table 10 below demonstrates where the outliers reside for each series. Notice that some occur at the same location contributing to the windfall at the same time, whereas others occur at different point of the time series. This applies equally to drawdowns. A Max Drawdown in one series will be offset by a lesser drawdown or even a high-water mark in the other series if they are uncorrelated.

**Table 10: Visual Chart highlighting the locations of Outliers in both Series (AUDJPY and EURUSD) using a Trend Following System 1 ^{st} Jan 1980 to 25 Mar 2021**

So, using this principle of outlier and drawdown offsets to produce better risk adjusted returns at the global portfolio level we would rather compile two separate lesser correlated series of 1% each than simply doubling down with a 2% application to a single return series.

So here we go. Let us see if the MAR ratio and the compounding effect is improved through this risk-adjusted process.

**Table 11: A Simple Portfolio Comprising two Markets (AUDJPY and EURUSD) using a Trend Following System 1 ^{st} Jan 1980 to 25 Mar 2021**

Table 11 highlights how under diversification, the risk adjusted process undertaken produces a superior result with a CAGR of 10.13% and a Maximum Drawdown of 30.56% and a more efficient MAR ratio of 0.33. We have a far better relationship between return and risk under this compounded solution than what could be achieved without diversification.

So what this Primer has shown you is that the reason trend followers always talk in terms of a ‘risk-adjusted’ process is that they know that ‘the path taken by the return stream’ is an essential criterion of wealth building. Having a weak edge is only the first step consideration for a Trend Follower. The real challenge then lies in how we shape the equity curve itself to allow compounding to do its magic.

To achieve this outcome:

- we must think long term as we can only see the work of compounding delivering wealth over a significant trade sample;
- we should not sacrifice our geometric returns through excessive leverage and be satisfied with trading a weak edge. That is all that is required for compounding to do its work and not be compromised in the process.;
- we must pay attention to the maximum favourable and unfavourable excursions of the equity curve and not be side-tracked by the balance of volatility that lies in the curve. The favourable outlier cannot be excluded from our assessment. A mere focus on drawdowns is not sufficient as outliers accelerate our ambitions;
- we must cut our losses short at all times and just let our profits run to embed the best path into the trade series; and
- we must diversify to not only reduce adverse volatility of the path of returns, but also significantly increase the chances of bumping into a favourable outlier or two, or three……

In our next Primer we will take a deeper dive into Diversification as this is a very valuable tool for the trend follower that does provides a free lunch in its treatment of adverse risk, but also just as important, increases our ability to capitalise on outliers. This is rarely mentioned as most trading methods focus on the peak of the distribution of returns. We don’t. We focus on the tails where the non-linear extraordinary event matters.

So much attention is placed on maximum drawdowns with so little attention placed on the outliers in delivering a trend followers windfall. We intend to address that discrepancy in this series.

**Trade well and prosper**

**The ATS mob**

## 19 Comments. Leave new

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]

[…] A Risk Adjusted Approach to Maximise Geometric Returns – Part 9 […]