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TREND-FOLLOWING STRATEGIES IN CRYPTOCURRENCIES, OPTIMIZED FOR DOWNSIDE RISK-ADJUSTED RETURNS PDF Free Download

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Master's Degree Program in

Statistics and Information Management

TREND-FOLLOWING STRATEGIES IN CRYPTOCURRENCIES,

OPTIMIZED FOR DOWNSIDE RISK-ADJUSTED RETURNS

Exploring Successful Trend-Following Algorithmic Trading Strategies

with a Deleveraging Mechanism in the Cryptocurrency Markets

Carlos Sakarías Koljonen Caballos

Master Thesis

presented as a partial requirement for obtaining a master’s degree in Statistics and Information Management

NOVA Information Management School

Instituto Superior de Estatística e Gestão de Informação

Universidade Nova de Lisboa

MEGI

NOVA Information Management School

Instituto Superior de Estatística e Gestão de Informação

Universidade Nova de Lisboa

TREND-FOLLOWING STRATEGIES IN CRYPTOCURRENCIES, OPTIMIZED FOR DOWNSIDE

RISK-ADJUSTED RETURNS

Exploring Successful Trend-Following Algorithmic Trading Strategies with a Deleveraging

Mechanism in the Cryptocurrency Markets

Carlos Sakarías Koljonen Caballos

The master's thesis was presented as a partial requirement for obtaining the master’s

degree in Statistics and Information Management, with a specialization in Risk Management.

Supervised by

Prof. Doutor Jorge Miguel Ventura Bravo (PhD)

Universidade Nova de Lisboa & Université Paris-Dauphine PSL

July,

2024

STATEMENT OF INTEGRITY

I hereby declare having conducted this academic work with integrity. I confirm that I have not

used plagiarism or any form of undue use of information or falsification of results along the

process leading to its elaboration. I further declare that I have fully acknowledged the Rules

of Conduct and Code of Honor from the NOVA Information Management School.

In Lisbon, 15/07/2024

DEDICATION

To my future wife

For tirelessly striving to bring out the best in me,

For understanding the importance of freedom in the world.

iii

ACKNOWLEDGMENTS

I would like to extend my deepest gratitude to Professor Jorge M. Bravo for his invaluable

inputs and ideas over the past months. His guidance has been instrumental in shaping this

thesis.

I also wish to express my heartfelt thanks to my friend Clifford D. Roman. Our countless

conversations, whether willingly or unwillingly on his part, have significantly contributed to

the enhancement of this work.

To my future wife, Katia F. Ferreira, I owe a special debt of gratitude for discovering this

master’s program, encouraging me to pursue it, and supporting me every step of the way. I

cannot imagine a better partner to share my life with.

I want to thank my parents for their unwavering support throughout this journey. Their

encouragement and belief in me have been the foundation upon which I have built my

academic and personal successes.

Finally, I would like to acknowledge Javier Milei for reviving my motivation to give the cultural

battle for the libertarian ideas. As Ludwig von Mises used to say: Tu ne cede malis, sed contra

audentior ito.

ABSTRACT

Despite its popularity, trend-following lacks a cohesive theoretical framework, resulting in

fragmented understanding and application. This thesis addresses this gap by integrating

principles from the Austrian School of Economics to provide a structured foundation for trend-

following. It posits two key assumptions: the unpredictability of market movements and the

existence of trends, introducing the theorem of the impossibility of accurate market

predictions based on dispersed human knowledge.

Traditional risk-adjusted metrics like the Sharpe, Sortino, and Calmar Ratios have a different

set of limitations. This thesis proposes the Koljonen Ratio, a novel downside risk-adjusted

return metric that combines drawdown and downside volatility for a more nuanced

evaluation, particularly in cryptocurrency markets.

The study aims to: (1) consolidate trend-following philosophy with Austrian economic theory,

(2) develop a superior downside risk-adjusted return metric, (3) assess traditional trend-

following strategies in cryptocurrency trading, and (4) implement an innovative and

sophisticated trading strategy with a deleveraging mechanism to enhance downside risk-

adjusted returns.

Anticipated contributions include a robust theoretical framework for trend-following,

improved performance evaluation metrics, practical insights into cryptocurrency trading, and

an advanced strategy for better downside risk-adjusted returns. This thesis aspires to advance

both academic research and practical applications in trading strategies.

KEYWORDS

Trend-Following; Austrian School of Economics; Cryptocurrencies; Downside-Risk;

Algorithmic Trading; Koljonen Ratio

Sustainable Development Goals (SDG):

v 
 
TABLE OF CONTENTS 
Statement of Integrity ........................................................................................................ i 
Dedication ......................................................................................................................... ii 
Acknowledgments ............................................................................................................ iii 
Abstract ............................................................................................................................ iv 
List of Figures.................................................................................................................. viii 
List of Tables ..................................................................................................................... ix 
List of Abbreviations and Acronyms.................................................................................. x 
 Introduction .................................................................................................................. 1 
 Trend-Following ............................................................................................................ 3 
1. Foundational Assumptions .................................................................................... 3 
1.1. On the Future’s Unpredictability .................................................................... 4 
1.1.1.  The Theorem of the Impossibility of Socialism .................................... 4 
1.1.2.  The Theorem of the Impossibility of Making Accurate Predictions .... 6 
1.1.3.  Trend-Following as a Philosophy of Reaction and Adaptation ............ 7 
1.2. On the Existence of Trends in Prices .............................................................. 8 
1.2.1.  Static Efficiency vs Dynamic Efficiency ................................................ 9 
1.2.2.  Austrian School of Economics (ASE) .................................................. 11 
1.2.3.  Behavioral Finance ............................................................................. 17 
1.2.4.  Newton’s First Law of Motion............................................................ 18 
2. Principles ............................................................................................................. 19 
2.1. Follow the Trend .......................................................................................... 19 
2.2. Systematic .................................................................................................... 21 
2.3. Directional Flexibility .................................................................................... 23 
2.4. Risk Management ......................................................................................... 24 
2.4.1.  Diversification .................................................................................... 24 
2.4.2.  Portfolio Heat ..................................................................................... 26 
2.4.3.  Stop-Loss ............................................................................................ 26 
2.4.4.  Position Sizing .................................................................................... 27 
2.5. Absolute Returns .......................................................................................... 29 
2.6. Sophisticated Simplicity ............................................................................... 30 
2.7. Emotional Discipline ..................................................................................... 32 
3. Historical Perspectives and Portfolio Properties................................................. 33 
3.1. Historical Perspectives ................................................................................. 33 
3.2. Portfolio Properties ...................................................................................... 36 

vi 
 
3.2.1.  Crisis Alpha ......................................................................................... 36 
3.2.2.  Low Correlation with Traditional Assets ............................................ 37 
3.2.3.  Low Drawdowns ................................................................................. 37 
3.2.4.  Positive Skewness .............................................................................. 38 
3.2.5.  Good Risk-Adjusted Returns .............................................................. 38 
3.2.6.  Good Diversifier ................................................................................. 38 
 Introducing a New Measure of Downside Risk: the Koljonen Ratio .......................... 39 
1. The Sharpe Ratio as a Measure of Risk-Adjusted Returns .................................. 39 
2. The Sortino Ratio as a Measure of Downside Risk-Adjusted Returns ................. 39 
3. The Calmar Ratio as a Measure of Downside Risk-Adjusted Returns ................. 40 
4. Combining Sortino and Calmar Ratios: The Koljonen Ratio ................................ 41 
5. Interpretation ...................................................................................................... 41 
6. Limitations ........................................................................................................... 42 
7. Conclusion ........................................................................................................... 43 
 Methodology .............................................................................................................. 44 
1. General Methodology ......................................................................................... 44 
1.1. Data Sources and Python Libraries Used ..................................................... 44 
1.2. Time Frame and Window ............................................................................. 44 
1.3. Cryptocurrencies and Commissions ............................................................. 44 
1.4. Performance Evaluation ............................................................................... 45 
2. Traditional Trend-Following Strategies Applied to Cryptocurrencies ................. 45 
3. An Ensemble Trend-Following Strategy, Optimized for Downside Risk-Adjusted 
Returns ............................................................................................................................ 46 
3.1. Strategies ...................................................................................................... 46 
3.2. Ensemble Signal Generation ........................................................................ 46 
3.3. Optimization Without a Deleveraging Mechanism ...................................... 47 
3.4. Optimization with a Deleveraging Mechanism ............................................ 47 
3.1. Application of the Kelly Criterion ................................................................. 49 
 Results and Discussion................................................................................................ 50 
1. Traditional Trend-Following Strategies Applied to Cryptocurrencies ................. 50 
1.1. Results .......................................................................................................... 50 
1.1.1.  50/100 Days SMA Crossover Long-Only ............................................ 50 
1.1.2.  20 Days Donchian Channel Long-Only ............................................... 51 
1.1.3.  Daily Heikin-Ashi Candles Long-Only ................................................. 52 
1.1.4.  50/100 Days SMA Crossover Long-Short ........................................... 52 
1.1.5.  20 Days Donchian Channel Long-Short .............................................. 53 

vii 
 
1.1.6.  Daily Heikin-Ashi Candles Long-Short ................................................ 54 
1.2. Discussion ..................................................................................................... 55 
1.2.1.  General Performance Trends ............................................................. 55 
1.2.2.  Key Metrics Analysis .......................................................................... 56 
1.2.3.  Conclusion .......................................................................................... 57 
2. An Ensemble Trend-Following Strategy for Cryptocurrencies, Optimized for Downside 
Risk-Adjusted Returns ..................................................................................................... 57 
2.1. Results .......................................................................................................... 57 
2.1.1.  Ensemble Model Strategy Without a Deleveraging Mechanism ....... 57 
2.1.2.  Ensemble Model Strategy With a Deleveraging Mechanism ............ 58 
2.1.3.  Ensemble Model Strategy With a Deleveraging Mechanism, Including the 
Application of the Kelly Criterion ........................................................................ 59 
2.2. Discussion ..................................................................................................... 60 
2.2.1.  Risk-Adjusted Return Metrics ............................................................ 61 
2.2.2.  Drawdowns Metrics ........................................................................... 62 
2.2.3.  Overall Perspective ............................................................................ 63 
2.2.4.  Conclusion .......................................................................................... 63 
Conclusions and Future Works.................................................................................... 65 
Bibliographical References .............................................................................................. 67 
Appendix A ...................................................................................................................... 71 
Appendix B ...................................................................................................................... 78 
 
 
 
 
 
 
 
 
  

viii

LIST OF FIGURES

Figure 2.1 – Drawdown vs Return to Recover ......................................................................... 26

Figure 2.2 – Price Evolution of the Tulip Bulbs ........................................................................ 36

Figure 2.3 – Barclay CTA Index Performance vs S&P 500 ........................................................ 37

LIST OF TABLES

Table 2.1 - Effect of Combining Trend-Following and Value Investing Portfolios .......... 35

Table 5.1 - 50/100 Days SMA Crossover Long-Only Strategy Metrics ............................ 50

Table 5.2 - 20 Days Donchian Channel Long-Only Strategy Metrics ............................... 51

Table 5.3 - Daily Heikin-Ashi Candles Long-Only Strategy Metrics ................................. 52

Table 5.4 - 50/100 Days SMA Crossover Long-Short Strategy Metrics ........................... 52

Table 5.5 - 20 Days Donchian Channel Long-Short Strategy Metrics ............................. 53

Table 5.6 - Daily Heikin-Ashi Candles Long-Short Strategy's Metrics ............................. 54

Table 5.7 - Ensemble Model Strategy Metrics without Deleveraging Mechanism ........ 58

Table 5.8 - Ensemble Model Strategy Metrics with Deleveraging Mechanism, Optimized for

the Koljonen Ratio ................................................................................................... 59

Table 5.9 - Ensemble Model Strategy Metrics with Deleveraging Mechanism, Optimized for

the Koljonen Ratio, with the Kelly Criterion applied ............................................... 60

Table 5.10 - Risk-Adjusted Return Ratio's Comparison - Pre-Kelly vs Post-Kelly ............ 62

Table 5.11 - Drawdown Metrics Comparison - Pre-Kelly vs Post-Kelly ........................... 63

LIST OF ABBREVIATIONS AND ACRONYMS

ABCT Austrian Business Cycle Theory

ASE Austrian School of Economics

CR Calmar Ratio

KR Koljonen Ratio

NFLM Newton’s First Law of Motion

SR Sharpe Ratio

SoR Sortino Ratio

TF Trend-following

1. INTRODUCTION

Despite its popularity, the literature on trend-following investment knowledge remains

fragmented and lacks a cohesive theoretical framework. This thesis addresses this gap by

consolidating scattered information and introducing a structured theoretical foundation based

on the Austrian School of Economics. Trend-following, renowned for its effectiveness and

popularity among practitioners, is often discussed across numerous disjointed sources,

necessitating a more organized and systematic approach. This fragmentation has long

hindered a comprehensive understanding and robust application of trend-following

principles. Drawing on the Austrian School of Economics teachings, this framework

significantly enriches and advances the trend-following philosophy, offering new insights and

a solidified approach to this successful trading methodology.

Trend-following as a trading philosophy is grounded in two fundamental assumptions: the

unpredictability of future market movements and the existence of trends in market prices. The

first assumption emphasizes the benefits of a reactive approach to investing, rather than

relying on predictive models, while the second acknowledges the persistence of trends over

time, making trend-following a viable strategy, especially due to its reactive and adaptive

nature. Drawing on the Austrian School of Economics, we will provide theoretical content to

support these two axioms. Additionally, this thesis introduces the theorem of the impossibility

of making accurate predictions, derived from the theorem of the impossibility of Socialism,

which argues that the vast and tacit nature of knowledge in human minds makes it impossible

for any central authority to coordinate society efficiently. Similarly, this impossibility extends

to accurately predicting market movements due to the dispersed, subjective, and non-

articulable nature of information. After establishing these foundational assumptions, we will

lay down the seven principles governing the trend-following philosophy, as well as some

historical perspectives and portfolio properties.

Traditional risk-adjusted measures like the Sharpe Ratio, Sortino Ratio and Calmar Ratio offer

valuable information but have also significant limitations. To address this, we introduce the

Koljonen Ratio, a new downside risk-adjusted return metric combining the Sortino Ratio and

Calmar Ratio. This metric combines actual drawdown and downside volatility in a single data

point, offering a more nuanced approach to evaluating the performance of trend-following

strategies in the context of highly volatile markets. This lays the groundwork for the practical

part of the thesis, where we analyze and optimize traditional and sophisticated trend-

following strategies applied individually to the five main cryptocurrencies by market cap. By

incorporating the Koljonen Ratio, this thesis provides a significant advancement in assessing

and managing downside risks, thereby enhancing the robustness of trend-following strategies.

The financial landscape has been irrevocably transformed by the advent of cryptocurrencies,

presenting novel opportunities and unprecedented challenges for trading strategies. Among

these, trend-following strategies are revered for their historical resilience and adaptability

across different market conditions. However, applying trend-following to this nascent asset

class underscores significant gaps in existing research due to their youth and, consequently,

the limited data. This thesis addresses these gaps by evaluating the efficacy of traditional

trend-following trading strategies in cryptocurrency markets and innovating strategies to

enhance risk-reward ratios when trading these markets.

This study sets four primary objectives. First, it seeks to consolidate and enrich the

understanding of trend-following philosophy, establishing its theoretical underpinnings with

the help of the Austrian School of Economics. Second, it seeks to obtain a downside risk-

adjusted return metric that will prove more helpful than existing metrics when performing

optimizations. Third, the study evaluates the performance of traditional trend-following

methods within the volatile context of cryptocurrency trading. Lastly, it aims to develop and

implement novel sophisticated strategies incorporating deleveraging techniques tailored to

mitigate the risk of overextended trends, thereby enhancing downside risk-adjusted returns.

The anticipated contributions of this research are multifaceted. First, by consolidating and

enriching the theoretical foundation of trend-following with insights from the Austrian School

of Economics, this thesis aims to provide a more cohesive and robust framework for

understanding this trading philosophy. Second, the introduction of the Koljonen Ratio offers

a new and more comprehensive downside risk-adjusted return metric, which is expected to

enhance the accuracy and effectiveness of performance evaluations in highly volatile markets,

particularly cryptocurrencies. Third, the empirical evaluation of traditional trend-following

strategies within the context of cryptocurrency markets addresses significant gaps in existing

research and provides practical insights into their efficacy. Finally, the development and

implementation of innovative and sophisticated strategies, including deleveraging techniques,

are expected to improve risk management and enhance downside risk-adjusted returns,

offering a more sophisticated approach to trading in digital financial markets. Through these

contributions, the thesis aspires to advance both academic research and practical applications

in the field of trading strategies.

The structure of the thesis is as follows. Section 2 provides an in-depth analysis of trend-

following as an investment philosophy, including their foundational assumptions, principles,

and historical perspectives. Section 3 introduces the Koljonen Ratio, a new measure of

downside risk, and discusses its advantages over traditional risk metrics. Section 4 outlines the

methodology used to apply traditional and sophisticated trend-following strategies to

cryptocurrencies, detailing data sources, strategy implementations, and performance

evaluations. Section 5 presents the results and discussion of the empirical analysis,

highlighting the effectiveness of the strategies and the impact of the Koljonen Ratio. The thesis

concludes with Section 6, which summarizes the findings, discusses their implications, and

suggests directions for future research.

2. TREND-FOLLOWING

Although trend-following (TF) is a pretty recent trading philosophy, following trends is an

innate part of human behavior.

TF consists of systematic and rules-based trading strategies

that involve identifying and taking advantage of the direction and persistence of market trends

until there is a trend reversal sign. It is based on the idea that financial markets tend to move

in trends over time and that traders can be profitable by recognizing them early and riding

them accordingly. TF strategies have been successfully applied to many markets, including

stocks, bonds, commodities, and currencies (Covel, 2017). This section will delve deeply into

TF's underlying assumptions, principles, and some other important considerations.

2.1. FOUNDATIONAL ASSUMPTIONS

We have seen that following trends is a natural psychological phenomenon embedded in

human nature, which could be seen as a spontaneous, evolutionary, adaptive, and irrational

behavior at times. TF attempts to take advantage of this phenomenon by applying a second

layer of behavior where there is a premeditated intelligent response to market action.

At the heart of TF strategies lie two fundamental assumptions, which, for practical purposes,

can be considered axioms due to their inherent and widely accepted nature.

The first assumption is acknowledging the impossibility of predicting the future, in general, and

future market movements, in particular. This tenet is based on the understanding that

financial markets are complex systems influenced by various factors, unpredictable or

unknown. The future has been, is, and will always be uncertain and unpredictable.

The second assumption is the belief that price movements in financial markets exhibit trends

over time. This axiom is grounded in the empirical observation that prices tend to move in

sustained directions, either upward, downward, or sideways, for various periods. TF strategies

aim to capitalize on this tendency by identifying and riding these trends for profit. Together,

these two axioms form the bedrock upon which TF strategies are built.

Axioms, as self-evident truths or propositions are the starting point used by the ASE to build

an entire system of economics (Rothbard, 1976)

In this chapter, we delve into the intricacies of these axioms, exploring their implications and

how they shape the practice of TF in the trading world. We also examine the effectiveness of

these strategies and how they fare in different market conditions, shedding light on their

Appendix A lists a brief history of TF.

https://www.trendfollowing.com/nature-origins-trend-following/

https://mises.org/library/praxeology-methodology-austrian-economics

strengths and limitations. Understanding these foundational assumptions is crucial for anyone

looking to navigate the complexities of TF trading strategies in the ever-evolving financial

markets.

2.1.1. ON THE FUTURE’S UNPREDICTABILITY

Although developed societies have created institutions

that reduce uncertainty over certain

aspects

, the future is not deterministic, and so remains inherently uncertain, and consistently

entirely accurate predictions are impossible, regardless of the data, analysis, speculation, or

computational methods used. The ASE brilliantly elucidates the rationale behind this

phenomenon through the Theorem of the Impossibility of Socialism, which will allow us to

apply those same arguments to the impossibility of having certainty of the future, of making

predictions of the future, in general, and future market prices, in particular. Doing so will

establish The Theorem of the Impossibility of Accurate Predictions.

2.1.1.1. THE THEOREM OF THE IMPOSSIBILITY OF SOCIALISM

Mises (1920, 1922, 1949), in his Theorem of the Impossibility of Economic Calculation under

Socialism

, contributed profoundly to our understanding of spontaneous market processes

and their importance for society’s coordination.

This theory later transformed into the Theorem of Impossibility of Socialism. From the

perspective of the social process, socialism is an intellectual error since it is not possible to

conceive that the governing body in charge of intervening through mandates can obtain the

necessary information to coordinate society successfully (Huerta de Soto, 1992).

For the governing body to be able to acquire the necessary information, a requirement is for

it to have a technology capable of reading human minds. However, even in that case, creating

coordinating mandates is impossible. The reasons are the following:

Defined as a set of spontaneously created rules or norms that reduce future uncertainty. Examples are the

institution of marriage, a calendar, or any timetable.

The State, private property, markets, money, savings, capital, and capital markets are some of these institutions.

According to Austrians, socialism is defined as any system of institutional aggression on the free exercise of

entrepreneurship (Huerta de Soto, 1992).

According to him, there are two separate worlds. One is the ordinal and internal world of subjective valuations,

which only allows for comparisons, not economic calculations. The other is the cardinal and external world, with

prices and where economic agents are able to perform economic calculations. The internal world of subjective

valuations drives changes in the external world. The institutions that bridge both worlds are free exchanges and

money. If both institutions are in place, every exchange will set market prices, creating a quantitative historical

reality that allows market participants to perform economic calculus. If, on the other hand, as it occurs in socialist

regimes, the free exchange of capital goods is prevented coercively or money is corrupted, market prices cannot

be set, and economic calculus is disabled, causing society’s discoordination and consequently a misallocation of

resources.

1. The Volume of the Information: The intervention body cannot consciously assimilate

the enormous number of bits of information dispersed in every mind. In order for the

entity in charge to be able to give coordinating content to its mandates, it would be

essential that the entity be able, in some way, to digest, understand, and comprehend

all the bits of information that are found in the internal world of each human actor in

the world.

2. The Character of the Information: The information the central planner needs is

essentially non-transferable due to its tacit, privative, dispersed

, and non-articulable

nature

. The knowledge is practical and subjective, not scientific nor articulable.

3. Timing: It is impossible to transmit information that has yet to be discovered or created

by the actors; it only arises from the free process of exercising human action. To rule

successfully, the central planner would need a constant stream of immediate and

future information and be able to impose its mandates immediately.

4. Coercion: Coercive mandates prevent the entrepreneurial process from discovering,

creating, and acting on the information necessary to coordinate society. It prevents

information creation and its transmission, coordination, and adjustment. This idea is

known as the socialism paradox.

These are definitive arguments as to why socialism is doomed to fail, even with the

advancement of computer technology (Huerta de Soto, 1992)

. In the next section, we will

apply those same arguments to explain why making consistently completely accurate

predictions is impossible.

Hayek elaborated on this theme in his seminal essay The Use of Knowledge in Society (Hayek, 1945), arguing

that knowledge is dispersed and decentralized among individuals. The price system in a free market act as a

mechanism for communicating information, allowing individuals to make decisions based on their local

knowledge and circumstances. For Hayek, the attempt to centralize economic planning failed because it

underestimated the complexity of economic systems and the impossibility of any single entity possessing all the

necessary knowledge to make efficient decisions.

Examples of this type of information are riding a bike or entrepreneurship. Most of the information humans

have is tacit, unable to be articulated, and privative. Indeed, one can know all the theories about riding a bike or

entrepreneurship, but the most relevant information is the practical one.

The advancement of computer technology will not make socialism more feasible; rather, it will further highlight

its impracticality. Computer technology, while powerful, cannot overcome the inherent challenges of socialism

related to the acquisition and utilization of dispersed, tacit knowledge necessary for societal functioning. Even as

computers enhance the ability of individuals to generate and utilize complex, detailed information, they cannot

replicate or replace the entrepreneurial creativity and discovery that drive social processes. Computers can

process explicit, articulated information but cannot act entrepreneurially to discover unrecognized opportunities

as humans do. Therefore, the belief that technological advancements in computing could facilitate the

management of a socialist system underestimates the complexity of social information and the indispensable

role of human creativity. Even the most advanced computer systems cannot address the fundamental issues

posed by socialism.

2.1.1.2. THE THEOREM OF THE IMPOSSIBILITY OF MAKING ACCURATE PREDICTIONS

Expanding upon the Theorem of the Impossibility of Economic Calculation under Socialism, it

becomes evident that the same foundational principles apply equally to the domain of making

accurate predictions, particularly within complex social systems. This application of the

theorem underscores the inherent limitations of predictive efforts due to the following

reasons directly stemming from the discussed theorem:

1. The volume of the Information: Just as a central planning body under socialism cannot

assimilate the vast number of information bits dispersed across every individual's

mind, predictive models face an analogous challenge. The sheer volume of data

required to make accurate predictions about future states of social, economic, or any

complex system exceeds the capacity of any existing or conceivable technology to

capture, process, and interpret effectively.

2. The character of the Information: Information necessary for accurate predictions often

possesses the same tacit, privative, and non-articulable nature that thwarts economic

calculation under socialism. Much of the knowledge that would inform accurate

predictions is subjective, context-dependent, and not readily quantifiable, making it

inherently resistant to being captured or utilized by predictive algorithms or

methodologies.

3. Timing and Dynamism: The dynamic nature of information, where new data is

constantly generated through human action, presents a timing challenge akin to that

faced by socialist planners. Predictive models must contend with existing data and

anticipate spontaneous future situations. This unpredictability and the need for

immediate and future-oriented information render consistently accurate predictions

unfeasible.

4. Impact of Prediction: Just as coercive mandates under socialism inhibit the discovery,

creation, and transmission of information necessary for societal coordination,

interventions based on predictions can similarly distort the very outcomes they aim to

forecast

. Predicting can alter behaviors and conditions, introducing feedback loops

that invalidate the premises of the predictions.

These parallels demonstrate that the difficulties inherent in central planning under

socialism—stemming from the challenges of information volume, character, timing, and

coercion's counterproductive effects— undermine the feasibility of making consistently

accurate predictions. When applied to predictions, the insights from the theorem highlight

the fundamental limitations of predictive endeavors, reaffirming the importance of humility

and adaptability in the face of complex systems' inherent unpredictability. This is fully

applicable to predicting price movements in markets.

For example, if a “perfect” model is predicting that the price of a stock is going to be 30% higher in one month,

the actions carried out using that prediction may distort the reality as it was initially predicted, making the

prediction not entirely accurate.

2.1.1.3. TREND-FOLLOWING AS A PHILOSOPHY OF REACTION AND ADAPTATION

Considering the challenges and limitations associated with making accurate predictions in

complex systems, the philosophy of trend-following (TF) emerges as a potent, heuristic, and

pragmatic approach to trading markets. Fundamentally, TF is a strategy that does not attempt

to predict future market movements but rather reacts to what has already occurred and

continues to unfold in the market.

TF in trading emphasizes adaptability and reduced risk by reacting to actual market trends,

enabling traders to adjust their positions in line with current market dynamics and mitigate

risks from speculative forecasts. These strategies capitalize on the market's natural tendency

for trends, allowing traders to profit without deciphering the underlying causes. It offers

resilience to volatility through systematic rules for entry, exit, and risk management, fostering

a disciplined framework that navigates market fluctuations effectively. Furthermore, by

adhering to predefined rules, TF curtails emotional biases and enhances consistency, which is

vital in the unpredictable realm of financial markets. In essence, TF embodies a pragmatic and

adaptable approach to trading, demonstrating the effectiveness of reacting to what the

market does, rather than what it might do.

Although saying the future is uncertain might seem unnecessary, many investment

philosophies and strategies are based on trying to predict or foresee future market

movements. Investments based on fundamentals, and more specifically, value investing, are

based on intrinsic value calculations based on free cash flow forecasts and other methods.

Although we are not arguing against the validity of these investing philosophies, we must

clarify that the timing component of these types of strategies is usually lacking. We argue that,

according to the axiom we are dealing with here, the position initiations should always be

accompanied by initial price movements that confirm the future price prediction of the asset.

The Adaptive Market Hypothesis (AMH), conceived by Andrew Lo (Lo, 2004), introduces a

revolutionary framework for understanding market dynamics through the lens of evolutionary

biology. This hypothesis posits that financial markets are not static realms governed solely by

efficiency or irrationality but are instead adaptive environments where survival and success

are predicated on the ability to evolve. In this complex ecosystem, market participants—akin

to species in the natural world—must continually adapt to survive amidst the relentless forces

of competition, mutation, and natural selection.

This evolutionary perspective provides a compelling explanation for the efficacy of dynamic

strategies like TF. It underscores the importance of adaptation as a critical factor in the long-

term survival and success of market participants. By framing markets as ecologies and traders

as species, AMH elucidates why TF strategies excel particularly during periods of market

divergence and financial crises. These scenarios represent significant environmental shifts

where price dislocations are pronounced, highlighting the adaptive advantage of TF

approaches that thrive in the face of such dislocations.

Contrasting sharply with the Efficient Market Hypothesis (EMH), which posits that market

prices reflect all available information (Fama, 1965, 1970; Malkiel & Fama, 1970), AMH and TF

stand in direct opposition. TF, with its systematic investment across asset classes based on

historical price trends, challenges the foundational premises of even the weakest form of

EMH. Instead, AMH offers a framework that reconciles these discrepancies by demonstrating

how markets evolve, how opportunities manifest, and how participants either flourish or fail

through mechanisms akin to those found in evolutionary biology.

AMH's depiction of markets as ecologies filled with competing 'species' of market participants

introduces a dynamic view of financial markets where profit opportunities vary with resource

availability and competitive intensity. It suggests that periods of high resources and low

competition foster profit opportunities. However, as competition intensifies, only those

participants who possess a competitive edge survive and adapt, thereby initiating a new cycle

of evolutionary dynamics.

Factors influencing adaptation in these 'market ecologies' include institutional restrictions,

market functionality, and behavioral biases. Constraints such as drawdown limits, risk limits,

allocation constraints, and market access limitations all shape the evolutionary fitness of

market participants. Likewise, market functionality aspects—such as liquidity and

counterparty risk—as well as prevalent behavioral biases like loss aversion and herding, play

crucial roles in determining who adapts successfully and who does not. By adopting the AMH

framework, one gains a deeper understanding of the inherent adaptability and resilience of

trend-following strategies. It reveals how these strategies, through their inherent adaptive

properties, not only navigate but thrive in the evolutionary cycle of financial markets. This

adaptability is key to their success, especially in navigating the tumultuous periods of market

dislocations and financial crises, where traditional strategies might falter.

2.1.2. ON THE EXISTENCE OF TRENDS IN PRICES

The persistent risk-adjusted returns observed in TF can be attributed to the inherent tendency

of free market prices to demonstrate trends and serial correlations. However, a largely

unaddressed inquiry in the realm of TF research pertains to the underlying reasons for the

existence of these trends

. To address this query comprehensively, it is imperative to

delineate between static and dynamic efficiency within market contexts. This bifurcation is

This cycle is particularly evident during financial crises, which represent drastic changes in the market

environment, testing the adaptability of market strategies to the extreme.

This idea is showcased in the following article: https://www.trendfollowing.com/2013/07/09/why-does-it-

trend/

crucial as the static perspective, rooted in the efficient market hypothesis, offers limited

explanatory power regarding price trends. Conversely, the dynamic framework provides a

more fertile ground for understanding the genesis of trends. Following the establishment of

this fundamental theoretical distinction, various explanations for the existence of trends will

be explored and articulated.

This examination will be conducted through the lenses of various disciplinary perspectives:

the Austrian School of Economics, Behavioral Economics, and, intriguingly, from the domain

of Physics, explicitly referencing Newton's First Law of Motion. Each framework offers a

unique vantage point for understanding the phenomenon, enriching the analysis with diverse

theoretical insights.

2.1.2.1. STATIC EFFICIENCY VS DYNAMIC EFFICIENCY

Although still under discussion in academic circles (Lekovic, 2018), throughout financial

history, the Efficient Market Hypothesis (EMH)

(in its weak

, semi-strong

, and strong

forms) has proven to be invalidated by a large number of papers and empirical studies

As hypothesized, the refutation of the weak form of market efficiency axiomatically entails

the concurrent negation of both the semi-strong and strong forms of market efficiency.

Efficient Market Hypothesis is a cornerstone of modern financial theory. It suggests that asset prices fully reflect

all available information. Developed by Eugene Fama in the 1960s, EMH posits that it is impossible to consistently

achieve higher-than-average returns by using any information that the market already knows because stock

prices already incorporate and reflect all relevant information. There are three versions of this theory, each

differing in terms of the degree to which information is reflected in stock prices.

The weak form efficiency asserts that all past trading information, including historical prices, volume, and

returns, is already incorporated into stock prices. Therefore, no one can predict future stock prices based on past

price trends or patterns. This form of EMH suggests that technical analysis, which relies on historical price data,

is ineffective in predicting future stock movements and beating the market.

The semi-strong form efficiency states that stock prices include not only all historical trading information but

also all publicly available information. This includes news, financial statements, economic data, and other publicly

disseminated information. This implies that neither technical analysis nor fundamental analysis can consistently

outperform the market, as any new information that could be used for trading is quickly and accurately reflected

in stock prices.

The strong form efficiency claims that stock prices fully reflect all information, both public and private (insider

information). Thus, no one, not even company insiders with undisclosed information, can consistently achieve

higher-than-average returns. If the market is strong-form efficient, even insider trading cannot lead to consistent

outperformance of the market. Testing strong form efficiency is challenging, as it involves assessing the illegal

use of private information.

Lo and MacKinlay (1999) discovered that in the short term, stock prices show serial correlations that differ

from zero, contradicting the random walk hypothesis and suggesting the presence of momentum in short-term

stock prices. Additionally, Moreover, Lo, Mamaysky and Wang (2000) employed advanced nonparametric

statistical methods to identify patterns in stock prices and found that certain technical analysis signals, like "head

and shoulders" formations and "double bottoms", may possess some modest predictive ability.

If historical trading data is not fully reflected in stock prices (contradicting the weak form), then it is unlikely

that more complex and diverse sets of information (like earnings reports, economic data, etc.) are fully reflected,

as posited by the semi-strong form. Similarly, if simpler, more readily available information (past trading data) is

Many simple rules-based strategies based on technical analysis have shown that it is possible

to consistently have higher-than-average returns in different markets employing the same

strategy in all of them (Covel, 2017), invalidating not only the weak form of efficiency but also

the other two hypotheses developed by Eugene Fama in 1970

This refutation, in our view, does not imply that free markets are inefficient, although it does

mean that Fama’s definition of efficiency is inaccurate

, as it misses the essence of how

markets work and fails to understand the importance of time, uncertainty, and human action

in market processes.

Frank Shostak (1997) explains it eloquently:

“…The major problem with the EMH is that it assumes that all market participants arrive at rational

expectations forecast. This, however, means that all market participants have the same expectations

about future securities returns. Yet, if participants are alike in the sense of having homogeneous

expectations, then why should there be trade? After all, trade implies the existence of heterogeneous

expectations. (…) Even if we were to accept that modern technology enables all market participants

equal access to news, there is still the issue of news interpretations. The EMH framework implies that

market participants have the same knowledge…”. (p. 27)

Although the static efficiency of the EMH does not offer us a viable framework to understand

market processes and why trends take place without departing from the assertion that

markets are efficient, understanding efficiency through a dynamic perspective allows us to

explain the existence of trends harmonized with the idea that free markets are efficient.

The dynamic efficiency perspective was developed by the ASE (Huerta de Soto, 2008). This

theory (and others from the same school of thought), in conjunction with the insights offered

by Behavioral Economics and Newton’s First Law of Motion, will give us a thorough theoretical

framework to establish a successful justification for the existence of trends.

not properly integrated into stock prices, it's even more implausible that more exclusive and complex information

(like insider information, as in the strong form) is fully reflected.

Berkshire Hathaway’s results of excess risk-adjusted rates of return over many decades is also a clear example

of an empirically invalidated EMH semi-strong form of efficiency since they use primarily fundamental analysis

(https://www.princeton.edu/~ceps/workingpapers/91malkiel.pdf).

Moreover, insider trading is clearly a profitable activity, as it gives the unfair edge to the investor to act on

material nonpublic information. This invalidates the strong form of efficiency.

(https://www.investopedia.com/articles/stocks/09/insider-trading.asp).

Fama’s framework is a static environment where time and uncertainty do not play a factor and where efficiency

is a static point. In this framework, prices virtually instantaneously appear in a state of “equilibrium”. In our view,

this is the wrong way to understand market processes. A more accurate view of efficiency has been developed

by Austrian School economists (Huerta de Soto, 2008). For them, efficiency is not a market result where a price

is in “equilibrium”, but a continuous market process (time) of trial and error (uncertainty) of many market

participants, where price has a strong tendency to move towards a dynamic level where their preferences are

coordinated (Kirzner, 1973). Fama’s view is, in this sense, an objective, mechanical, and uniform way of

understanding efficiency and markets.

https://mises-media.s3.amazonaws.com/rae10_2_2_5.pdf

2.1.2.2. AUSTRIAN SCHOOL OF ECONOMICS (ASE)

From the standpoint of the ASE, it is possible to interpret and explain the existence of trends

through three distinct theoretical lenses: the theory of entrepreneurship discovery and

dynamic efficiency, the subjective theory of value, and the business cycle theory.

Theory of Entrepreneurship Discovery and Dynamic Efficiency

From the theory of entrepreneurship

discovery and dynamic efficiency perspective, to

understand the reason trends are an inherent characteristic of free market prices from the

Austrian perspective, it is essential to first understand the role that free prices have in an

economy. From an ASE perspective, markets function as intricate social learning processes in

which knowledge

is communicated through prices

. In this sense, prices are a signal, a

medium, through which this learning is facilitated (Hayek, 1945)

. In these social learning

processes, knowledge is communicated and utilized by individuals for economic calculation

and coordination (Mises, 1922 & 1949)

But what causes knowledge to change and spread? What is the agent of change? The answer

to this question was only fully developed in 1973 with Kirzner’s (Kirzner, 1973) theory of

entrepreneurial discovery.

According to Kirzner, the agent of change is the alertness to

Etymologically, the term entrepreneur comes from the French verb entreprendre (inter prehendere in Latin,

from the verb in prehendo-endi-ensum), which is closely related to every human actor. ‘Prehendere’ in Latin

means to seize, grasp, take hold of, or take possession of, and, in a broader sense, to discover, see, perceive,

realize, and catch.

Most of this knowledge, as it encompasses individual scarcity expectations and preferences, is information

that entrepreneurs are constantly creating when they act. This information is subjective, practical (in the sense

that it is only created through the exercise of business action in its corresponding contexts), dispersed (since it is

scattered in the mind of all human beings), and tacit (in the sense of which is very difficult to articulate in a

formalized way) (Huerta de Soto, 2008). In this sense, free prices are the only reliable mechanism and signs

through which this knowledge is spread.

In this sense, prices are mechanisms of data compression.

According to Hayek in ‘The Use of Knowledge in Society’, prices are a mechanism for communicating

information. Prices in a market economy reflect the relative scarcity of goods and services, and the preferences

of consumers. By observing prices, individuals can make informed decisions about where to allocate their

resources. Prices act as a signal that helps coordinate the actions of millions of individuals, each with their unique

knowledge and preferences. Hence, free prices are an indispensable requirement for the economic calculation

and coordination of economic agents that leads to a dynamic efficiency.

Mises, in his critique of socialism, argued that without market prices it would be impossible for central planners

to allocate resources efficiently. Prices, in the Austrian view, emerge from voluntary exchanges in the market

and are crucial for entrepreneurs to calculate profits and losses. This calculation is essential for coordinating

economic activities and ensuring that resources are used where they are most valued by consumers.

Kirzner in his theory of entrepreneurial discovery, provided a Misesian answer (Mises, 1945) to a Hayekian

question (Hayek, 1937). For Hayek, markets are social learning processes in which knowledge is communicated

through prices, enabling people to better coordinate their plans. What Hayek was not able to fully explain was

exactly how that learning process took place and what causes knowledge to change and spread to generate that

learning. Hayek argued that prices are the medium by which knowledge is conveyed, but he struggled to explain

who or what is the agent of change. Kirzner’s answer to that question was to pick up on Mises’ emphasis on

human action and the entrepreneurial element of human behavior and apply it to Hayek’s argument. Hence,

what causes knowledge to change, and spread is the alertness to opportunities by the entrepreneurial and

speculative spirit that every human has, which permits us to grasp pure profit.

opportunities

by the entrepreneurial and speculative spirit that every human actor has,

which permits us to grasp pure profit

in a competitive environment

through a process of

entrepreneurial and price discovery

, which leads to dynamic efficiency (Huerta de Soto,

2008)

, describing a never-ending market process where prices constantly attempt to

converge

towards a dynamic efficient price where market participants’ preferences are

coordinated. Time

plays a crucial role in this framework, as changes in the market do not

happen instantaneously or discretely but unfold gradually and continuously instead.

It is this constant and gradual evolution and accumulation of knowledge and opportunities

that give rise to the observable trends in market prices.

Kirzner is referring to our ability to foresee ways of doing things that others have overlooked, of seeing

possibilities not given by the data. It is the act of seeing new means-end relationships rather than optimizing

based on a given economic and static framework. Entrepreneurship is a moment of discovery, of genuine

surprise, of serendipity. Successful entrepreneurship brings the expectations of market actors into greater

coordination by using resources in new ways to better satisfy wants.

Profit and losses are key, as they signal the success or failure of entrepreneurship. Note that the entrepreneur

imagines a new set of means and ends, of future reality, but they might be right or wrong about whether those

will be successful. Entrepreneurship and competition are two sides of the same coin. As long as people are free

to envision alternative uses of resources and act on that vision, markets are competitive. Profits and losses play

a crucial role in this context. They serve as indicators of the speculator's success or failure in anticipating market

trends correctly. These financial outcomes are crucial feedback mechanisms, informing speculators whether

their insights and actions have brought their expectations in line with market realities.

Competition here is not understood as the perfectly competitive market of mainstream economics, where

people react passively to given prices and cost curves, or where there is a large number of small firms, but

instead, competition refers to the process by which people constantly engage their entrepreneurial alertness, to

see the world in new and better ways. Viewing competition as a discovery procedure is more helpful for

understanding the world than the very different conceptions of competition and monopoly used by many

economists. Kirzner’s understanding of competition as rivalry better aligns with the sorts of market behavior we

normally think of as competitive (lowering prices, advertising aggressively, or differentiating one's products).

In the markets, speculators do not merely react to existing price signals; instead, they actively anticipate future

market movements. This anticipation is akin to Kirzner’s concept of seeing new means-end relationships.

Speculators imagine new scenarios and outcomes, assessing the potential for profit in these foresights. Their

actions, based on these anticipations, contribute significantly to the price discovery process, a critical component

of market efficiency. The price discovery process is a never-ending process where many rational actors (from a

subjective point of view) apply their entrepreneurial alertness to their speculation over the future, and where

prices are constantly attempting to converge to a dynamic efficient price that successfully coordinates the limited

availability of the asset (scarcity) and the utility of the different actors.

The theory of dynamic efficiency was formulated by Jesús Huerta de Soto, a prominent Spanish economist. The

theory criticizes the mainstream economic focus on static efficiency, which is concerned with the optimal

allocation of given resources at a point in time. Instead, Huerta de Soto advocates for dynamic efficiency, which

is about how well an economy adapts to changes over time, promotes innovation, and creates wealth.

This attempt to converge is not perfect, but there is a strong tendency for this convergence to occur. This

convergence over time and not instant can also be understood as caution from the market participants, due to

the fact that the so-called optimal price is constantly moving.

The concept of time is integral to dynamic efficiency. It recognizes that economic conditions, preferences, and

technology change, and it values the capacity of an economy to adapt and evolve in response to these changes.

Subjective Theory of Value

The subjective theory of value

solved the diamond-water paradox

, as it stated that the

price of a good is determined by the marginal utility

, which considers not only the subjective

utility

of a good or service but also its perceived scarcity

The means-end dynamics of every actor, which in turn determines the utility of goods and

services, are highly dynamic, and in constant change.

By investing in financial markets, market participants seek to achieve profits by applying their

entrepreneurship alertness, speculating

over the uncertain future cash flows and risk

premiums

(Covel, 2017) of a specific asset, which are the elements of the utility a financial

asset can bring. Commodities and other real assets, on the other hand, do not necessarily

provide cash flows, but their price is also explained by their perceived utility (which can be

productive or non-productive) and scarcity.

In the same way that an actor's means and ends are constantly changing due to their

entrepreneurship alertness, the perceived utility and scarcity of any financial or real asset also

Notoriously developed by Menger (Menger, 1871), Jevons (Jevons, 1871) and Walras (Walras, 1874) in

different geographical points and little to no communication between them. This marked the Marginal

Revolution in economic thought, shifting the focus from classical economics to a new era of understanding

economics.

This is the contradiction that, although water is more useful in terms of survival, diamonds are more expensive.

Marxist labor theory of value and other theories emphasizing production costs failed to explain this paradox.

Marginalists focused on the utility of each additional unit of a good, rather than its total utility. While water's

total utility is high due to its necessity for survival, its abundant supply results in low marginal utility. Therefore,

the value and price of water are lower because consuming an additional unit doesn't significantly increase its

usefulness or the willingness to pay for it.

Value is defined as the subjective and psychic appreciation, more or less intense, that the actor gives to his

ends. Utility, on the other hand, is also a subjective and psychic appreciation, that the actor gives to a means

more or less intense, depending on the value the actor gives to the end which that means is perceived to help

achieve. The utility of a good or service (means) is, hence, directly proportional to the value we give to the end

it is perceived to help achieve. Value is projected to a means through the concept of utility. In this sense, value

and utility are two sides of the same subjective coin.

Scarcity here, from the Mengerian Austrian School perspective, must also be understood as a subjective

concept applied to the means. The actor must think that the means at his disposal are insufficient to achieve all

the ends that are chased. Without perceived scarcity, a good or service is not a means.

The concepts of speculation, entrepreneur and human action are intricately related and must be understood

as such. Human action is every deliberate behavior performed by a person. This happens because the person

acts to change from a situation of relative lower satisfaction to a situation of higher satisfaction. Speculation is

the individual and subjective aspiration to forecast the future. Entrepreneurs are humans that speculate, but also

every human has an innate entrepreneurial spirit.

When risk premiums increase or decrease, the underlying assets are repriced. Since investors have different

expectations and their views are sticky, significant shifts in the market generally occur over several months or

years as expectations are gradually adjusted. Markets do not reflect perfectly efficient prices at all moments (as

is understood in mainstream economics). However, they tend to asymptotically move towards them through a

process of trial and error. This means that, as long as there is uncertainty about the future, we can safely assume

there will be trends.

have a dynamic nature

. This inherent characteristic explains the constant changes in the

supply and demand structure

of a specific asset, which in turn explains the movement of

prices, although not necessarily the reason they exhibit trends.

Although the utility and perceived scarcity might have a discrete and immediate shift due to

changes in the perception of a specific individual, this is not typically the case for market

processes

, where knowledge is spread and interpreted in different ways and speeds. This is

why prices tend to move gradually over time, creating the trends we see in the prices of

commodities and financial assets.

Business Cycle Theory

Although there are many different explanations for why business cycles take place, most of

these explanations, although some of them plausible, have major flaws, and refuting them

goes beyond the scope of this thesis.

The Austrian Business Cycle Theory (ABCT) can also serve as a theoretical framework to explain

the existence of trends in market prices, especially the overextended ones. To understand this

theory is imperative to start from the theory of capital, elaborated by Menger (1888) and

Böhm-Bawerk (1889). Mises (1912 & 1949) and Hayek (1933) expanded on this knowledge,

effectively creating the ABCT. From their subjective perspective, capital goods (as well as

consumption goods) are considered a means to reach an end. They are the means of

production; therefore, they are considered economic goods of a higher order than

consumption goods.

They appear thanks to the accumulated conjunction of three essential elements: work, time,

and natural resources. The essential requirement for creating capital goods lies in savings,

which means choosing not to consume in the present moment and to be able to potentially

consume more sometime in the future

. The production project using higher order goods

Changes in the perceived utility and/or scarcity can have many reasons. It does not need to be based in reality.

That is why behavioral economics, when explaining human biases, play an important role complementing the

explanation of shifts in perceived utility and scarcity that are not based in reality.

Which is manifested in the changes in the liquidity in the orderbook structure in centralized exchanges and

brokers. In the case of decentralized exchanges it is directly manifested in the prices, as there are no orderbooks.

For example, the sentiment of a market participant might be different than the market general sentiment of a

specific moment.

The actor, therefore, will only be able to create and reach successive intermediate stages of production

increasingly distant in time from consumption if he has given up immediate satisfaction of his human needs

(consumption). Böhm-Bawerk’s example of Robinson Crusoe on his land is very illustrious: Robinson, who

recently arrived on the island, has as his only means of subsistence picking blackberries by hand. With all his

effort he can collect more than necessary for his daily subsistence. After some time at that regime, he realizes

that he could be much faster with a wooden stick. But he finds that he believes that he must dedicate five days

of work to get the stick ready, during which he will not be able to pick any blackberries. To do this he must

consume a smaller number of blackberries than he collects. He must, therefore, save a portion of the berries, by

reducing his consumption or collecting more than he currently consumes. This saving represents an unavoidable

than previously is more prolonged from a time perspective, as it incorporates more productive

stages. In modern economies, capital goods are transitory

, and the complexity of these

productive processes is extremely intricate and prolonged

Every human actor has a time preference

, so a delay in consumption will only occur if the

actor thinks that ends of higher value may or will be achieved in the future. The actor must

coordinate their present behavior with their foreseeable future one

. This coordination occurs

through interest rates

, which are the most important price signals for consumers, savers,

investors, and entrepreneurs

. The manipulation of interest rates from the natural level to

sacrifice, but he subjectively thinks that it compensates him concerning the end he intends to achieve in the

uncertain environment in which he finds himself. During the following weeks, he reduces his consumption, going

somewhat hungry, saving berries until he reaches five days' worth of subsistence while he produces the stick.

Once its end is reached, it can reach previously inaccessible places, hitting with more power, and thus managing

to multiply its productive capacity by ten. Now, in a tenth of a day, he harvests the berries necessary to support

himself, and can dedicate the rest of the time to higher purposes or leisure. In modern economies this function

is performed by capitalists, who make available to workers the necessary resources to sustain themselves until

the production has concluded.

Capital goods are non-perpetual due to physical expenditure and economic or technological obsolescence. To

increase the sophistication and number of capital goods, savings must be higher than the capital expenditure.

These processes are divided in multiple subprocesses, where since the beginning of production the

consumption good can take a few years to be sold. Additionally, there is a higher division of labor as people

specialize in different parts of the productive processes. The difference between poor and rich nations is that

rich ones have a greater sophistication and number of well-invested capital assets, due to their previous savings.

They are the ones that have achieved more time accumulation in the form of capital goods. It is important to

distinguish the stages depending on their degree of proximity to consumption; they closer they are to the

consumer goods the more difficult it is to repurpose them for other uses.

Human beings, ceteris paribus, prefer to satisfy their needs or achieve their ends as soon as possible. In other

words, between two identical ends, the actor will prefer the one that is closest in time. Or rather, with identical

circumstances, present means are preferred to future means. Time preference is not a psychological or

physiological category, but a requirement of the logical structure of every human action. The intensity of this

preference varies from person to person. This difference in psychic intensity gives rise to beneficial exchanges

between economic agents.

If the actor undertakes action processes that are excessively long in relation to their savings (if they save too

little), they would be left without savings before having reached their end. In contrast, if they have excess savings

in relation to their future needs, it means they made an excessive and unnecessary sacrifice. The subjective

estimation of his time preference is what leads the actor to appropriately coordinate and adjust his present

behavior in relation to his future behaviors and needs.

Although it may seem that interest rates are a social and monetary phenomenon, this is not the case. In our

example, Robinson Crusoe, in a solitary environment without an indirect means of exchange, had a certain time

preference, a certain interest rate, which led him to create a rod and not a blast furnace or to continue picking

the blackberries with the hands. In developed societies, gross (market) interest rates on the credit market

contains society’s natural interest plus a liquidity premium, risk premium and a premium for expected inflation

or deflation.

As we previously saw, prices convey a vast amount of information and are mechanisms of coordination.

Specifically, interest rates are prices that coordinate intertemporal behavior and the relationship between

consumption, savings, and investments; this is, present behavior with future foreseeable one with regards to

consumption. It is the price of present goods or services with regards to future goods or services. For instance, a

society that has a high rate of savings will have a high amount capital, and its interest rates will tend to be lower.

With lower interest rates, the discount factor of long-term investment projects makes them more appealing to

entrepreneurs. This must be interpreted in the following way: higher savings and lower interest rates work as a

signal, where society is conveying the information that actors do not want to consume goods and services today

and want to consume them in the future instead. This signal is transmitted to entrepreneurs, who have the

artificially lower ones, conducted by Central Banks

, causes the banking system to excessively

lend, incentivizing an expansion of credit (lending and borrowing) in the economy

. This

creates a disproportionate and exaggerated optimism and an unsustainable economic boom

based on malinvestments

, where a widespread resource misallocation

takes place over

time. Eventually, the Central Bank starts normalizing interest rates

to stave off high levels of

inflation or address other economic concerns

. In this process, the malinvestments carried

out during the period of low rates become apparent; unprofitable projects are abandoned,

leading to higher unemployment and a decrease in economic activity.

These artificially induced business cycles, with booms and busts, exacerbate the volatility and

trends that otherwise assets would experience. This phenomenon generates an unsustainable

cycle of apparent prosperity, wherein asset prices predominantly exhibit an upward trajectory.

However, as malinvestments come to light, another period emerges there where asset prices

trend downwards.

incentive to pull productive resources from stages that are closer to consumption and convert them into stages

that are farther. For this transition to happen efficiently, production factors (specially the original ones) need to

have flexible markets where agents can exchange property rights with the lowest possible social and economic

costs. Additionally, entrepreneurs lengthen the productive process by investing more in goods and services that

take longer to be produced and less in the ones that take shorter, increasing the stages of production and making

the productive process longer and more productive.

In current modern societies, financial systems do not operate with several private central banks (with gold and

other types of reserves) in competition, but with a public monopolistic one governed by the State. This, and the

fact that Central Banks do not operate with full convertibility to the reserves they hold, opens the door for

monetary policies which manipulate interest rates and the quantity of fiat money in the economy.

Low interest rates cause this credit expansion due to the fact that the banking system operates with fractional

reserves, which is the idea that banks can lend the money of their clients’ deposits. Many Austrian economists

propose a 100% cash ratio for client’s deposits, where banks behave as trustees. This does not mean that banks

would not be able to lend and operate as a financial institution, but they would do so only with the money that

is lent to them by their clientele.

This term refers to poor investment decisions based on low interest rates, made not because consumers have

saved more and will have a higher future demand, but because of the distorted signals sent by the artificially low

interest rates. Certain sectors (like housing or technology, which are longer-term investment projects) might

experience a boom as a result of this influx of cheap credit. This is because with lower interest rates, many long-

term investment projects that were not profitable on paper now become profitable. Lower interest rates cause

a proportional reduction in the discount factors applied to investment projects. A reduction in the discount factor

has more incidence in cash flows that are farther in the future than cash flows occurring in the near term.

Low interest rates cause resource misallocation due to the fact that there is a distortion between savings and

consumption. The economy looks it is doing well, but it is not aligned with actual consumer preferences and

savings rates. This causes a shift in the production structure towards longer term projects, where capital is

directed away from sectors that truly reflect consumer preferences.

This process of normalization entails the interest rates hikes and credit tightening policies towards banks, who

are then financially compelled to implement similar measures with their clients.

These concerns can be an overheating economy, asset bubbles, exchange rate stability, current account

deficits, debt levels and credit quality, excessive risk of financial institutions, etc.

2.1.2.3. BEHAVIORAL FINANCE

The existence of trends in the markets can also be understood and justified through the

behavioral finance perspective; this is, through the lens of human psychology and cognitive

biases. Kahneman's (Kahneman, 2011) work often highlights the divergence from the rational

agent model assumed in classical economics

, and provides insight into why and how trends

develop in financial markets.

Behavioral finance posits that investors are not always rational actors who make decisions

solely based on objective data and logical analysis. Instead, their decisions are often

influenced by subjective reference points with psychological biases and emotional responses.

This leads to behavioral patterns in market behavior that can manifest as overreactions and,

ultimately, overextended trends.

Some of these biases are overconfidence, herd mentality, loss aversion

, and confirmation.

These biases can lead to excessive trading, and the formation of market bubbles, as investors

pile into trending assets, further driving up prices without regard to their fundamental value.

One key concept in behavioral finance is the idea of heuristics, which are mental shortcuts

that people use to make judgments and decisions. While heuristics can be useful, they can

also lead to systematic errors or biases

Behavioral finance theorists posit that investors frequently exhibit a proclivity for suboptimal

responsiveness to novel information, precipitating a gradual adjustment in asset prices

towards the equilibrium level that fully reflects the new data. This phenomenon, ascribed to

the investor's delayed assimilation of the information's implications, contributes to the

observable momentum in price movements. Concurrently, these theorists acknowledge the

occurrence of excessive reactions, often attributed to the bandwagon effect engendered by

collective behavior dynamics, which can lead to an exaggerated prolongation of prevailing

market trends.

In summary, from a behavioral finance perspective, market trends are not just reflections of

economic fundamentals but are also deeply influenced by human psychology. Cognitive biases,

Behavioral finance posits a divergence from the rational objectivity inherent in classical economic theories,

asserting the absence of a wholly rational agent within the economic milieu. However, it is crucial to acknowledge

that behavioral finance does not inherently contravene the subjective rationality delineated by the ASE, wherein

economic actors operate rationally in subjective terms, since (with every action) they attempt to turn from a

subjectively less satisfactory situation to a subjectively more satisfactory one, although this happens, inevitably,

within the framework of their limited knowledge and biases.

Prospect theory, another key contribution by Kahneman, explains how people make decisions in situations of

risk and uncertainty, which are commonplace in financial markets. This theory suggests that people value gains

and losses differently, leading to irrational financial decisions that can contribute to market trends.

For example, the representativeness heuristic might lead investors to assume that a good company is always

a good investment, overlooking fundamental analysis. This can create and perpetuate trends based on popular

sentiment rather than intrinsic value.

heuristics, overconfidence, loss aversion, and the asymmetry in how gains and losses are

perceived all play a significant role in how trends are formed and sustained in financial

markets. Understanding these psychological factors is crucial for explaining and anticipating

market movements.

2.1.2.4. NEWTON’S FIRST LAW OF MOTION

Another alternative explanation for the existence of trends in prices can come from the realm

of physics, not only economics.

In 1687, Isaac Newton introduced the Newton's First Law of Motion

(NFLM) (Newton, 1687),

which has remarkable similarities to TF ideas in its foundational principles. NFLM, which

addresses the persistence of an object's state of motion, offers a compelling framework to

understand the behavior of financial markets, especially the continuation and reversal of

trends.

In NFLM, we can find the following principles:

1. Persistence of State (Inertia): An object will maintain its state of motion (either at

rest or in uniform motion) unless an external force is applied.

2. Resistance to Change: The inertia of an object makes it resist changes in its state of

motion.

3. Impact of External Forces: It takes an external force to change the motion of an

object, either by accelerating it, decelerating it, or changing its direction.

4. Predictability and Reaction: The law allows for the prediction of the motion of an

object if the forces acting on it are known.

5. Momentum: The concept of momentum in physics (mass times velocity) is closely

related to the first law, indicating how an object will continue moving in the same

direction.

We could say that TF strategies are based on the same ideas and principles, identifying any

free market price in economics to what any object would be in physics. By exchanging the

words object for price, state of motion for trend, and external forces for variations in the

supply-demand dynamics, we can apply the same principles to trend following and

simultaneously explain (from a physics perspective) why trends exist. In this sense:

An object at rest stays at rest, and an object in motion stays at the same speed and direction unless acted upon

by an unbalanced force.

1. Persistence of trends: A price will maintain its trend until it experiences an

antagonistic force with enough strength. This force can be either supply or

demand.

2. Resistance to Change: The inertia of a price makes it resist changes in its trend.

3. Impact of Variations in the Supply-Demand Dynamics: It takes a variation in the

supply-demand dynamics to modify the momentum or trend of a price, either by

accelerating it, decelerating it, or changing its direction.

4. Predictability and Reaction: The prospective evolution of supply-demand dynamics

is always uncertain. However, considering the considerations, it is prudent to assert

that the most reliable forecast typically entails the continuation of the existing

trend.

5. Momentum: It is already a widely used concept in technical analysis in trading,

borrowed from physics. It has to do with the strength of a certain price direction.

2.2. PRINCIPLES

The following are the core TF principles:

2.2.1. FOLLOW THE TREND

The main characteristic of TF is to follow and stay inside the trend until there is a reversal sign.

This idea unfolds into three essential elements

1. To initiate positions based on the perceived direction of the trend.

2. To hold positions based on the perceived direction of the trend.

3. To liquidate positions based on the perceived direction of the trend.

There is a high reliance on the price and its sustained direction

, on which most decisions and

actions are based. The fundamental idea behind this is that before a market price can

substantially shift in a particular direction, it typically experiences a modest movement in that

direction. This suggests that initiating a position at this modest stage can ride the rest of the

trend for an extended duration and ultimately close the position with a profit. While this

concept might not hold in every instance, if it proves accurate frequently enough and with

sufficient magnitude, it could result in profitable trading over the long term.

https://www.trendfollowing.com/nature-origins-trend-following/

Note that initiating positions cannot only occur at the beginning of the trend, but also at any moment of the

trend, as long as it is perceived as such. In the early trend-following days, the evidence seems to show that large

and well-known traders used to initiate their positions based in economic fundamentals.

It is important to mark here that TF is not a long volatility type of strategy, but rather long market divergence.

This is because it might be the case that volatility increases and there are no trends, in which case a TF strategy

would not perform well (Greyserman & Kaminski, 2014).

In the famous David Ricardo maxim

, we can see that, although there is nothing about

initiating positions, it contains the second and third essential elements of TF described above,

eloquently exposing a central tenet of TF philosophy: traders should not get out of a trade as

long as it is going their way.

There are many ways of putting this into practice, which will be covered later in this thesis.

One important idea to consider is that if the initiation and liquidation decisions are specified

with certainty, the decision to hold the position becomes something irrelevant or of a

secondary nature, as it will depend on the set liquidation rule. Although the reason to initiate

positions could just be a fundamental one, most trend-followers only act after a price

confirmation signal. There are two main signals used for initiating a position (Greyserman &

Kaminski, 2014): breakouts and moving averages.

When breakouts are used, the investor initiates a position when the price surpasses a certain

critical point. Some examples are:

▪ Previous Tops/Bottoms: this might be a local or historical maximum or minimum.

▪ Patterns: head and shoulders, triangles, wedges, double top or bottom, flags and

pennants, cups and handles, rounded bottoms, gaps, etc.

▪ Channels: Donchian Channels or Bollinger Bands.

▪ Candles: Heikin Ashi

On the other hand, moving averages can be simple or exponential. Some strategies involving

moving averages are:

▪ Price vs. Moving Average: a signal is created when the price crosses a moving average

in a certain direction.

▪ Double Moving Average: a signal is created when the fast-moving average crosses the

slow-moving average in a certain direction.

▪ Triple Moving Average: a signal is created when one moving average crosses the other

two moving averages.

Cut short your losses; let your profits run on.

One strategy might be to initiate a position once a Heikin Ashi candle has closed with a different color than the

previous one. In this strategy, a confirmation of n backcandles can be introduced. In the wide sense, this strategy

can be understood as a breakout one.

2.2.2. SYSTEMATIC

Although systematically performing trend-following strategies is not an absolute

requirement

, currently, most trend followers use a purely systematic approach.

We could divide technical traders into discretionary (predictors) and systematic (reactors)

groups. The first group relies on the ability to read charts or use indicators to predict or

forecast a specific market direction or price action. In contrast, the second group neither

predicts nor forecasts but reacts to price action using a rules-based decision-making process

based on a series of if statements (Covel, 2017).

Trend followers identify market trends; they do not attempt to predict them. They codify a

valid basic philosophy into a specific plan encompassing all possible contingencies. They

believe that, in the long run, a systematic investment strategy can only be as successful as the

extent of the investor's discipline to comply with the system in the face of adversity. If traders

adhere to their initial strategy, their decisions will not be subject to behavioral biases. The

following list contains some of the behavioral biases that are relevant for traders and can be

avoided with systematic trading systems (Kahneman, 2011):

1. Prospect Theory: Kahneman's Prospect Theory suggests that people value gains

and losses differently, leading to irrational decision-making. This can lead to

holding losing positions too long in the hope of them bouncing back or selling

winning positions too early to lock in gains. It is also called Loss Aversion.

2. Representativeness Heuristic: traders may judge the probability of an event by

finding a 'comparable known event' and assuming the probabilities will be similar.

This can lead to misjudging the actual risks involved.

3. Anchoring: occurs when individuals rely too heavily on an initial piece of

information (the "anchor") to make subsequent judgments. In the context of stock

prices, if an anchor is set (like a historical high), traders might interpret future price

movements concerning this anchor, influencing their expectations and decisions

and thereby affecting price trends.

4. Overconfidence and Illusion of Control: Kahneman's work highlights how

overconfidence in one's judgment and the illusion of control can lead to irrational

investment decisions. Traders might believe they can predict or control market

movements, contributing to the persistence of trends as they make trades based

on these beliefs.

5. Confirmation Bias: this leads individuals to favor information that confirms their

beliefs and ignore information that contradicts them. In financial markets, if

It is possible to be a subjective trend follower, or even to combine systematic and subjective elements in a

trend-following system (https://www.trendfollowing.com/nature-origins-trend-following/).

investors believe a trend exists, they're more likely to notice information that

supports this belief and disregard contrary evidence. This can lead to prolonged

trends as investors collectively reinforce their initial beliefs.

6. Availability Bias: Decisions are influenced by what is most immediately recallable

to a person. Recent market events or news can disproportionately influence

traders’ trading decisions.

7. Hindsight Bias: After an event has occurred, individuals often believe they could

have predicted the outcome. In trading, this can lead to overconfidence in one's

predictive abilities.

8. Framing Effect: How information is presented (framed) can affect decision-making.

In financial markets, the way news or financial data is framed can influence

investors' perceptions and actions, contributing to trending behaviors.

For trend followers, their opinions about what the markets will do are irrelevant; hence, they

do not act on them. Some have publicly stated that some of the best trades are the ones where

the market does something completely different from what they thought it would do.

This systematic approach not only allows for the avoidance of behavioral biases but also allows

the strategy to be automated using computer programs to perform all the necessary checks

and actions. For a strategy to be susceptible to automation, the following aspects should be

considered:

▪ Trend Identification: When does the trading system consider that there is a trend?

When does the trend end?

▪ Entry Point: When are we going to decide to act? Typically, it is at the start of

identifying a trend, but the entry point does not need to be at the beginning of a

specific trend, as many trend followers will act even if the trend has been going on for

a while.

▪ Risk Involved: What risk will be taken from the total portfolio in that specific trade?

▪ Stop-Loss Order: Where are we going to set our stop-loss order?

▪ Position Size: What is the number of units of that asset or contract that you can buy

or sell in that specific trade?

▪ Exit Point: When are we going to exit the trade? For trend-followers, this usually

happens when the price hits the stop-loss, as it will be set where a trend reversal is

considered materialized.

Take-profit orders are generally not adopted by trend followers because their strategy focuses

on remaining in a trade until there are clear indications of a trend reversal or a transition to a

non-trending market. Instead of targeting a predetermined profit level, trend followers exit

trades based on specific conditions indicative of trend changes. This approach avoids

prematurely limiting potential profits, which could lead to a positively skewed distribution of

returns.

2.2.3. DIRECTIONAL FLEXIBILITY

Directional flexibility is a cornerstone principle in trend-following trading strategies. Unlike

traditional investment approaches that primarily focus on buying low and selling high, trend-

following strategies embrace the notion of profiting from upward and downward market

trends. This approach aligns with the philosophy that markets can be unpredictable, and

directional biases may limit profitability.

In practice, directional flexibility involves using technical indicators to identify potential

trends. Traders might use moving averages, momentum oscillators, or breakout systems to

gauge market direction. Once a trend is identified, the strategy may involve going long in rising

or short-selling in falling markets. This approach requires a disciplined risk management

strategy to mitigate the potential for significant losses, especially in volatile market conditions.

Research by authors like Covel (2017) illustrates the efficacy of directional flexibility. By

analyzing various market scenarios, Covel demonstrates how TF traders have capitalized on

bullish and bearish markets. Similarly, Clenow (2012) provides empirical evidence of the

success of TF strategies across different market conditions.

Strategies that do not have directional flexibility, like Buy-and-hold ones, are often at odds

with the principles of TF investing. Trend followers typically view the buy-and-hold mentality

as suboptimal, primarily due to its passive nature and potential for significant drawdowns.

Trend followers usually criticize buy-and-hold strategies because (1) they ignore market

trends

, (2) there is potential for large drawdowns

, (3) there is a low or a lack of

responsiveness to market dynamics

, and (4) they have an overreliance on the idea that

markets are going to recover relatively quickly

Trend followers believe in actively and systematically respond to market conditions. The buy-and-hold

strategy, by contrast, often entails remaining invested in an asset regardless of prevailing market trends. Trend

followers argue that it is more logical to maintain a position in an asset and consistently lose value when market

trends suggest a different course of action.

A key concern with the buy-and-hold approach is the risk of substantial drawdowns during market downturns.

Trend followers emphasize risk management and capital preservation, strategies that often involve cutting losses

early. Buy-and-hold investors, in contrast, may experience significant portfolio devaluations during market

declines, going against the trend followers' principle of protecting capital.

Trend followers critique the buy-and-hold strategy’s lack of responsiveness to changing market dynamics. They

argue that this static approach fails to capitalize on profitable opportunities presented by market trends, both

upward and downward, and does not adequately adjust to evolving economic and financial landscapes.

Buy-and-hold assumes that markets will always recover and continue to grow over the long term. However,

trend followers contend that this assumption can be risky, especially during prolonged bear markets or when

specific sectors or assets do not rebound as expected.

Although the default for a TF strategy might, in theory, be agnostic to long and short bias,

some managers intentionally impose either a market or a directional bias. Directional biases

can create dispersion in returns among systems and change some of the statistical properties

of the strategy. For example, TF strategies with a large equity long bias can exhibit negative

skewness similar to equity market returns (Greyserman & Kaminski, 2014).

2.2.4. RISK MANAGEMENT

Risk management is a fundamental principle in TF trading strategies. Trend followers place

significant emphasis on managing and mitigating risk over profit maximization. This approach

acknowledges financial market uncertainties and volatilities, prioritizing capital preservation

over speculative gains. This approach is critical for institutional investors pursuing Liability

Driven Investment (LDI) asset-liability management (ALM) strategies whose goal is to match

assets to liabilities and manage risks (e.g., interest rate, inflation, credit) so that income is

available to satisfy specific (e.g., pension fund, insurance, banking) financial obligations (Bravo

& Silva, 2006; Simões et al., 2021; Bravo & Nunes, 2021; El Mekkaoui et al. 2021; Bravo, 2019,

2022; Bravo & El Mekkaoui, 2018). For trend followers, the focus must be on the risk, as the

profits will automatically appear if the strategy is good and is followed accordingly.

As the ASE has a different method for studying the economy

than mainstream academia,

trend followers also have a different way of understanding risk. Instead of understanding risk

as volatility, they understand it as the possibility of loss

. This highly affects the way they

trade, mitigate and measure risk.

To manage the inherent risk of trading in the markets, trend followers typically focus on four

pillars: diversification, portfolio heat, stop loss, and position sizing.

2.2.4.1. DIVERSIFICATION

Thanks to the simplicity of their heuristic approach, trend followers are known for trading

many different markets simultaneously. This is easily done because they do not need to be

experts in understanding the drivers that move a specific asset or asset class.

Austrian economists have a distinct view of approaching the economic field from classical, neoclassical, and

other schools that transcend the economic discipline. Their subjectivism (instead of objectivism) and the theory

of human action (instead of human decision) are understood as a dynamic process (praxeology) instead of a

static one (Huerta de Soto, 1998). Since its formal foundation in 1871, the ASE has gone through different stages

of academic debates where it has defended and perfected its methodological positions. The first round of this

notorious methodenstreit started with Carl Menger against the German Historical School, then Böhm-Bawerk

versus John Bates Clark, Marshall, and Marx. In the third round, it was Mises, Hayek, and Mayer versus socialism,

Keynes, and the neoclassical. Finally, the Neo-Austrians versus the mainstream and methodological nihilisms.

See Appendix B for more on this topic.

Diversification is an essential strategy that followers employ to manage risk and enhance risk-

return ratios

. It involves spreading investments across various assets, markets, or strategies

to reduce exposure to any single source of risk. Trend followers use diversification in several

ways, each addressing different aspects of market risk.

Types of diversification:

▪ By Asset Class: This involves allocating investments across different asset classes, such

as stocks, bonds, commodities, and currencies. Each asset class responds differently to

market conditions, so this form of diversification helps reduce the impact of volatility

in any single asset class on the overall portfolio.

▪ Geographic Diversification: Trend followers often diversify investments across various

regions and countries. Different markets can respond differently to global economic

events, and geographic diversification can mitigate the risk associated with a downturn

in a particular region.

▪ Directional Diversification: This type of diversification involves taking long and short

market positions. By doing so, trend followers can profit from rising and falling

markets, reducing their reliance on market direction for returns.

▪ Timeframe Diversification: Involves trading across different timeframes. Some trend

followers might engage in short-term trades, while others focus on medium- or long-

term trends. Diversifying across timeframes can help capture trends of different

durations and reduce the risk associated with any specific trading horizon.

▪ Sector and Industry Diversification: This strategy involves investing across different

sectors and industries. Since sectors and industries can react differently to economic

events, this diversification helps mitigate sector-specific risks.

▪ Methodological Diversification: Trend followers may diversify their methodologies,

using different trend identification and trading strategies. This diversification ensures

that the portfolio's performance is not dependent on a single analytical approach or

trading system.

Diversification is essential in TF because it reduces the risk

and increases the performance

stability

and the market adaptability

of the portfolio.

It is believed that no one ever knows which market or strategy will be the big trend that will pay for the losses.

Hence the need for diversification.

It spreads risk across different assets, markets, and strategies, reducing the impact of any single adverse event

on the overall portfolio. This risk reduction occurs not only in terms of a reduction in volatility but also in a

reduction in the possibility of loss.

By diversifying, trend followers aim to achieve more consistent performance, avoiding significant fluctuations

that might occur in less diversified portfolios.

Diversification allows trend followers to adapt to changing market conditions, capitalizing on opportunities

across a broad spectrum of assets and markets.

2.2.4.2. PORTFOLIO HEAT

Trend followers place high importance on the overall percentage of the portfolio at risk or the

portfolio heat

to a level that never exceeds a small amount of the entire portfolio

. This is

not only important for the peace of mind of the investors but also because it gets exponentially

harder to recover the portfolio's losses in percentage terms.

Figure 2.1 – Drawdown vs Return to Recover

Source: Own preparation.

The drawdowns achieved in TF strategies tend to be lower than in buy-and-hold strategies

(Greyserman & Kaminski, 2014; Covel, 2017), mainly because of the directional flexibility and

the focus on maintaining the portfolio heat at a reasonably low level using stop losses.

2.2.4.3. STOP-LOSS

The stop-loss order is a primary tool in trend followers' risk management arsenal. It is designed

to close a trade automatically at a predetermined price level, effectively capping any potential

loss. By setting these limits, trend followers ensure that losses are cut early and remain small,

aligning with the Ricardian maxim of ‘cutting losses short’.

Contrastingly, trend followers typically avoid setting take-profit orders. The rationale behind

this is closely tied to their risk management philosophy. Take-profit orders, which

automatically close a trade at a specified profit level, can prematurely limit the potential gains

from a trade. Since trend followers aim to capitalize on the full extent of market trends, setting

Portfolio heat was a term coined by Ed Seykota. Considering the stop-losses in place, it is defined as the

percentage of the portfolio that is susceptible to being lost at any given time. On the contrary, core equity is the

percentage of the portfolio that is not at risk.

This is a subjective decision, but typically it is shared that the portfolio heat should be between 10% and 20%.

0.00%

50.00%

100.00%

150.00%

200.00%

250.00%

300.00%

350.00%

510 15 20 25 30 35 40 45 50 55 60 65 70 75

Drawdowns vs Return to Recovery

Drawdown Return to Recovery

a take-profit limit could prevent them from fully benefiting from prolonged favorable trends.

This also aligns with the other part of the Ricardian maxim of letting your profits run on.

Although there are many types of stop-losses

, this thesis will differentiate between two

types that will become useful and relevant in the practical part: explicit and implicit. The

explicit ones are set directly in the exchange or broker. The implicit ones are not set in the

exchange directly but are instead set indirectly through the logic of the code. These two forms

of stop losses may coexist in the same strategy.

Ideally, stop losses should consider the asset's historical volatility over the last n periods. This

way, they will be more meaningful and adaptive to the asset's volatility when setting the stop

loss. Some examples of initial stop losses based on the latest historical volatility of the assets

are: average true ranges (ATR)

, support or resistance levels

, channels or bands

, volatility

stop losses

, moving averages crossovers

and fibonacci retracements

After the initial stop loss is set, designing the rules for adjusting the stop loss as the price

evolves is paramount. Most of these methods already incorporate a dynamic approach where

the stop is adjusted automatically. In contrast, others are static, and additional rules might

need to be in place to correctly adjust the stop loss over time (ATR, support or resistance

levels, and Fibonacci retracements).

2.2.4.4. POSITION SIZING

For trend-followers trading several markets, a portfolio allocation to each market is usually

decided before deciding the size of a specific position inside a specific market. The main ways

Standard stop loss, stop limit order, trailing stop loss, guaranteed stop loss, volatility stop loss, and time stop

are some of them.

The ATR is the average of the last n (typically 14) true ranges. A true range is the maximum of three alternatives

(TR=max[(High−Low),(High−Previous Close),(Low−Previous Close)]. Typically, the ATR is used with a multiplier

(usually 2 or 3) to set a stop loss level. For example, if the multiplier is 2, in long positions, the stop loss will be

put at the purchase price – ATR*2.

The stop loss is set in long positions below the relevant support level; in short positions, the stop loss is set

above the resistance level. These supports or resistances correspond to previous local bottoms or tops,

respectively. A buffer of 1% to 2% is typically used.

Donchian Channels or Bollinger Bands for instance.

Similar to using the ATR, but this method might involve other volatility indicators such as the Standard

Deviation or the Volatility Index (VIX) for a broader market.

A stop loss is set relative to a moving average. For long positions, a stop could be placed below a relevant

moving average (such as the 50-day or 200-day MA), believing that the uptrend is intact as long as the price

remains above this average.

After a significant price move, traders can use Fibonacci levels to set stop losses, anticipating that retracements

will respect these levels. For example, placing a stop loss just below a 38.2% or 61.8% Fibonacci retracement

level in anticipation of the continuation of the original trend.

to allocate risks per market are equal dollar risk allocation (EDR)

, equal risk contribution

(ERC)

, and market capacity weighting (MCW)

(Greyserman & Kaminsky, 2014).

Position sizing is an essential part of risk and money management. Trend-followers use two

main ways to size their positions: investing the same portfolio percentage per trade or risking

the same portfolio percentage per trade. Investing in the same portfolio percentage per trade

is often seen as less desirable than risking the same percentage per trade due to the latter

distributing the risk equally. Investing in the same portfolio percentage per trade typically

leads to risking a different percentage of the portfolio per trade, especially if the stop losses

are set depending on the specific volatility of the asset.

A strategy that risks the same percentage per trade inside a specific market and considers the

volatility of the asset to set the stop loss follows an EDR method on an asset level. This is very

common among trend followers. In this case, the historical volatility determines where the

stop loss will be set, and the position size (PS) will depend on the absolute value of the

difference between the initialization price (IP) and the stop loss (SL), divided by the dollar

amount of risk allocated to the asset ($Ra):

 



(1)

The dollar amount of risk allocated to the asset ($Ra) depends on the portfolio value (PV),

portfolio heat (Hp), the percentage of the portfolio heat allocated to the specific market (Hm),

and the number of assets (n) that will be traded within that market:

 



(2)

where:

  

Although this allocating method does not consider the correlation between assets traded, this

does not pose a serious drawback for trend followers. This is because they emphasize the

importance of following market trends, largely disregarding other factors, such as market

EDR is a strategy that allocates the same dollar risk to each market. This approach does not consider the

correlation between markets. This approach is similar to the 1/N approach.

ERC is a strategy that allocates risk based on the risk contribution of each market, taking correlation into

account. This approach is similar to risk parity.

MCW is an approach where capital is allocated as a function of individual market capacity. In future markets,

a market capacity weighting will depend on the market size as measured by both volume and daily price volatility.

Ideally, stop losses should consider the historical volatility of the asset of the last n periods. This way, stop

losses will be adapted to the current volatility of the investment and will be more meaningful.

correlations. They understand that correlations are dynamic and may change drastically over

different periods, making them unreliable for consistent TF strategies. Instead of relying on

the stability of correlations, trend followers can focus on the robustness of their trend-based

models, which are designed to capture trends regardless of how assets move in relation to

each other. This approach accepts that the nature of correlations can vary significantly during

different market phases, such as during crises or calm periods, and thus does not integrate

correlation analysis into the core of their trading strategy. Instead, trend followers accept the

ever-changing correlations as a market reality and concentrate on the trend behavior of

individual markets to drive their trading decisions. Nevertheless, with proper diversification

between markets and directional flexibility, the issue of exaggerated losses due to a high

correlation between some of those markets is usually mitigated to a high extent.

2.2.5. ABSOLUTE RETURNS

The principle of absolute return is central to trend-following investing. Unlike traditional

investment strategies that focus on relative returns, measuring performance against a

benchmark or index, TF strategies aim for positive returns independent of external

benchmarks. This approach is grounded in the belief that the primary goal is to generate profit

in absolute terms, regardless of the broader market's performance.

“The concept of indexing and benchmarking is beneficial in the EMT world of traditional long-only

passive investing, but it has almost zero usefulness for an absolute return process. […] At its core, the

concept of absolute return investing is antithetical to benchmarking, which encourages traditional

managers to have similarly structured portfolios and look at their performance on a relative basis”.

(Covel, 2017, p. 92-93).

Traditional investment strategies often emphasize relative returns, where the success of an

investment is judged against a specific benchmark, like the S&P 500, Russell 2000, or another

market index or a combination of them. This approach can sometimes lead investors to

prioritize outperforming the benchmark over generating positive returns. In contrast, the

absolute return approach adopted by trend followers is not bound by the performance of any

index or sector. Their success is solely measured by the ability to generate profits, not by

outperforming a benchmark.

Some of the benefits of the absolute return approach are market independence

, risk

mitigation

and adaptability to market conditions

Investors who adopt an absolute return approach must be comfortable with a methodology

that may diverge significantly from traditional market indices. This divergence can sometimes

mean underperformance relative to a booming market. However, it can also lead to positive

returns in a declining market, highlighting the non-correlation of absolute return strategies

with market trends

2.2.6. SOPHISTICATED SIMPLICITY

The principle of simplicity is present in many of our society’s history’s best thinkers, from the

physicist Albert Einstein

to the musicians Charles Mingus

or Frédéric Chopin

, or the

notorious innovator and entrepreneur Steve Jobs

Following this principle, trend followers like to keep it sophisticatedly simple (Covel, 2017). TF

strategies have a rather simplistic way of dealing with markets. It simplifies the trader's life as

much as possible by eliminating all the noise (news, market events, etc.) and focusing on one

essential aspect of the asset: the price action, which is the aggregation of everyone’s

expectations, containing a vast amount of heterogeneous information.

100

By focusing on absolute returns, trend followers are not confined to the constraints of matching or beating a

benchmark. This independence allows for greater flexibility in investment choices and strategies.

Absolute return strategies often emphasize risk management. Since the goal is to make positive returns under

market conditions, trend followers typically employ methods like diversification, position sizing, and rigorous

stop-loss orders to protect against significant losses.

TF strategies, with their focus on absolute returns, are inherently adaptable. They can capitalize on market

trends, whether upward or downward, without adhering to a specific benchmark’s constraints or composition.

This non-correlation of TF strategies with a specific market creates diversification opportunities. For instance,

the introduction of Greyserman & Kaminski (2014) showcased how a 50:50 portfolio of the S&P 500 Total Return

Index and the Barclay CTA Index (leveraged to have the same volatility as the equity index) would have increased

the equity market’s Sharpe Ratio by 66%. Also, in Part I, in a study of over 3 centuries, is shown how combining

traditional 60/40 equity bond portfolios with TF (to 48/32/20) increases the Sharpe Ratio from 1 to over 1.2.

With the quote “genius is making complex ideas simple, not making simple ideas complex”.

With the quote “anyone can make the simple complicated. Creativity is making the complicated simple”.

With the quote “simplicity is the final achievement. After one has played a vast quantity of notes and more

notes, it is simplicity that emerges as the crowning reward of art”.

With the quote, “simplicity is the ultimate sophistication. It takes a lot of hard work to make something simple,

to truly understand the underlying challenges, and come up with elegant solutions. […] It’s not just minimalism

or the absence of clutter. It involves digging through the depth of complexity. To be truly simple, you have to go

really deep. […] You have to deeply understand the essence of a product in order to be able to get rid of the parts

that are not essential”.

100

Free market prices are pieces of information that contain and convey a vast amount of heterogeneous data

(Hayek, 1945) and help coordinate society’s preferences (Mises, 1949). They are beacons that tell society where

to produce, how to produce, how much to produce, when to produce, where to transport and sell, how to

advertise, how to sell, etc. In the same way, prices in financial markets contain a vast amount of heterogeneous

information that goes beyond the extent of the information or knowledge that any given individual may have

without insider knowledge. That is why trend followers focus on the price.

Although price and volume can be manipulated in extreme scenarios, they are, in most cases,

the most reliable and current information that market participants can rely on, much more

than annual or quarterly reports

101

While developing a trading system, it's crucial to be aware of the propensity to incur

overfitting, an unavoidable danger highlighted by Lopez de Prado (2018), who points out that

traders cannot know ex-ante if they have effectively avoided overfitting. However, the risk of

overfitting, particularly during the back-testing and systematization phases, can be reduced

through the adoption of simple strategies, such as TF ones, and by not selecting the exact

combination that performed the best in back-testing but rather opting for strategies that have

shown consistent and robust performance across different assets or markets. This approach

is further supported by employing multiple hypotheses testing, as suggested by Covel (2017),

to mitigate the danger of overfitting, underscoring the importance of simplicity and

generalizability in strategy development.

As opposed to the criticism that Kahneman (2011) does of using heuristics, Gigerenzer (1999)

proved that it is an effective method for decision-making in complex and uncertain situations,

like financial markets. His premise is the following: “Fast and frugal heuristics employ a

minimum of time, knowledge, and computation to make adaptive choices in real

environments. […] Fast and frugal heuristics can guide behavior in challenging domains when

the environment is changing rapidly (for example, in stock market investment), when the

environment requires many decisions to be made in a successively dependent fashion. These

particular features of social environments can be exploited by heuristics that make rapid

decisions rather than gathering and processing information over a long period during which a

fleeter-minded competitor could leap forward and gain an edge”.

Trend followers employ heuristics to simplify identifying profitable trends, relying on

straightforward rules that can be consistently applied across various market conditions. These

rules are often based on price action and volume, which provide direct and immediate

information, making them less prone to the biases and overfitting that can accompany more

complex and discretionary strategies. By focusing on these clear, measurable criteria, TF

strategies can swiftly adapt to market changes while minimizing the impact of noise, such as

news or market events. This simplicity in approach aligns with the principle of Ockham's

razor

102

, which suggests that the simplest solution is often the most effective. The heuristic-

101

Annual or quarterly reports not only contain past and, on many occasions, outdated information, but also can

be biased and manipulated with conservative or aggressive practices or bad faith altogether. That is why, on

many occasions, prices behave in very different ways compared to what the analysis of the last quarterly report

would suggest.

102

In its original Latin form, Pluralitas non est ponenda sine necessitate, which could be translated as plurality

should not be postulated without necessity. With this in mind, Ockham wanted to state that the entities or causes

should not be more than what is strictly necessary to explain the observed events. This methodological and

philosophical principle has been constantly applied to modern sciences, interpreted as the simplest of two or

based methods in TF not only streamline the decision-making process but also enhance the

robustness and reliability of the trading system, ensuring that the strategies remain effective

even when faced with the unpredictable nature of financial markets.

2.2.7. EMOTIONAL DISCIPLINE

In exploring TF philosophy, emotional discipline stands out as a critical element, even within

a systematic, rules-based approach designed to minimize behavioral biases. This approach,

while effective in reducing the sway of such biases, is not entirely immune to the psychological

complexities that traders face, particularly during the development of their trading systems

and through challenging periods of system performance.

Understanding emotional discipline begins with recognizing the limitations of human

knowledge and the prevalence of biases, a concept illuminated by Daniel Kahneman's

prospect theory. Kahneman and Amos Tversky's work revealed how typical behaviors, like the

law of small numbers and a disproportionate loss aversion, lead to irrational decision-making

in financial markets. Such behaviors explain the common tendency among investors to sell

winning stocks too hastily and hold onto losing ones for too long, driven by a fear of loss and

an over-optimistic hope for recovery.

A trader's emotional discipline is anchored in humility, patience, and self-discipline. Humility

in trading acknowledges that trying to outsmart the market is futile, advocating for an open-

minded approach free from personal biases. Patience is emphasized in TF trading, which often

requires minimal active management, highlighting the importance of restraint. Self-discipline

is crucial, especially when it comes to executing a trading strategy, requiring traders to follow

established rules and resist the temptation to deviate. This involves having the courage and

conviction to act when is needed and the patience to not act when it is not needed.

Covel (2017) identifies a range of market behaviors that are antithetical to successful trading,

such as lack of discipline, impatience, greed, and the inability to remain objective. These

behaviors stress the importance of admitting mistakes and cutting losses early, practices that

necessitate humility and acknowledging one's fallibility.

Furthermore, the concept of sunk costs plays a significant role in emotional discipline. It

represents costs that have already been incurred and cannot be recovered. The challenge lies

in not letting these sunk costs influence future trading decisions, a common pitfall for many

traders who might invest further in a declining stock in the hope of recovery, often leading to

greater losses.

more competing theories is preferable. Ockham’s razor does not guarantee the most straightforward solution

will be correct, but it focuses priorities (Covel, 2017).

In conclusion, emotional discipline in TF trading transcends mere adherence to a set of rules.

It involves a deep understanding of one's psychological predispositions and biases. By

cultivating humility, patience, and self-discipline, traders can navigate the emotional

complexities of the market, making informed decisions that reflect a systematic, bias-aware

approach. Mastering emotional discipline is thus essential for safeguarding against irrational

behaviors that can undermine the foundations of successful trading.

2.3. HISTORICAL PERSPECTIVES AND PORTFOLIO PROPERTIES

2.3.1. HISTORICAL PERSPECTIVES

The performance of TF has been discussed extensively in the applied and academic finance

literature. Perhaps the most thorough investigation presented to date can be found in the

work of Greyserman & Kaminski (2014), which examines an expansive timeframe spanning

nearly eight centuries, from 1223 to 2013. While such an analysis may not achieve absolute

rigor due to its vast scope

103

, the extensive period covered provides substantial evidence to

underscore the advantages of TF as a trading philosophy. Overall, after analyzing 84 markets

(equity, fixed income, foreign exchange, and commodities), this study documents low

correlation with traditional asset classes

104

, lower drawdowns

105

and positive skewness

106

and robust performance during crisis periods, generating an average annual return of 13

percent, with annualized volatility of 11.2 percent. This results in a Sharpe ratio of 1.16. In

comparison, a buy-and-hold portfolio of equities, bonds and commodities

107

obtains an

average annual return of 4.8 percent, volatility of 10.3 percent and consequently a Sharpe

ratio of 0.47. This study suggests that there may be a premium to active management with TF

principles.

103

This is because in this type of analysis, with so many centuries studied and with limited information for some

assets, there are inevitably numerous assumptions, questions on data reliability, and other biases used. These

are appropriately addressed by the author.

104

The overall correlation between the monthly returns of the representative TF system and the equity index is

0.05, and 0.09 with the bond index. This causes the betas of TF with equity and bond markets to be generally

extremely low as well.

105

The portfolio demonstrated significantly reduced drawdowns across various measures, including drawdown

duration, maximum drawdown, and the aggregate of the five largest drawdowns. Specifically, the maximum

drawdown decreased by more than 23 percent compared to the rebalanced buy-and-hold portfolio. The total of

the five largest drawdowns also saw a reduction of over 33 percent against the same benchmark. Remarkably,

the duration of the longest drawdown was cut by more than 90 percent, and the average duration of the five

longest drawdowns was 83 percent shorter than those experienced by the benchmark portfolio.

106

The skewness for monthly returns is 0.3. Positive skewness indicates that the chance for left tail risk or large

drawdowns in TF is relatively small, which is a somewhat unique characteristic, as most asset classes and

strategies exhibit negative skewness.

107

This buy-and-hold portfolio is monthly rebalanced to maintain equal risk with the corresponding TF portfolio.

The study also breaks TF performance over different interest rate

108

and inflation

109

regimes,

with robust results, and shows that TF strategies tend to perform especially well in financial

crises

110

and bubbles

111

throughout history. This is because TF tends to perform well during

moments when market divergence is the largest.

112

These characteristics make TF a good candidate to diversify traditional portfolios. The study

shows that the improvement of the Sharpe ratio is substantial, not only by combining

separately TF with equities and bonds

113

, but also when combining TF with the traditional

60/40 equity bond portfolio

114

. This explains why the use of TF as an alternative investment

strategy has grown over the past 40 years.

Sabar (2013)

115

performed a study to see why TF underperformed during the 2009-2013

period and discovered that TF performs best in regimes when correlation and volatility are

both high or low, and not when one of them is high and the other one is low.

116

Crises are

108

The division is done over four different regimes: high interest rates, low interest rates, rising interest rates and

falling interest rates. The return is robust across different regimes, performing better over high interest rates

(1.56 Sharpe ratio) and falling interest rates (1.3 Sharpe ratio).

109

The division is done over 3 different regimes: inflation less than 5 percent, inflation between 5 and 10 percent

and inflation over 10 percent. The return is robust across different regimes, with better results in environments

with high inflation (1.02 Sharpe ratio when inflation is over 5% vs. 0.87 when it is less than 5%).

110

The Great Depression and the 1929 Wall Street Crash, or housing bubble of 2007-2008.

111

Like the Dutch Tulip Bubble of 1936-1937

112

A key characteristic of TF strategies is known as the CTA smile. This phenomenon refers to the observed

pattern where the highest returns are achieved during both the periods of strongest and weakest performance

of equities or other assets.

113

The study merges the TF strategy with an equal distribution of first equities and then bonds, to confirm that

performance metrics are enhanced. Analyzing the period from 1695 to 2013, equities demonstrated a Sharpe

ratio of 0.7, while TF strategies outperformed with a Sharpe ratio of 0.83. When equities and TF strategies were

combined in equal proportions, the Sharpe ratio impressively increased to 1.1. In the case of bonds, evaluated

from 1300 to 2013, the Sharpe ratio stood at 0.9, but for TF strategies, it was significantly higher at 1.16. By

integrating bonds and TF strategies equally, the Sharpe ratio further rose to 1.42. This significant improvement

highlights the robust and substantial enhancement of investment performance through the strategic

combination of TF with traditional asset classes.

114

The research introduces TF strategies into the classic 60/40 equity-bond mix, adjusting the allocation to 48%

equities, 32% bonds, and 20% TF. Throughout the extensive period from 1695 to 2013, incorporating a 20%

investment in TF into the portfolio has successfully elevated the Sharpe ratio from 1.0 to 1.2, indicating a notable

enhancement in risk-adjusted returns.

115

https://www.cmegroup.com/education/files/when-do-trend-followers-make-money.pdf

116

According to the author, these are the four possible regimes in terms of volatility and correlation:

Low Volatility, Low Correlation: This regime is favorable for trend followers because assets respond less

dramatically to news, increasing the chance of underreaction and subsequent momentum opportunities. Low

correlation between markets means that trends can emerge gradually across related markets, allowing trend

followers to capitalize on these developments over time.

High Volatility, Low Correlation: Although low correlation still offers opportunities to benefit from lead-lag

relationships between assets, high volatility increases the risk of overreaction to news, leading to possible market

reversals. This makes it challenging for trend followers, as the two forces counterbalance each other, resulting

in a neutral outcome for trend following strategies.

Low Volatility, High Correlation: High correlation among assets diminishes the potential for lead-lag profits and

can lead to trend followers taking large positions at inopportune times due to a lack of asset-specific momentum

characterized by high volatility and high correlation. The other environment where TF works,

according to this author, is one where assets do not react violently to information arrival. This

increases the likelihood of underreaction to news (and thereby follow-on momentum), which

is good for trend followers.

Hurst, Ooi, and Pedersen (2017) found that TF strategies have generally performed well across

a variety of economic environments. However, they identified that the most crucial factor

influencing TF performance is the level of correlation among assets. Specifically, TF strategies

tend to perform better during periods of low correlation between assets. This characteristic

allows TF strategies to more effectively capture trends and generate returns when the markets

are not moving in a highly synchronized manner.

Covel (2017) presents the findings of Bernard Drury and his TF firm, Drury Capital. Drury

explored the potential enhancement of the already successful Berkshire Hathaway stock by

integrating it with other assets. Drury Capital met the criteria of delivering strong positive

returns on a standalone basis while maintaining a low correlation with BRKA. The study

utilized data from May 1997 to February 2015. The results were clear. Combining Drury and

BRKA improved significantly not only the return/risk metrics but also the maximum drawdown

percentage-wise and time-wise.

Table 2.1 – Effect of Combining Trend-Following and Value Investing Portfolios

SUMMARY

Drury

BRKA

50% / 50%

Rate of Return (ROR)

32.50%

10.40%

10.90%

Standard Deviation (Vol)

32%

20.60%

14.40%

Maximum Drawdown (DD)

23%

44.50%

23.90%

ROR/DD

0.35

0.23

0.50

ROR/Vol

0.57

0.23

0.83

Peak to trough (months)

Trough to peak (months)

Total (months)

Note. Adapted from Covel (2017). Trend Following (5th Edition): How to Make a Fortune in

Bull, Bear and Black Swan Markets (p. 112-113). Wiley.

and synchronized movements across asset classes. This scenario is mixed for trend followers, as it combines

opportunities in asset-specific momentum with the risk of being overly exposed during exogenous shocks.

High Volatility, High Correlation: Characterized as a crisis regime, high volatility and correlation are generally

negative for trend followers due to reduced asset-specific trends and synchronized movements across asset

classes. However, during periods of crisis-induced deleveraging, the large positions taken by trend followers can

result in significant gains, provided the deleveraging occurs over an extended period. The performance of CTAs

(Commodity Trading Advisors) in such conditions has varied, with success in early samples but challenges more

recently, indicating faster deleveraging since 2008.

2.3.2. PORTFOLIO PROPERTIES

From Greyserman & Kaminski’s (2014) work, as well as Covel’s example of Drury’s case, we

can see that TF has some unique characteristics. It is a good performer in periods of crises,

with low correlation with traditional assets, low drawdowns, positive skewness, excess

kurtosis and good risk-adjusted returns. These main properties make TF a good candidate to

qualitatively diversify traditional portfolios.

2.3.2.1. CRISIS ALPHA

TF has consistently demonstrated strong performance across various conditions compared to

buy-and-hold strategies, particularly during financial downturns

117

and bubbles. This aligns

with the concept of the CTA smile, which describes how the largest gains are often made in

times when equities or other assets are performing at their best and worst.

In the study by Greyserman & Kaminski (2014), the author investigates the application of a

standard channel breakout TF strategy to the historic tulip bulb market during 1636 to 1637.

He suggests that a TF investor might have initiated a long position before November 25th,

1636, when the price was under or around 50, and then might have closed the position and

potentially begun short selling (if that would have been possible) around February 9th, 1637,

when the price was around 148.

Figure 2.2 – Price Evolution of the Tulip Bulbs

Source: https://www.cambridge.org/core/journals/financial-history-review/article/explaining-the-

timing-of-tulipmanias-boom-and-bust-historical-context-sequestered-capital-and-market-

signals/20BEB345A7BB4BF2E84C07F9077361A1

117

https://quantpedia.com/trend-following-in-the-times-of-crisis/

The author gets a similar result in the Dow Jones Industrial Index from October 1928 to

October 1930, with roughly a 90% profit in a span of two years comprising the October 28,

1929 crash. Additionally, in Figure 2.3 we can see the performance of the Barclay CTA Index

118

during two difficult periods: the dotcom and the housing bubbles.

Figure 2.3 – Barclay CTA Index performance vs S&P 500

Source: https://www.iasg.com/blog/2019/09/13/frequently-asked-questions-about-managed-futures

From the graph we are not able to conclude there were bubbles or crises, with an extremely

low volatile, although very mild, returns.

2.3.2.2. LOW CORRELATION WITH TRADITIONAL ASSETS

TF, due to its high diversification across markets and its directional flexibility tends to achieve

low levels of correlation with any specific market.

2.3.2.3. LOW DRAWDOWNS

In Greyserman & Kaminski (2014), the portfolio demonstrated significantly reduced

drawdowns across various measures, including drawdown duration, maximum drawdown,

and the aggregate of the five largest drawdowns. Specifically, the maximum drawdown

decreased by more than 23 percent compared to the rebalanced buy-and-hold portfolio. The

total of the five largest drawdowns also saw a reduction of over 33 percent against the same

benchmark. Remarkably, the duration of the longest drawdown was cut by more than 90

percent, and the average duration of the five longest drawdowns was 83 percent shorter than

those experienced by the benchmark portfolio. Additionally, in Drury’s case in Covel (2017)

we saw a significant reduction in drawdowns, not only percentagewise but also timewise.

118

The Barclay CTA Index serves as a prominent benchmark reflecting the performance of commodity trading

advisors in the industry. As of 2023, it incorporates 412 programs in its calculation. This Index is balanced equally

and undergoes a rebalancing process at the start of each year, and it is a good proxy for analyzing how diversified

TF strategies performed.

2.3.2.4. POSITIVE SKEWNESS

In Greyserman & Kaminski (2014), the skewness of monthly returns was recorded at 0.3,

indicating a distribution leaning towards positive extreme values. Such a positively skewed

distribution suggests a pattern of more common small losses contrasted with less frequent but

significantly larger gains. This characteristic is often sought after in investment strategies as it

hints at the possibility of achieving exceptional positive returns, which can markedly improve

the aggregate performance of an investment portfolio. Essentially, positive skewness implies

that, despite the regular occurrence of minor losses, the potential for securing considerable

profits exists, potentially outweighing the smaller losses over the long term.

2.3.2.5. GOOD RISK-ADJUSTED RETURNS

Greyserman & Kaminski’s 2014 study offers a comprehensive examination of trading

outcomes over an extensive period, stretching nearly eight centuries from 1223 to 2013.

Despite potential limitations due to its broad scope, the research highlights the effectiveness

of TF as a trading strategy. By analyzing 84 markets across equity, fixed income, foreign

exchange, and commodities, the study reveals TF's low correlation with traditional asset

classes, reduced drawdowns, positive skewness, and strong performance during crises. It

showcases an impressive average annual return of 13 percent with an annualized volatility of

11.2 percent, leading to a Sharpe ratio of 1.16. This contrasts markedly with the buy-and-hold

strategy across equities, bonds, and commodities, which shows an average annual return of

4.8 percent, a volatility of 10.3 percent, and a Sharpe ratio of 0.47. Greyserman & Kaminski’s

findings indicate a potential premium for active management following TF principles,

suggesting that investors might achieve better risk-adjusted returns through this approach.

2.3.2.6. GOOD DIVERSIFIER

The integration of TF strategies into traditional portfolios has been validated as a method to

significantly enhance investment performance and diversify asset allocations. A

comprehensive study, citing data from 1695 to 2013, revealed that TF strategies not only

outperform equities and bonds individually in terms of the Sharpe ratio but also considerably

boost the performance metrics of the conventional 60/40 equity-bond portfolio. Specifically,

equities and bonds, when paired separately with TF strategies in equal proportions, saw their

Sharpe ratios climb to 1.1 and 1.42, respectively, from their standalone ratios of 0.7 for

equities and 0.9 for bonds. This improvement is also pronounced when TF strategies are

incorporated into a modified 60/40 portfolio, adjusting the allocation to include 20 percent

TF, which elevated the Sharpe ratio from 1.0 to 1.2. This strategic enhancement, underscored

by Greyserman & Kaminski’s research in 2014, demonstrates the robust benefit of including

TF in diversified investment strategies, underscoring its growing popularity over the last four

decades to achieve superior risk-adjusted returns.

3. INTRODUCING A NEW MEASURE OF DOWNSIDE RISK: THE

KOLJONEN RATIO

In the field of portfolio management, accurately measuring and managing risk is paramount.

Traditional metrics, such as the Sharpe Ratio (SR), offer a partial understanding of risk by

equating it with volatility. However, true risk is better represented by the possibility of losing

money. This section introduces the Koljonen Ratio (KR), a comprehensive measure, created

by the author of this thesis, which integrates two critical downside risk metrics: the Sortino

Ratio (Sor) and the Calmar Ratio (CR).

3.1. THE SHARPE RATIO AS A MEASURE OF RISK-ADJUSTED RETURNS

The SR is widely used to measure risk-adjusted returns, defined as:

   



(3)

Where:

▪ Rp = Portfolio return

▪ Rf = Risk-free rate

▪ Op = Standard deviation of the portfolio

Despite its strengths

119

, the SR has significant limitations that are often not adequately

addressed by mainstream academia and traditional practitioners

120

. Although its many

limitations, in our view, the main one lies in its use of total volatility (standard deviation) as a

measure of risk. This approach does not distinguish between upside and downside volatility,

treating all fluctuations as equally undesirable. Consequently, the SR may penalize portfolios

that exhibit positive volatility, providing a skewed perception of risk.

3.2. THE SORTINO RATIO AS A MEASURE OF DOWNSIDE RISK-ADJUSTED RETURNS

The SoR addresses which in our view is the main SR’s limitation, by focusing exclusively on the

downside volatility. Although it still understands risk as volatility, this is a step in the right

direction in comparison with the SR. It is defined as:

 



(4)

119

Simplicity, standardization, widely usage and flexibility (it can be applied to any portfolio/asset).

120

Assumes a normal distribution, ignores extreme events, does not distinguish between upside and downside

volatility and assumption of linear relationship between risk and return, among other drawbacks.

Where:

▪ Rp = Portfolio return

▪ Rf = Risk-free rate

▪ Od = Standard negative deviation of the portfolio

By considering only the volatility of negative returns, the SoR provides a more accurate

measure than the SR of the risk that investors are primarily concerned with: the possibility

permanent losses. However, a limitation of the SoR is that it still understands risk as volatility.

In our view, volatility represents the risk only in a partial way, as it fails to represent and

address the possibility of permanent losses.

Despite this, the SoR offers a more targeted approach by focusing on the downside risk, which

is a critical concern for most investors. This focus on downside volatility makes the Sortino

ratio a better tool for assessing investments, as it aligns more closely with the practical

concerns of risk management and the investor's aversion to losses. While it is not a perfect

measure and does not completely encapsulate the concept of risk as the possibility of loss, it

nonetheless enhances the evaluation of risk-adjusted returns by honing in on the most

detrimental aspect of volatility: negative deviations. A good SoR is typically considered to be

over 2.

3.3. THE CALMAR RATIO AS A MEASURE OF DOWNSIDE RISK-ADJUSTED RETURNS

The CR is a measure that focuses on drawdowns, notoriously relevant for long-term investors,

who are concerned about the potential for large sustained losses. It is defined as:

  



(5)

Where:

▪ Rp = Portfolio return

▪ Rf = Risk-free rate

▪ Od = Downside standard deviation

▪ MD = Maximum peak-to-trough decline during the period

The primary limitation of the CR is its disregard for downside volatility, which is a significant

strength of the SoR. The SoR and CR thus complement each other effectively, providing a more

comprehensive evaluation of risk-adjusted performance when used together.

A higher CR indicates better performance in terms of risk-adjusted returns and drawdown

management. A good CR is typically considered to be over 1.

3.4. COMBINING SORTINO AND CALMAR RATIOS: THE KOLJONEN RATIO

Combining these two downside risk metrics creates a comprehensive measure of risk-adjusted

performance based on pure downside risk. The KR is introduced to integrate the strengths of

both the SoR and CR, providing a one-stop metric for evaluating overall downside risk.

The KR is defined as the geometric mean of the CR and the maximum of 0 or the SoR minus 1:

  󰇛󰇛󰇜󰇜

(6)

By subtracting 1 from the SoR, we adjust for portfolios that perform only adequately (SoR =

1), setting the baseline contribution to zero. This adjustment ensures that only portfolios with

a SoR greater than 1 contribute positively to the KR, emphasizing superior performance over

the downside standard deviation. This approach also helps align the scales of the SoR and CR,

making normalization less critical.

In detailed form, the KR formula is:

  󰇛 

  

 󰇜

(7)

Where:

• Rp = Portfolio return

• Rf = Risk-free rate

• Od = Downside standard deviation of the portfolio

• MD = Maximum peak-to-trough decline during the period

This step-by-step combination ensures that the metric reflects both downside volatility risk

management and drawdown risk-adjusted performance. The use of the maximum function

ensures that the ratio does not produce negative values, making it more interpretable.

3.5. INTERPRETATION

The Koljonen Ratio provides a nuanced view of risk-adjusted performance:

▪ KR = 0: The portfolio's return has not exceeded the minimum required return to

compensate for downside risk. This indicates that the portfolio's performance is

inadequate when considering downside risk.

▪ 0 < KR < 1: While the portfolio has managed to achieve higher returns than the

minimum required (i.e. SoR > 1), these returns are not sufficient to cover the downside

risk adequately. This indicates that the portfolio's performance, when adjusted for

downside risk, is lacking, suggesting a higher vulnerability to losses and insufficient

reward for the risks taken.

▪ KR = 1: The portfolio's downside risk is perfectly balanced with the actual or predicted

return, indicating an equal trade-off between return and downside risk.

▪ KR > 1: The portfolio's downside risk-adjusted return is higher than the actual or

predicted return, indicating that the portfolio is effectively managing downside risk

while achieving superior returns.

3.6. LIMITATIONS

While the KR offers a comprehensive measure of downside risk, it is not without limitations:

▪ Complexity: The KR is more complex to calculate than either the SoR or the CR alone.

This complexity may make it less accessible or understandable for some investors,

particularly those without a strong mathematical background.

▪ Scale Differences: Although the subtraction of 1 helps align the scales of the SoR and

CR, they might not be perfectly aligned, but this adjustment is a good enough proxy

for practical purposes.

▪ Assumption of Normality: Like the SoR and CR, the KR still assumes a certain degree of

normality in the distribution of returns. While it focuses on downside risk, it may not

fully account for extreme events or fat tails in the distribution.

▪ Historical Data Dependency: The KR, like its component ratios, relies on historical data.

This reliance can be problematic if past performance is not indicative of future results,

especially in volatile or rapidly changing markets.

▪ Subjectivity in Target Return: The SoR requires a target or minimum acceptable return,

which can be subjective. The choice of this target can significantly impact the KR,

introducing potential bias.

▪ Overemphasis on Downside Risk: While focusing on downside risk is beneficial, it might

lead to an overemphasis on avoiding losses at the expense of achieving high returns.

Investors might overlook opportunities with higher volatility but also higher potential

returns.

▪ Negative SoR Handling: The KR sets the contribution of the SoR to zero when it is less

than or equal to one, which might oversimplify scenarios where slightly below-average

performance still needs to be considered. This binary approach might not capture

nuanced performance differences adequately.

▪ Volatility vs. Risk: The KR, like the SoR and CR, still equates volatility with risk. For many

investors, risk is more accurately defined as just the possibility of loss rather than

volatility alone. While the KR aims to address this by focusing on downside risk, it might

still not fully capture all aspects of risk that concern investors.

▪ Non-Standardization: The use of the maximum function and the subtraction of one

from the SoR might make the KR less standardized and harder to compare across

different portfolios or investment strategies. The normalization and interpretation

might require additional context.

▪ Data Requirements: Calculating the KR requires detailed data on portfolio returns, the

risk-free rate, downside deviations, and maximum drawdowns. Ensuring the accuracy

and completeness of this data can be challenging and resource-intensive.

3.7. CONCLUSION

By introducing the KR, we aim to create a more robust and balanced metric that effectively

captures all aspects of downside risk. This new metric not only assesses the actual drawdowns

of the portfolio but also accounts for downside volatility, providing a comprehensive view of

risk-adjusted performance.

4. METHODOLOGY

We will divide the practical section into three distinct parts. In the first part, we will outline

the general methodology used in our analysis. The second part will examine the application

of traditional TF strategies to significant cryptocurrencies, aiming to verify the robustness of

TF strategies in both traditional and emerging asset classes. The third part will focus on the

methodology used to implement TF strategies in cryptocurrencies, incorporating techniques

to reduce exposure during overextended trends to mitigate high maximum drawdowns.

4.1. GENERAL METHODOLOGY

4.1.1. DATA SOURCES AND PYTHON LIBRARIES USED

The data for our analysis will be fetched using the ‘yfinance’ library

121

. For trading decisions,

we will utilize the 'Adj. Close' prices, as this adjusted closing price accounts for all corporate

actions and provides a more accurate reflection of the asset's value.

We are going to use Python 3.9.6. The primary library used for back testing our strategies will

be ‘backtesting.py’

122

, a Python library designed for this purpose. Additionally, we will employ

several other libraries for various tasks, including data processing and technical indicator

calculations.

4.1.2. TIME FRAME AND WINDOW

We will use daily candlesticks for our analysis, focusing on the 'Adj. Close' column from the

data frame provided by ‘yfinance’. The backtesting period will span two Bitcoin halving cycles,

starting on July 9, 2016, and ending on April 19, 2024. This period is chosen to capture a

comprehensive view of market behavior across significant cryptocurrency market events.

For cryptocurrencies that were not in existence at the beginning of this period, we will use the

earliest available data from Yahoo Finance as the starting point for our analysis.

4.1.3. CRYPTOCURRENCIES AND COMMISSIONS

We are going to study the top 5 cryptocurrencies excluding stablecoins and duplicates

123

These are Bitcoin, Ethereum, BNB, Solana and XRP, which combined represent over 70% of

121

https://pypi.org/project/yfinance/

122

https://kernc.github.io/backtesting.py/

123

For example, Lido Staked Ether is considered as a duplicate of Ethereum, as it a derivative of Ether and follows

closely the same price.

the total cryptocurrency market capitalization, including stablecoins, according to

Coingecko.

124

The default explicit commission used is the typically charged among the different exchanges

(0.1% per trade amount). No interest has been applied to the open positions, as long-only

strategies have been considered.

4.1.4. PERFORMANCE EVALUATION

The performance metrics that we will use are the following: Annualized Return, Annualized

Volatility, Maximum Drawdown, Sharpe Ratio, Sortino Ratio, Calmar Ratio, Koljonen Ratio and

Hit Ratio, among other less relevant metrics.

4.2. TRADITIONAL TREND-FOLLOWING STRATEGIES APPLIED TO CRYPTOCURRENCIES

TF strategies will be applied to cryptocurrencies, and the results will be compared with a buy-

and-hold approach for the same cryptocurrency, which will serve as the benchmark.

The strategies we are going to test to determine the effectiveness of traditional TF strategies

when applied to cryptocurrencies are as follows:

▪ 50/100 Days SMA Crossover: This strategy uses two simple moving averages (SMA)

with different periods. If the fast-moving average (50 days) crosses above the slow-

moving average (100 days), it generates a buy signal. Conversely, if the fast-moving

average crosses below the slow-moving average, it generates a sell signal.

▪ 20 Days Donchian Channel: This strategy is based on Donchian channels, which use the

highest high and lowest low over the last 20 days to create upper and lower bands. A

buy signal is generated if the upper band moves upwards without the lower band

moving downwards in the same candle. A sell signal is generated if the lower band

moves downwards without the upper band moving upwards.

▪ Daily Heikin-Ashi Candles: This strategy uses Heikin-Ashi candlestick patterns. If the

most recent Heikin-Ashi candle closes green, it generates a buy signal. If the candle

closes red, it generates a sell signal.

We will test both long-only and long-short strategies to evaluate their performance in the

cryptocurrency market. In all cases, buy means to go long, and sell means to sell the long

position. In the case of long-short strategies, sell also means to go short.

124

https://www.coingecko.com/

4.3. AN ENSEMBLE TREND-FOLLOWING STRATEGY, OPTIMIZED FOR DOWNSIDE RISK-

ADJUSTED RETURNS

In this section, we will develop an ensemble long-short model comprising four distinct trend-

following trading strategies: SMA crossover, Donchian channel, Heikin-Ashi candles, and the

Ichimoku Cloud. The ensemble approach leverages the strengths of each individual strategy

to create a more robust trading system. The use of ensembles (combinations) to cope with

conceptual uncertainty, accurately capture information on the underlying structure of the

data, and complement the errors associated with each strategy or classifier, has been

advocated recently by many authors (see, e.g., Tsai et al., 2011, 2014; Ayuso et al., 2021; Bravo

et al., 2021, 2023; Stell, 2020; Ashofteh et al., 2022).

4.3.1. STRATEGIES

The ensemble model comprises four distinct trend-following strategies, each with its unique

approach to generating trading signals. These strategies are as follows:

▪ SMA Crossover: This strategy involves two Simple Moving Averages (SMA) of different

periods. A buy signal is generated when the short-term SMA crosses above the long-

term SMA, and a sell signal is generated when the short-term SMA crosses below the

long-term SMA.

▪ Donchian Channel: The Donchian Channel strategy tracks the highest high and lowest

low over a specified period. The bid band is the average between the high and low

band. A buy (sell) signal is generated when the price closes above (below) the mid

band.

▪ Heikin-Ashi Candles: This strategy uses modified candlestick charts to smooth out

price action. A series of green (red) Heikin-Ashi candles generates a buy (sell) signal.

We use the variable ‘backcandle’ to reflect the number of candles needed to generate

a given signal.

▪ Ichimoku Cloud: The Ichimoku Cloud strategy uses multiple components to identify

support, resistance, and trend direction. A buy signal is generated when the

conversion line is above the base line. A sell signal is generated when the conversion

line is below the baseline.

4.3.2. ENSEMBLE SIGNAL GENERATION

The trading signals from each of the four strategies will be combined using a majority rule.

Specifically:

▪ If three or four strategies generate a buy signal, we will take a long position.

▪ If zero or one strategy signals a buy, we will take a short position.

▪ If exactly two strategies signal a buy, we will remain out of the market to avoid

ambiguity and reduce potential drawdowns.

4.3.3. OPTIMIZATION WITHOUT A DELEVERAGING MECHANISM

Bitcoin is going to be our training dataset for optimization, which will be tested in the other 4

cryptocurrencies. We are going to optimize this ensemble model for the Koljonen Ratio

described in Chapter 3.

These are the parameters and the list of possible values that we are going to optimize:

SMA Crossover

▪ fastSMA_range = range(2, 9, 2)

▪ slowSMA_range = range(40, 101, 5)

Donchian Channel

▪ donchian_period_range = range(20, 81, 5)

Heikin-Ashi Candles

▪ backcandles_range = range(1, 5)

Ichimoku Cloud

▪ tenkan_range = range(2, 10, 2)

▪ kijun_range = range(10, 56, 5)

4.3.4. OPTIMIZATION WITH A DELEVERAGING MECHANISM

To try and enhance the risk-adjusted results obtained from the ensemble model we will

introduce a deleveraging mechanism and we will compare the results of the ensemble model

without the deleveraging mechanism and with the deleveraging mechanism.

The deleveraging mechanism consists in systematically reducing the position size when we

detect an overextension of the trend when a certain risk threshold is met. Specifically, the

strategy will monitor the ratio of the fast SMA to the slow SMA. If the ratio exceeds a

predefined threshold (indicating potential overextension), a portion of the current position

will be closed. This portion will start small and increase incrementally each time the threshold

is met again, thus gradually and incrementally deleveraging the position. This method aims to

lock in gains and reduce exposure during periods of high volatility or potential reversals.

This approach helps in managing risk dynamically by adjusting the position size based on

market conditions, thereby aiming to improve the overall risk-adjusted performance of the

strategy.

These are the parameters and the list of possible values that we are going to optimize:

SMA Crossover

▪ fastSMA_range = range(2, 5, 2)

▪ slowSMA_range = range(55, 76, 5)

Donchian Channel

▪ donchian_period_range = range(60, 101, 5)

Heikin-Ashi Candles

▪ backcandles_range = range(1, 3)

Ichimoku Cloud

▪ tenkan_range = range(3, 8, 2)

▪ kijun_range = range(10, 30, 10)

Deleveraging Mechanism

▪ SMARatio_long_range = np.arange(1.5, 1.8, 0.05)

▪ SMARatio_short_range = np.arange(1.4, 1.7, 0.05)

▪ st_portion_range = [0.001]

▪ inc_portion_range = np.arange(0.003, 0.007, 0.001)

The deleveraging mechanism works in the following way:

▪ Long Positions:

o When the fast SMA to slow SMA ratio exceeds the threshold set by

SMARatio_long, a portion of the long position will be closed.

o The initial portion closed will be st_portion.

o If the condition is met again, the portion closed will be incremented by

inc_portion each time, gradually reducing the position size.

▪ Short Positions:

o When the slow SMA to fast SMA ratio exceeds the threshold set by

SMARatio_short, a portion of the short position will be closed.

o The initial portion closed will be st_portion.

o If the condition is met again, the portion closed will be incremented by

inc_portion each time, gradually reducing the position size.

The deleveraging mechanism helps manage risk dynamically for long and short positions by

reducing the position size when the market may be overextended. It locks in gains and reduces

exposure and risk.

Overall, this mechanism aims to improve the strategy's risk-adjusted performance by

systematically managing position sizes based on market conditions.

4.3.1. APPLICATION OF THE KELLY CRITERION

After optimizing for the Koljonen Ratio with 100% equity invested in each trade, we will apply

the Kelly Criterion (Kelly, 1956) using the results from this optimization. By determining the

optimal exposure through Kelly's formula

125

, we will backtest the strategy with this specific

exposure. Finally, we will compare the results obtained from both scenarios to evaluate the

impact of the Kelly Criterion on the strategy's performance, main risk-adjusted return ratios

and drawdown measures.

125

Expected excess return divided by the portfolio’s expected variance.

5. RESULTS AND DISCUSSION

5.1. TRADITIONAL TREND-FOLLOWING STRATEGIES APPLIED TO CRYPTOCURRENCIES

5.1.1. RESULTS

5.1.1.1. 50/100 DAYS SMA CROSSOVER LONG-ONLY

For the 50/100 days SMA crossover long-only strategy, the results obtained are the following:

Table 5.1 – 50/100 Days SMA Crossover Long-Only Strategy Metrics

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-04-10

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

58.55

51.36

54.25

46.23

47.41

Equity Final [$]

8,410,267

506,187

3,246,302

3,132,084

8,217

Equity Peak [$]

12,828,055

1,446,548

6,123,737

4,472,177

121,911

Return [%]

8310.27

406.19

3146.30

3032.08

-91.78

B&H Return [%]

9707.60

853.39

27773.10

14902.36

131.64

Return (Ann.) [%]

76.69

28.59

71.53

135.05

-32.12

Volatility (Ann.) [%]

114.35

91.42

156.45

254.76

63.85

Sharpe Ratio

0.67

0.31

0.46

0.53

0.0

Sortino Ratio

1.94

0.64

1.52

2.49

0.0

Calmar Ratio

1.16

0.37

0.91

1.68

0.0

Koljonen Ratio

1.05

0.0

0.689511

1.579611

0.0

Max. Drawdown [%]

-66.06

-77.88

-78.25

-80.52

-93.80

Avg. Drawdown [%]

-10.103976

-13.655578

-14.20844

-16.332745

-29.42

Max. Drawdown Dur.

1102 days

1074 days

1082 days

856 days

1991 days

Avg. Drawdown Dur.

51 days

76 days

75 days

49 days

537 days

# Trades

Win Rate [%]

53.846154

45.454545

40.0

37.5

27.78

Best Trade [%]

1505.54

366.95

1725.53

895.630359

43.98

Worst Trade [%]

-33.34

-38.60

-49.19

-48.471351

-48.69

Avg. Trade [%]

40.67

15.87

41.63

53.80867

-12.96

Max. Trade Duration

484 days

230 days

393 days

173 days

132 days

Avg. Trade Duration

127 days

109 days

127 days

84 days

61 days

Profit Factor

18.42

4.83

17.68

16.206803

0.362

Expectancy [%]

141.53

39.80

195.59

157.277485

-10.03

SQN

1.2144

0.5737

0.9680

1.039354

-2.66

Source: Own preparation.

5.1.1.2. 20 DAYS DONCHIAN CHANNEL LONG-ONLY

For the 20-Day Donchian Channel strategy, the results gotten are the following:

Table 5.2 – 20 Days Donchian Channel Long-Only Strategy Metrics

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-04-10

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

60.555947

52.548853

51.869159

53.365058

45.157179

Equity Final [$]

10,158,056

3,007,902

71,185,530

77,803,033

739,384

Equity Peak [$]

11,289,009

4,366,964

79,416,301

91,462,233

1,790,170

Return [%]

10058.06

2907.90

71085.53

77703.03

639.38

B&H Return [%]

9707.60

853.39

27773.10

14902.36

131.64

Return (Ann.) [%]

81.02

69.52

176.87

421.61

36.37

Volatility (Ann.) [%]

104.59

121.13

275.98

728.04

144.75

Sharpe Ratio

0.78

0.57

0.64

0.58

0.25

Sortino Ratio

2.30

1.65

4.13

6.94

0.78

Calmar Ratio

1.26

1.20

2.28

5.11

0.44

Koljonen Ratio

1.28

0.883

2.67

5.51

0.0

Max. Drawdown [%]

-64.50

-57.79

-77.67

-82.50

-83.41

Avg. Drawdown [%]

-8.56

-13.01

-12.84

-14.20

-23.82

Max. Drawdown Dur.

1051 days

813 days

565 days

778 days

1184 days

Avg. Drawdown Dur.

44 days

62 days

51 days

34 days

210 days

# Trades

Win Rate [%]

45.95

51.52

61.29

47.06

42.42

Best Trade [%]

388.26

325.10

1386.36

2366.96

177.12

Worst Trade [%]

-21.79

-29.86

-15.69

-57.61

-32.54

Avg. Trade [%]

13.35

10.87

23.60

47.93

6.25

Max. Trade Duration

190 days

134 days

149 days

138 days

109 days

Avg. Trade Duration

46 days

37 days

39 days

46 days

32 days

Profit Factor

5.776

4.15

23.09

21.52

2.89

Expectancy [%]

24.06

19.01

68.15

200.54

12.66

SQN

1.23

1.22

1.82

1.20

0.67

Source: Own preparation.

5.1.1.3. DAILY HEIKIN-ASHI CANDLES LONG-ONLY

For the Daily Heikin-Ashi Candles strategy, the results gotten are the following:

Table 5.3 – Daily Heikin-Ashi Candles Long-Only Strategy’s Metrics

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-04-10

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

58.163265

54.672897

54.970263

52.413324

49.830076

Equity Final [$]

3,104,913

396621

6397067

4986047

2532466

Equity Peak [$]

5,001,514

607064

8771477

6732450

4512053

Return [%]

3004.91

296.62

6297.07

4886.05

2432.47

B&H Return [%]

9707.60

853.39

27773.10

14902.36

131.64

Return (Ann.) [%]

55.46

23.82

90.56

163.80

65.05

Volatility (Ann.) [%]

77.23

73.87

170.55

282.14

170.24

Sharpe Ratio

0.72

0.32

0.53

0.58

0.38

Sortino Ratio

1.91

0.66

2.35

3.19

1.57

Calmar Ratio

0.78

0.40

1.54

2.78

1.10

Koljonen Ratio

0.84

0.0

1.44

2.46

0.791

Max. Drawdown [%]

-71.525872

-59.360322

-58.946378

-58.965071

-59.046711

Avg. Drawdown [%]

-9.381619

-17.924788

-13.83378

-15.198037

-17.806941

Max. Drawdown Dur.

1133 days

957 days

1074 days

434 days

1101 days

Avg. Drawdown Dur.

66 days

94 days

90 days

45 days

138 days

# Trades

305

273

263

163

283

Win Rate [%]

39.672131

38.461538

44.86692

43.558282

38.162544

Best Trade [%]

110.453132

71.011366

202.449382

108.650055

200.684844

Worst Trade [%]

-13.397021

-22.335779

-13.695981

-25.352849

-28.705672

Avg. Trade [%]

1.13286

0.503889

1.59372

2.427291

1.148518

Max. Trade Duration

25 days

21 days

19 days

17 days

20 days

Avg. Trade Duration

5 days

4 days

Profit Factor

1.874445

1.4119

2.183334

2.21885

1.962516

Expectancy [%]

1.620768

0.96793

2.56541

3.847515

2.238953

SQN

0.961639

0.727959

1.040321

1.730006

0.675348

Source: Own preparation.

5.1.1.4. 50/100 DAYS SMA CROSSOVER LONG-SHORT

For the 50/100 days SMA crossover long-short strategy, the results obtained are the following:

Table 5.4 – 50/100 Days SMA Crossover Long-Short Strategy Metrics

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-10-04

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

96.375792

94.604928

94.647409

5.098572

45.751912

Equity Final [$]

2,611,566

154,753

417,036

0.0

Equity Peak [$]

9,534,430

1,430,213

2,070,309

128,394

203,890

Return [%]

2511.57

54.75

317.04

-100

B&H Return [%]

9707.60

853.39

27,773.10

14902.36

131.64

Return (Ann.) [%]

52.05

7.01

24.78

0.0

Volatility (Ann.) [%]

121.04

100.10

147.41

633.91

750.96

Sharpe Ratio

0.43

0.07

0.17

0.0

Sortino Ratio

1.09

0.13

0.41

0.0

Calmar Ratio

0.61

0.08

0.27

0.0

Koljonen Ratio

0.23

0.0

Max. Drawdown [%]

-85.588807

-93.126272

-91.733439

-100

Avg. Drawdown [%]

-10.746792

-11.963261

-17.955789

-40.125708

-16.197287

Max. Drawdown Dur.

1102 days

1074 days

1082 days

1213 days

1991 days

Avg. Drawdown Dur.

49 days

59 days

96 days

318 days

149 days

# Trades

Win Rate [%]

40.909091

0.0

17.647059

Best Trade [%]

1505.544359

366.953544

1725.534938

-101.058378

33.327732

Worst Trade [%]

-47.392891

-50.14898

-70.24009

-101.058378

-126.427603

Avg. Trade [%]

13.942439

2.008767

7.403983

0.0

Max. Trade Duration

484 days

231 days

393 days

74 days

121 days

Avg. Trade Duration

110 days

102 days

112 days

74 days

64 days

Profit Factor

7.137347

2.348432

7.172271

0.0

0.123289

Expectancy [%]

71.044072

16.804793

92.339025

-101.058378

-26.978264

SQN

0.392236

0.074061

0.291984

NaN

-1.26721

Source: Own preparation.

5.1.1.5. 20 DAYS DONCHIAN CHANNEL LONG-SHORT

For the 20 Day Donchian Channel long-short strategy, the results gotten are the following:

Table 5.5 – 20 Days Donchian Channel Long-Short Strategy Metrics

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-10-04

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

99.155524

99.065421

98.980459

97.756628

98.513169

Equity Final [$]

4,154,707

2,541,858

37979422.97

82,862,651

879,701

Equity Peak [$]

4,776,855

9,330,242

41315092.06

125,228,046

4,185,539

Return [%]

4054.71

2441.86

37879.42297

82762.65

779.70

B&H Return [%]

9707.60

853.39

27773.09871

14902.36

131.64

Return (Ann.) [%]

61.39

65.15

151.17

429.83

40.10

Volatility (Ann.) [%]

121.75

155.22

315.12

958.47

206.91

Sharpe Ratio

0.50

0.42

0.48

0.45

0.19

Sortino Ratio

1.36

1.24

2.73

5.74

0.62

Calmar Ratio

1.00

0.82

1.72

4.88

0.46

Koljonen Ratio

0.60

0.45

1.72

4.81

0.0

Max. Drawdown [%]

-61.686989

-79.527845

-88.086529

-88.110916

-86.749336

Avg. Drawdown [%]

-10.736621

-12.648331

-13.527449

-14.149101

-26.919123

Max. Drawdown Dur.

1046 days

615 days

761 days

676 days

956 days

Avg. Drawdown Dur.

50 days

39 days

46 days

29 days

144 days

# Trades

Win Rate [%]

43.939394

53.225806

48.571429

43.939394

Best Trade [%]

388.264244

325.102474

1386.362559

2366.959438

177.123406

Worst Trade [%]

-38.970098

-29.858367

-47.944309

-57.613273

-50.05324

Avg. Trade [%]

5.12957

5.027725

10.054083

21.166294

3.349441

Max. Trade Duration

190 days

134 days

149 days

138 days

109 days

Avg. Trade Duration

38 days

36 days

38 days

42 days

36 days

Profit Factor

2.963142

2.496204

6.991898

12.508827

2.127987

Expectancy [%]

11.272564

10.266663

34.341896

98.766785

7.800997

SQN

0.931961

0.470484

1.768483

0.779981

0.299111

Source: Own preparation.

5.1.1.6. DAILY HEIKIN-ASHI CANDLES LONG-SHORT

For the Daily Heikin-Ashi Candles strategy, the results gotten are the following:

Table 5.6 – Daily Heikin-Ashi Candles Long-Short Strategy’s Metrics

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-10-04

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

99.894441

99.872557

99.796057

99.872557

Equity Final [$]

125,824

447,952

187,791

2,089,182

37,615,004

Equity Peak [$]

414,634

622,064

307,687

2,194,460

52,844,582

Return [%]

25.82

347.95

87.79

1,989.18

37,515.00

B&H Return [%]

9,707.60

853.39

27,773.10

14,902.36

131.64

Return (Ann.) [%]

3.00

26.18

10.26

112.58

150.80

Volatility (Ann.) [%]

67.34

112.74

122.34

373.52

371.39

Sharpe Ratio

0.04

0.23

0.08

0.30

0.41

Sortino Ratio

0.08

0.52

0.19

1.45

2.60

Calmar Ratio

0.04

0.36

0.12

1.46

2.07

Koljonen Ratio

0.0

0.81

1.81

Max. Drawdown [%]

-80.624918

-72.109228

-82.834256

-77.298076

-72.956527

Avg. Drawdown [%]

-19.870803

-17.498674

-31.410489

-18.049135

-14.597072

Max. Drawdown Dur.

2250 days

1062 days

2218 days

538 days

597 days

Avg. Drawdown Dur.

157 days

98 days

293 days

52 days

39 days

# Trades

536

469

446

281

481

Win Rate [%]

39.552239

45.628998

44.618834

46.263345

50.10395

Best Trade [%]

115.225665

61.163377

203.2428

108.903469

217.432737

Worst Trade [%]

-23.446652

-24.525691

-49.394895

-44.746086

-61.223609

Avg. Trade [%]

0.017329

0.320961

0.141588

1.087603

1.240477

Max. Trade Duration

25 days

21 days

19 days

17 days

20 days

Avg. Trade Duration

5 days

4 days

Profit Factor

1.164366

1.291927

1.320749

1.616929

1.985839

Expectancy [%]

0.378558

0.795772

0.941917

2.244831

2.126359

SQN

0.071106

0.521958

0.238549

1.617653

1.490067

Source: Own preparation.

5.1.2. DISCUSSION

Our comprehensive analysis of TF strategies applied to various cryptocurrencies reveals

several key insights. The performance of these strategies was evaluated using crucial risk-

adjusted metrics: Sharpe Ratio, Sortino Ratio, Calmar Ratio, and the newly introduced

Koljonen Ratio. Additionally, Maximum Drawdown was considered to understand the

downside risk.

5.1.2.1. GENERAL PERFORMANCE TRENDS

Long-Only vs. Long-Short Strategies:

▪ In general, long-only strategies significantly outperformed their long-short

counterparts across all cryptocurrencies. The long-only approaches demonstrated

higher returns and better risk-adjusted performance, indicating that capturing the

upward trends in these volatile markets was more beneficial than attempting to

profit from both upward and downward movements.

▪ Long-short strategies often struggled with higher volatility and deeper drawdowns,

which reduced their overall performance. This could be due to the persistent

upward trend in cryptocurrency markets over the analyzed period, where short

positions were more likely to incur losses. Traditional strategies tend to not work

in cryptocurrencies, as they exhibit a much different speed of movement than

other traditional assets.

Performance Across Cryptocurrencies:

▪ Bitcoin: Bitcoin consistently achieved solid returns across different strategies. Its

historical data, longer market presence, and relative stability compared to other

cryptocurrencies contributed to more reliable performance metrics. For example,

Bitcoin showed a strong Sortino Ratio and Calmar Ratio in most long-only

strategies, indicating efficient management of downside risk relative to the returns

achieved.

▪ Ethereum: Ethereum's performance was moderate, showing reasonable returns

but with higher volatility and drawdowns. It had lower Sharpe and Sortino Ratios

compared to Bitcoin, reflecting a higher risk relative to its returns.

▪ BNB and Solana: BNB and Solana exhibited exceptional returns in several

strategies, particularly in long-only approaches. Solana, being a newer

cryptocurrency with fewer data points, showed extraordinary results, especially in

strategies that capitalized on its significant price movements. However, these high

returns came with substantial volatility and drawdowns.

▪ XRP: XRP generally underperformed across all strategies. It showed lower returns

and higher drawdowns, leading to poor Sharpe and Sortino Ratios. This

underperformance highlights its higher susceptibility to adverse market

conditions.

5.1.2.2. KEY METRICS ANALYSIS

1. Sharpe Ratio: The Sharpe Ratio, which measures the risk-adjusted return of an

investment, was higher for long-only strategies. Bitcoin and Solana showed the highest

Sharpe Ratios among the cryptocurrencies, indicating better risk-adjusted returns. For

instance, in the Donchian Channel long-only strategy, Bitcoin and Solana

demonstrated strong Sharpe Ratios, reflecting efficient reward per unit of risk.

2. Sortino Ratio: The Sortino Ratio, which focuses on downside risk by measuring returns

relative to the negative deviation, was also higher for long-only strategies. Solana

achieved outstanding Sortino Ratios, especially in the Donchian Channel strategy, due

to its significant upward price movements. Bitcoin maintained a consistently good

Sortino Ratio, underscoring its stable performance relative to downside risk.

3. Calmar Ratio: The Calmar Ratio, which evaluates performance relative to maximum

drawdown, highlighted the robustness of long-only strategies. Solana and Bitcoin again

stood out with higher Calmar Ratios, indicating their ability to generate substantial

returns while managing drawdowns effectively. In contrast, long-short strategies

generally showed lower Calmar Ratios, reflecting deeper drawdowns and lower

returns.

4. Koljonen Ratio: The newly introduced Koljonen Ratio provided a comprehensive

measure of risk-adjusted performance, focusing on downside risk. Long-only strategies

exhibited higher Koljonen Ratios, with Solana and Bitcoin leading. This ratio helped

highlight the strategies' effectiveness in balancing returns and managing downside

risk. For example, Solana's Koljonen Ratio was particularly high in the Donchian

Channel long-only strategy, reflecting its strong performance despite high volatility.

5. Maximum Drawdown: Maximum Drawdown, a critical measure of downside risk, was

significantly lower for long-only strategies compared to long-short strategies. Bitcoin

and Solana showed better drawdown management, with Solana achieving higher

returns despite experiencing high drawdowns. The maximum drawdown for long-short

strategies was notably severe, particularly for newer cryptocurrencies like Solana and

XRP, which experienced complete losses in some instances.

5.1.2.3. CONCLUSION

In summary, our analysis indicates that long-only strategies are more effective for

cryptocurrencies when it comes to traditional TF strategies, delivering better risk-adjusted

returns and managing downside risks more efficiently than long-short strategies. Bitcoin

emerged as the most reliable performer across various strategies, while Solana demonstrated

exceptional but extremely volatile returns due to its recent market entry and significant price

movements. The inclusion of the Koljonen Ratio provided a valuable perspective on downside

risk management, highlighting the strengths of long-only approaches in this high-risk, high-

reward market. Moving forward, optimization of these strategies will focus on enhancing

returns while further minimizing drawdowns and volatility, aiming to achieve a balanced and

sustainable investment approach in the cryptocurrency space.

5.2. AN ENSEMBLE TREND-FOLLOWING STRATEGY FOR CRYPTOCURRENCIES, OPTIMIZED

FOR DOWNSIDE RISK-ADJUSTED RETURNS

5.2.1. RESULTS

5.2.1.1. ENSEMBLE MODEL STRATEGY WITHOUT A DELEVERAGING MECHANISM

Without the deleveraging mechanism in place yet, the ensemble strategy’s optimization took

about 2 hours, with 108,160 combinations checked at around 15 items per second. The best

combination gotten was the following:

fastSMA = 4; slowSMA = 65; donchian_period = 80; backcandles = 1; tenkan = 5; kijun = 10

The results obtained are summarized in the table below:

Table 5.7 – Ensemble Model Strategy Metrics without Deleveraging Mechanism

Metrics

Values

Bitcoin126

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-10-04

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

96.903589

96.474087

96.431606

94.289599

96.389125

Equity Final [$]

81,273,734.44

1,238,722.41

4,753,665.18

11,463,147.86

6,396.45

Equity Peak [$]

92,270,500.84

5,607,762.42

5,611,893.63

12,041,743.31

379,348.71

Return [%]

81,173.73

1,138.72

4,653.67

11,363.15

-93.60

B&H Return [%]

9,707.60

853.39

27,773.10

14,902.36

131.64

Return (Ann.) [%]

136.44

47.73

81.98

224.32

-34.71

Volatility (Ann.) [%]

170.04

129.13

187.34

557.71

78.59

Sharpe Ratio

0.80

0.37

0.44

0.40

0.0

Sortino Ratio

3.44

0.97

1.64

3.05

0.0

Calmar Ratio

2.63

0.60

1.17

2.85

0.0

Koljonen Ratio

2.53

0.0

0.87

2.42

0.0

Max. Drawdown [%]

-51.82

-79.34

-69.94

-78.62

-98.44

Avg. Drawdown [%]

-8.21

-10.81

-15.71

-19.34

-12.70

Max. Drawdown Dur.

419 days

1,074 days

856 days

340 days

1,242 days

Avg. Drawdown Dur.

22 days

34 days

65 days

37 days

94 days

# Trades

234

241

230

127

267

Win Rate [%]

36.75

31.12

32.17

38.58

28.09

Best Trade [%]

201.55

262.66

734.21

676.77

152.59

Worst Trade [%]

-14.85

-22.45

-19.19

-39.98

-70.84

Avg. Trade [%]

2.91

1.05

1.69

3.80

-1.02

Max. Trade Duration

112 days

115 days

96 days

110 days

90 days

Avg. Trade Duration

12 days

10 days

11 days

9 days

Profit Factor

3.04

1.78

2.85

3.40

1.03

Expectancy [%]

4.41

2.27

4.98

11.75

0.11

SQN

1.72

0.35

1.14

1.78

-0.28

Source: Own preparation.

5.2.1.2. ENSEMBLE MODEL STRATEGY WITH A DELEVERAGING MECHANISM

The ensemble strategy with the deleveraging mechanism, optimized for the Koljonen Ratio,

took about 4 hours, with 211,680 combinations checked at around 14 items per second. The

best combination gotten was the following:

fastSMA = 4; slowSMA = 65; donchian_period = 100; backcandles = 1; tenkan = 5; kijun = 10;

SMARatio_long = 1.55; SMARatio_short = 1.40; st_portion = 0.001; inc_portion = 0.003

126

In this study, Bitcoin was utilized as the training asset for the optimization process. The remaining assets

(Ethereum, BNB, Solana, and XRP) were designated as testing assets to evaluate the robustness and

generalizability of the optimized strategies.

The results obtained are summarized in the table below:

Table 5.8 – Ensemble Model Strategy Metrics with Deleveraging Mechanism, Optimized for

the Koljonen Ratio

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-10-04

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

96.199859

95.581988

92.92998

95.539507

Equity Final [$]

178978544.80

1519649.52

3045129.63

25282843.80

2896.17

Equity Peak [$]

203202923.40

9158905.43

3592999.93

26558992.30

246363.04

Return [%]

178878.54

1419.65

2945.13

25182.84

-97.10

B&H Return [%]

9707.60

853.39

27773.10

14902.36

131.64

Return (Ann.) [%]

161.67

52.49

69.84

294.65

-42.26

Volatility (Ann.) [%]

185.22

130.00

172.84

641.72

68.37

Sharpe Ratio

0.87

0.40

0.46

Sortino Ratio

4.17

1.10

1.40

4.18

Calmar Ratio

2.82

0.61

1.02

3.76

Koljonen Ratio

2.987

0.24

0.64

3.46

Max. Drawdown [%]

-57.38

-86.09

-68.27

-78.34

-98.91

Avg. Drawdown [%]

-7.714332

-9.557522

-17.165602

-13.005034

-13.401285

Max. Drawdown Dur.

419 days

1074 days

856 days

328 days

1242 days

Avg. Drawdown Dur.

19 days

29 days

77 days

25 days

98 days

# Trades

364

478

436

500

532

Win Rate [%]

60.989011

64.435146

61.697248

84.8

57.894737

Best Trade [%]

272.878997

358.082057

1080.828084

626.671947

296.576995

Worst Trade [%]

-14.849735

-18.527556

-19.190339

-39.983628

-67.486115

Avg. Trade [%]

22.727737

29.038485

38.131885

85.071859

18.458747

Max. Trade Duration

106 days

115 days

96 days

91 days

90 days

Avg. Trade Duration

21 days

24 days

22 days

28 days

17 days

Profit Factor

24.572971

27.992035

49.289297

105.584052

12.651983

Expectancy [%]

31.161307

39.665504

78.541117

119.571802

24.343669

SQN

1.928059

0.312677

1.043971

1.882989

-0.487188

Source: Own preparation.

5.2.1.3. ENSEMBLE MODEL STRATEGY WITH A DELEVERAGING MECHANISM, INCLUDING THE

APPLICATION OF THE KELLY CRITERION

With these results in the table above, when we apply the Kelly Criterion formula to the asset

optimized for this strategy (Bitcoin), assuming the risk-free rate is 0, we determine that the

optimal exposure should be 47.14%.

127

The results with this exposure of the equity per trade,

keeping the rest in cash, are the following:

127

f* = 1.6167/1.85222 = 0.4714.

Table 5.9 – Ensemble Model Strategy Metrics with Deleveraging Mechanism, Optimized for

the Koljonen Ratio, with the Kelly Criterion applied

Metrics

Values

Bitcoin

Ethereum

BNB

Solana

XRP

Start

2016-07-09

2017-11-09

2020-10-04

2017-11-09

End

2024-04-19

Duration

2841 days

2353 days

1470 days

2353 days

Exposure Time [%]

96.199859

95.581988

92.92998

95.539507

Equity Final [$]

7036055.53

632873.34

1365948.47

5133650.26

39172.13

Equity Peak [$]

7582307.60

1377985.39

1508565.45

5266113.73

198947.45

Return [%]

6936.06

532.87

1265.95

5033.65

-60.83

B&H Return [%]

9707.60

853.39

27773.10

14902.36

131.64

Return (Ann.) [%]

72.68

33.12

49.99

165.71

-13.53

Volatility (Ann.) [%]

58.00

54.00

82.43

203.44

44.03

Sharpe Ratio

1.25

0.61

0.81

Sortino Ratio

3.62

1.29

1.80

3.99

Calmar Ratio

2.22

0.55

1.23

2.91

Koljonen Ratio

2.41

0.40

0.99

2.95

Max. Drawdown [%]

-32.70

-60.06

-40.60

-56.95

-81.04

Avg. Drawdown [%]

-4.07

-5.62

-9.40

-9.94

-8.74

Max. Drawdown Dur.

366 days

1074 days

853 days

300 days

1242 days

Avg. Drawdown Dur.

19 days

30 days

66 days

27 days

98 days

# Trades

363

478

436

500

532

Win Rate [%]

60.055096

64.435146

61.697248

84.8

57.894737

Best Trade [%]

272.878997

358.082057

1080.828084

626.671947

296.576995

Worst Trade [%]

-16.269498

-18.527556

-19.190339

-39.983628

-67.486115

Avg. Trade [%]

21.559231

29.038485

38.131885

85.071859

18.458747

Max. Trade Duration

106 days

115 days

96 days

91 days

90 days

Avg. Trade Duration

20 days

24 days

22 days

28 days

17 days

Profit Factor

21.998216

27.992035

49.289297

105.584052

12.651983

Expectancy [%]

29.721287

39.665504

78.541117

119.571802

24.343669

SQN

2.609287

0.85202

1.367105

1.991066

-0.492616

Source: Own preparation.

5.2.2. DISCUSSION

In a related study (PLOS ONE, 2021), the researchers examined various TF strategies across

multiple asset classes, including equities, commodities, and currencies . The study highlighted

the importance of optimizing the averaging window to improve the adaptability and

performance of TF strategies, particularly in managing downside risks during significant

market reversals. Notably, their findings indicated that an adaptive approach could

significantly enhance risk-adjusted returns by mitigating the impact of large drawdowns.

Comparing these insights with the results of our ensemble TF strategy optimized for

cryptocurrencies, we observe several similarities and distinctions. Similar to the PLOS ONE

study, our research underscores the critical role of dynamic risk management techniques. For

instance, our ensemble model, especially with the integration of the deleveraging mechanism

and the Kelly Criterion, demonstrated improved risk-adjusted performance across

cryptocurrencies like Bitcoin and Solana. However, the challenge of managing extreme

volatility in newer cryptocurrencies like Solana and XRP remains pronounced, as evidenced by

the persistent high drawdowns despite optimization efforts .

These findings reinforce the notion that while adaptive TF strategies can enhance

performance and reduce risks, the inherent volatility and unique market behaviors of

cryptocurrencies require continuous refinement and adjustment of the strategies employed.

By integrating the adaptive principles from the PLOS ONE study, future research could further

optimize our approach, potentially leading to more resilient and effective trend-following

models in the cryptocurrency market.

The ensemble strategy's optimization across different cryptocurrencies provided valuable

insights. Here is a comparison of the strategy's performance with and without the

deleveraging mechanism and the deleveraginh mechanism with the addition of the Kelly

Criterion for the exposure per trade:

5.2.2.1. RISK-ADJUSTED RETURN METRICS

The addition of the deleveraging mechanism notably improved the performance of Bitcoin

and Solana:

▪ Bitcoin: The Koljonen Ratio increased from 2.53 to 2.99, with annual returns rising from

136.44% to 161.67%. The maximum drawdown slightly worsened from -51.82% to -

57.38%, but the improved risk-adjusted returns justified the trade-off.

▪ Solana: The Koljonen Ratio rose from 2.42 to 3.46, with annual returns jumping from

224.32% to 294.65%. Although the maximum drawdown remained high (-78.62% vs. -

78.34%), the strategy's risk-adjusted performance significantly improved.

▪ BNB: There was a slight decrease in performance with deleveraging. The Koljonen

Ratio dropped from 0.87 to 0.64, and annual returns decreased from 81.98% to

69.84%. The maximum drawdown improved marginally from -69.94% to -68.27%.

▪ Ethereum: Ethereum saw moderate improvement with the deleveraging mechanism.

The Koljonen Ratio increased from 0 to 0.24, and annual returns improved from

47.73% to 52.49%. The maximum drawdown remained high (-79.34% vs. -86.09%),

indicating the difficulty for mid-term TF strategies in cryptocurrencies to achieve good

results with acceptable drawdowns.

▪ XRP: XRP showed extremely poor performance in both scenarios. The deleveraging

mechanism did not significantly improve XRP's results, with the annual return

remaining negative and high drawdowns persisting. This highlights the difficulty of

applying trend-following strategies to non-trending assets like XRP

128

, where the

maximum drawdown was over 98% in both cases.

On the other hand, although the application of the Kelly criterion decreased the performance,

it decreased more the overall volatility of the portfolio, especially in terms of the Sharpe ratio,

obtaining more robust results. We can see the results in the following table:

Table 5.10 – Risk-Adjusted Return Ratio’s Comparison – Pre-Kelly vs Post-Kelly

Metrics

Bitcoin

Ethereum

BNB

Solana

XRP

Pre-Kelly Criterion

Sharpe Ratio

0.87

0.4

0.46

Sortino Ratio

4.17

1.1

1.4

4.18

Calmar Ratio

2.82

0.61

1.02

3.76

Koljonen Ratio

2.99

0.24

0.64

3.46

Post-Kelly Criterion

Sharpe Ratio

1.25

0.61

0.81

Sortino Ratio

3.62

1.29

1.8

3.99

Calmar Ratio

2.22

0.55

1.23

2.91

Koljonen Ratio

2.41

0.4

0.99

2.95

Source: Own preparation.

5.2.2.2. DRAWDOWNS METRICS

It seems that for a mid-term TF strategy is extremely difficult to reduce the high maximum

drawdowns below the 50% mark. Even though we optimized for a downside risk-adjusted

return metric (the Koljonen Ratio), we still got extremely high volatilities and drawdowns. The

deleveraging mechanism helped with the downside risk-adjusted returns, but the overall risk

remains too high.

▪ Bitcoin: The maximum drawdown slightly worsened from -51.82% to -57.38%.

▪ Solana: The maximum drawdown remained high but slightly improved from -78.62%

to -78.34%.

▪ Ethereum: The maximum drawdown worsened from -79.34% to -86.09%, indicating a

need for further risk management strategies.

128

This phenomenon does not just happen in XRP within the cryptocurrency universe. There are some other

notable examples of assets that are not trending most of the time. Meme coins like Dogecoin and Shiba Inu are

examples of this. These are particularly difficult assets when it comes to using mid-term TF strategies, according

to the price action seen in the past.

This is why we decided to apply the Kelly Criterion to this strategy, maintaining a specific

position's exposure at 47.14% of the equity per trade. This approach significantly decreased

downside risks to a much more reasonable level, resulting in reduced maximum drawdowns

as follows:

Table 5.11 – Drawdown Metrics Comparison – Pre-Kelly vs Post-Kelly

Metrics

Bitcoin

Ethereum

BNB

Solana

XRP

Pre-Kelly Criterion

Max. Drawdown [%]

-57.38

-86.09

-68.27

-78.34

-98.91

Avg. Drawdown [%]

-7.71

-9.56

-17.17

-13.01

-13.40

Max. Drawdown Duration

419 days

1074 days

856 days

328 days

1242 days

Avg. Drawdown Duration

19 days

29 days

77 days

25 days

98 days

Post-Kelly Criterion

Max. Drawdown [%]

-32.70

-60.06

-40.60

-56.95

-81.04

Avg. Drawdown [%]

-4.07

-5.62

-9.40

-9.94

-8.74

Max. Drawdown Duration

366 days

1074 days

853 days

300 days

1242 days

Avg. Drawdown Duration

19 days

30 days

66 days

27 days

98 days

Source: Own preparation.

By applying the Kelly Criterion and maintaining a 47.14% exposure per trade, we effectively

reduced the maximum drawdowns and achieved a more balanced risk-reward profile. The

results illustrate significant improvements in downside risk management, enhancing the

overall robustness of the trading strategy.

5.2.2.3. OVERALL PERSPECTIVE

From an overall perspective, the deleveraging mechanism generally enhanced risk-adjusted

returns across multiple assets. The overall improvement in the average Koljonen Ratio from

1.164 to 1.4654 reflects better risk management and return balance. This suggests that a good

deleveraging mechanism can contribute to a more robust and resilient portfolio, despite some

individual asset challenges. The high maximum drawdowns in all instances point out the

importance of combining cryptocurrencies with other asset classes in the portfolio (like stocks,

bonds, commodities, cash, etc.). With the application of the Kelly Criterion, we observed a

significant improvement in the Sharpe Ratio, indicating better risk-adjusted returns. This

method reduced overall portfolio volatility and made the investment strategy more robust,

balancing the trade-off between risk and return more effectively. It highlights the potential of

optimizing exposure per trade to enhance portfolio performance and resilience.

5.2.2.4. CONCLUSION

The combination of the deleveraging mechanism and the Kelly Criterion has demonstrated its

efficacy in improving risk-adjusted returns and reducing downside risks across a range of

cryptocurrencies. While the deleveraging mechanism alone provided substantial

improvements in the performance of assets like Bitcoin and Solana, the application of the Kelly

Criterion further optimized exposure per trade, leading to reduced volatility and more robust

results. However, the persistent high drawdowns, especially in assets like XRP, indicate the

necessity of integrating cryptocurrencies with other asset classes to achieve a well-rounded

and resilient portfolio. Overall, these strategies highlight the importance of dynamic risk

management techniques in enhancing the performance and stability of cryptocurrency

investment strategies.

6. CONCLUSIONS AND FUTURE WORKS

This thesis has made several significant contributions to the field of trend-following strategies,

particularly within the context of cryptocurrency markets. Through a combination of

theoretical exploration and empirical analysis, we have advanced the understanding and

application of trend-following in several ways:

1. Enhanced Understanding of Trend-Following Philosophy: By applying a theoretical

framework grounded in the Austrian School of Economics, we have provided a more

structured and cohesive understanding of the trend-following philosophy. This

framework has enriched the theoretical basis of trend-following, offering new insights

and solidifying its principles.

2. Introduction of the Koljonen Ratio: One of the key contributions of this research is the

introduction of the Koljonen Ratio, a novel metric designed to measure downside risk-

adjusted returns more accurately and comprehensively. This metric addresses the

limitations of existing measures and provides a more nuanced evaluation of the

performance of trend-following strategies, especially in highly volatile cryptocurrency

markets.

3. Applicability of Trend-Following in Cryptocurrency Markets: Our study has

corroborated that trend-following strategies can be effectively applied in the

cryptocurrency space, particularly for cryptocurrencies that exhibit clear trending

behavior. However, it was noted that trend-following is less effective for

cryptocurrencies that spend prolonged periods without trending.

4. Development of an Ensemble Trend-Following Strategy: We developed an ensemble

mid-term trend-following strategy for daily candles. This strategy proved to be very

profitable in most scenarios, demonstrating the viability of trend-following approaches

in the cryptocurrency market.

5. Incorporation of Deleveraging Mechanisms: By integrating deleveraging mechanisms

into the trend-following strategy, we enhanced the downside risk-adjusted returns.

This adjustment helps mitigate the risks associated with overextended trends,

improving the overall performance of the strategy.

6. Challenges in Reducing Drawdowns: Our research highlighted the difficulty in reducing

drawdowns to traditionally acceptable levels within cryptocurrency trend-following

strategies. This finding underscores the need for a diversified portfolio that includes

not only crypto assets but also other asset classes like stocks, bonds, and commodities

to manage risk effectively.

7. Importance of the Kelly Criterion: The application of the Kelly Criterion has proven

crucial in ensuring that mid-term trend-following trading strategies in cryptocurrencies

do not result in significant capital loss. By optimizing the position size per trade, the

Kelly Criterion enhances the strategy's robustness and sustainability, providing a

critical safeguard against the high volatility and risk inherent in cryptocurrency

markets.

There are numerous avenues for future research to build upon the findings and contributions

of this thesis:

1. Expansion to More Cryptocurrencies: While this study focused on five

cryptocurrencies, representing a substantial portion of the market, future research

could extend this analysis to include a broader range of cryptocurrencies. This

expansion would provide a more comprehensive understanding of trend-following

applicability across different digital assets.

2. Portfolio Perspective: This study took an individual asset perspective. Future research

could adopt a portfolio perspective, examining trend-following strategies both within

the crypto space and in combination with traditional and alternative assets. This

approach would provide insights into how these strategies perform within a diversified

portfolio.

3. Further Development of Trend-Following Philosophy: While this thesis laid the

groundwork for understanding trend-following as a philosophy, there is potential for

further enhancement and development. Future studies could explore additional

theoretical frameworks or refine the existing one to provide deeper insights into trend-

following principles.

4. Advancement of the Koljonen Ratio: The Koljonen Ratio has proven to be highly useful

in practical terms within this thesis. Future research could further validate and refine

this metric, potentially adapting it for different asset classes or market conditions to

enhance its applicability and robustness.

5. Exploration of Additional Deleveraging Mechanisms: In this work, we used simple

moving averages to make deleveraging decisions. Future research could explore other

reactive techniques or predictive methods, including Machine Learning or Deep

Learning, to develop more sophisticated and effective deleveraging mechanisms.

6. Integration of Advanced Technologies: The incorporation of advanced technologies

such as Machine Learning and Deep Learning in trend-following strategies could

provide predictive insights and enhance decision-making processes. Future research

could investigate the potential of these technologies to improve the accuracy and

profitability of trend-following strategies.

In conclusion, this thesis has made significant contributions to the understanding and

application of trend-following strategies in cryptocurrency markets. By addressing theoretical

gaps, introducing the Koljonen Ratio, and developing innovative strategies, we have provided

valuable insights and tools for practitioners. Future research can build on these findings to

further advance the field and enhance the effectiveness of trend-following strategies in the

rapidly evolving digital financial landscape.

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APPENDIX A

HISTORY OF TREND-FOLLOWING

Humans have followed trends since primitive societies

129

, where survival needs, and

environmental factors primarily influenced trends. In more civilized societies, traders and

merchants observed and followed the patterns of price movements in various markets

(Greyserman & Kaminski, 2014). This behavior, which has critical social implications

130

, has

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These trends were essential for the sustenance, safety, and environmental factors. In early hunter-gatherer

societies, survival depended on efficiently hunting animals and gathering edible plants. The migration patterns

of animals dictated the trends in these activities, the seasonal availability of plants, and the development of tools

and techniques for hunting and gathering. For instance, using spears and later bows and arrows revolutionized

hunting practices, representing a significant trend in these societies. Early humans followed trends in shelter-

building that were influenced by their environment. In colder regions, trends included the construction of

insulated dwellings using materials like animal hides, while in warmer climates, the use of natural materials like

leaves and branches was common. The trend of transitioning from nomadic lifestyles to settled communities was

a significant change driven by the development of agriculture. Clothing trends in primitive societies were dictated

by climate and the availability of materials. Animal furs and skins were common in colder regions, while lighter

materials like woven grass or leaves were used in warmer climates. The invention of sewing, leading to more

fitted and protective clothing, was a significant trend in these societies. With the advent of agriculture, trends

shifted towards domesticating plants and animals. The climate and soil fertility of the region largely influenced

this shift. For example, wheat and barley cultivation emerged in the Fertile Crescent, while maize, beans, and

squash were domesticated in the Americas. Primitive societies also had social and cultural trends influenced by

their environment and survival needs. For example, in societies where hunting was predominant, cultural trends

often revolved around hunting rituals and glorifying skilled hunters. In contrast, agricultural societies developed

rituals and societal structures around planting and harvest seasons. The evolution of toolmaking was a significant

trend in human history. Early humans started with simple stone tools and developed more sophisticated tools

like axes, significantly improving their hunting efficiency and other activities. The trend of tool specialization,

where different tools were developed for specific tasks, marked a significant advancement in human societies.

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Trend-following serves as a mechanism for social cohesion and identity formation. In medieval societies,

trends in clothing and architecture were strongly influenced by the ruling classes, reflecting social status and

power dynamics. The Renaissance era saw art and science trends promoting individualism and humanism,

significantly shifting societal values and norms.

evolved over millennia

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, adapting to the complexities of modern society

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, yet retaining its

core psychological and social drivers

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Trend-following is an inherent part of human societies, reflecting and shaping our values,

beliefs, and behaviors across different eras. From ancient civilizations to the digital age, the

nature and impact of trends have continuously evolved, mirroring the dynamic progression of

human societies.

Modern history is replete with instances of bubbles 6 emerging. Although they are rooted in

monetary phenomena (Huerta de Soto, 1998), these bubbles are exacerbated manifestations

of the innate and profound aspects of human behavior and societal dynamics characterized

by the propensity to adhere to prevailing trends.

Although trend-following has been a popular trading philosophy, it has a largely

undocumented history. This is due to the scarcity of records before the early 20th century and

the fact that trend-following was not fully articulated until about 50 years ago

134

. Despite its

widespread use by the early 1950s, trend-following lacked a formal definition or name. The

passive nature implied

135

by the term might have contributed to its underappreciation, as

human nature often favors bold and discretionary action

136

. Additionally, the simplicity of the

concept, similar to ideas like negative numbers or zero, might have led to its slow acceptance.

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In ancient civilizations, trends often revolved around agricultural practices, religious beliefs, and social

hierarchies. For example, in Ancient Egypt, the trend of building monumental pyramids was a religious and

cultural expression and a reflection of the society's technological advancements and labor organization. Similarly,

in classical Greece, trends in philosophy, art, and politics were deeply intertwined, influencing the Greek city-

states and laying foundational ideas for Western civilization.

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With the advent of industrialization and globalization, following trends has become increasingly prominent in

consumer culture. Fashion trends, for instance, are now rapidly changing and globally influenced, driven by a

combination of media, technology, and economic factors. Similarly, technology trends, like the rise of

smartphones and social media, have transformed how we communicate, work, and entertain ourselves.

Recently, there has been a growing trend towards sustainability and environmental consciousness. This shift

responds to the global challenges of climate change and resource depletion. Companies are increasingly adopting

'green' practices, and consumers are more mindful of their ecological footprint, reflecting a significant change in

societal values and priorities. The digital age has accelerated trend dissemination and adoption. Trends in digital

technology, like Artificial Intelligence and virtual reality, are rapidly evolving, influencing various aspects of life,

from healthcare to entertainment. Social media has also become a powerful platform for trend propagation,

enabling trends to emerge and spread globally at unprecedented speeds.

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The psychological and social drivers behind following trends are multifaceted and deeply rooted in human

behavior and societal dynamics. Understanding why people follow trends involves delving into aspects of

psychology, sociology, and even evolutionary biology. Some of the key drivers are (1) social belonging and

acceptance, (2) identity and self-expression, (3) status and prestige, (4) fear of missing out (FOMO), (5) novelty

seeking, (6) cognitive conformity (conformity bias or herd-mentality), (7) influence of media and influencers, (8)

economic and marketing strategies.

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https://www.trendfollowing.com/nature-origins-trend-following/

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The implication of “following” is one of reaction, of passivity, instead of an assertive, bold, and discretionary

action.

136

Historical records focus on more sensational stories and prominent figures, such as market manipulators and

famous traders like Daniel Drew, Jay Gould, James A. Patten, and Arthur Cutten. As a result, less is known about

the lesser-known traders, or "followers", who might have been quietly analyzing the markets and potentially

Arguably, one of the first trend followers known in the investment world was the notorious

economist David Ricardo

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. Although he is most known for his contributions to economics,

he laid down his trading maxims, which were (1) cut short your losses, let your profits run on,

and (2) never overtrade or trade too frequently.

Ricardo's success as a trader and his principles, which emphasize discipline, risk management,

and the asymmetrical treatment of gains and losses, align closely with the core tenets of trend-

following. While Ricardo did not use the modern tools and methods of trend followers (such

as technical analysis and computerized systems), his trading philosophy and principles share

a fundamental similarity with the trend-following approach. This is why some consider him an

early, if not the first, proponent of concepts that would later be formalized into trend-

following strategies in the financial markets.

Before the mid-19th century, financial speculation was predominantly an activity for the elite

and a small group of semi-elite trend followers, with the broader public engaging mainly

during financial bubbles. The period following saw a dramatic increase in market participants

and significant shifts in market practices and thought.

138

Although the prominent market players of yesteryears aligned with the trend, they were not

trend followers in the modern sense of the term. However, evidence of trend-following

practices exists from those times. For instance, when Benjamin P. Hutchinson

139

made a

purchase, the phrase "Hutch is buying" quickly spread, prompting others to follow suit.

140

Similarly, in the early 20th century, the prevailing question was "What are the trusts (or pools,

or rings) doing?” and trend followers would mimic their actions. This approach to trend

following, albeit not particularly scientific, still qualifies as such. This highlights the notion that

trend-following has a humble and plebeian origin. It serves as a strategy for those outside the

financial elite to glean trading profits by emulating the elite's moves based on their economic

insights and overcoming their limited knowledge.

In the late 19th century, speculation was widely practiced but needed a solid theoretical

foundation. The need emerged for a method that could objectively analyze market behavior

and price trends over time, leading to the development of Dow Theory

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by Charles H. Dow

(1851-1902) and his business partner Edward Jones in the late 1800s. This theory, expanded

achieving greater success than their more famous counterparts. Despite this, valuable insights can still be gleaned

by examining historical records considering the topic of trend-following.

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David Ricardo (1772-1823) succeeded in the London markets trading stocks and consols (perpetual

government bonds) for over 20 years between the end of the 18th century and the beginning of 19th century,

which allowed him to focus on the field of economics, his primary interest in life.

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https://www.trendfollowing.com/nature-origins-trend-following/

139

https://www.saddleandsirloinportraitfoundation.org/post/benjamin-peters-hutchinson-inducted-by-1920

140

https://www.trendfollowing.com/nature-origins-trend-following/

141

Dow Theory suggests buying at the breakout of an old high and selling at the breakout of an old low, with

additional rules for confirmation and volume.

upon by William Hamilton (Hamilton, 1922) and refined by Robert Rhea (Rhea, 1932) and

Richard Russell (Russell, 1961), laid the groundwork for modern trend-following by defining

bull and bear markets through a series of higher highs and lower lows, respectively.

Dow Theory is the earliest modern expression of an objective trend-following system, setting

precise entry and exit levels for trades. Its principles have been generalized and adapted,

influencing subsequent trend-following methodologies. Due to the lack of computing power,

the theory relied on logical observations rather than mathematical models.

Elliot wave theory, developed by Ralph Nelson Elliot in the 1930s through the contemplation

of the Dow theory, also attempts to describe and explain patterns that evolve naturally in

market prices. Both theories are based on the existence of trends and the importance of the

psychology of the market participants behind those trends.

Significant contributions to developing trend-following methodologies also came from Robert

Prechter, Richard W. Schabacker, Robert D. Edwards

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, and John Magee, whose works

focused on technical patterns and trendlines as tools for identifying market trends. Although

not explicitly labeled as trend-following, these strategies aimed to capitalize on recognizing

trends' beginnings, continuations, and reversals. Frederic Drew Bond, William D. Gann, and

Richard D. Wyckoff emphasized the importance of following market trends and recognized

the role of influential market participants in creating these trends. The evolution of trend-

following strategies was driven by the necessity of adapting to market behaviors, focusing on

technical analysis and pattern recognition to navigate and profit from market movements.

As we have seen, the essential roots of trend-following can be traced back to the early 20th

century. Famous traders like Jesse Livermore (1877-1940) used principles akin to trend-

following. Livermore's trading style, documented in the books Reminiscences of a Stock

Operator (Lefèvre, 1923) and How to Trade in Stocks (Livermore, 1940), emphasized the

importance of following the market's direction, which is a core principle of trend-following.

From this book, some paragraphs show that Livermore appeared to be a breakout trader and

uses the words following the trend.

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Alfred Cowles III and Herbert E. Jones, through their 1937 study at the Cowles Commission

(now Cowles Foundation), demonstrated the existence of serial correlation in stock market

prices, laying the groundwork for trend-following methodologies. Their findings suggested

that markets tend to continue in the direction they were moving, offering a basis for the use

of trend-following trading strategies.

142

Quoting him: “Profits are made by capitalizing on up or down trends, by following them until they are

reversed”.

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The quote is the following: “It may surprise many to know that in my method of trading, when I see by my

records that an upward trend is in progress, I become a buyer as soon as a stock makes a new high on its

movement, after having had a normal reaction. The same applies whenever I take the short side. Why? Because

I am following the trend at the time. My records signal me to go ahead!”

Alfred Winslow Jones, in his 1949 Fortune article, further explored stock forecasting

techniques, underscoring the momentum in psychological trends that underpin trend-

following. Jones's analysis acknowledged the potential for trends to perpetuate beyond

rational values before reversing, influenced by psychological factors and market dynamics.

In the 1950s, William Dunnigan significantly advanced the conceptualization of trend-

following. He differentiated between trap forecasting and continuous forecasting, suggesting

a shift from prediction-based trading to a model that focuses on identifying and acting on the

market signals or trends as they occur. Dunnigan's work, particularly in publications like New

Blueprints for Gains in Stocks and Grains, articulated the essence of trend-following as

leveraging the momentum of current trends without attempting to predict future market

movements.

Richard Donchian, often hailed as the father of trend-following, played a pivotal role in

formalizing this trading approach during the 1940s and 1950s through the development of a

system grounded in moving averages, which would pave the way for modern trend-following

methodologies. His creation of the Donchian Channel, a rules-based system, continues to be

a successful tool for traders today, highlighting his lasting impact on the trading world. As the

innovator behind the managed futures industry, Donchian's systematic approach to futures

money management and his establishment of the first publicly managed futures fund

(Futures, Inc. in 1948), marked a significant advancement in making trend-following a

recognized and viable trading methodology. Further solidifying his contributions in the late

1950s, particularly with his 1957 article, Donchian stressed the critical strategy of limiting

losses while not capping potential gains, and he advocated for holding market positions as

long as the trend continued. His advocacy for a diversified approach in commodities trading

and the development of the 5 – 20 moving average method showcased the practicality and

efficacy of trend-following strategies, underscoring his instrumental role in shaping the

field.

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Founded in the 1960s, Commodities Corporation (now part of Goldman Sachs) was a key

player in developing and popularizing trend-following strategies. Traders like Ed Seykota and

Bruce Kovner, who started their careers there, were instrumental in refining and spreading

trend-following methodologies.

In the 1980s, The Turtles became a famous group in the history of trading, known for an

experiment conducted by two commodity traders, Richard Dennis, and William Eckhardt, to

settle a debate about whether great traders are born with a unique talent or if they can be

trained.

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https://www.trendfollowing.com/whitepaper/donchian-commodities.pdf

Richard Dennis was a highly successful commodity trader known for his trend-following

approach. He believed that trading skills could be taught. William Eckhardt, his long-time

friend and business partner, disagreed, believing that successful trading was innate.

To settle this debate, they decided to conduct an experiment. In 1983, they placed an ad in

The Wall Street Journal and Barron's, looking for applicants to train in the art of trading. From

over 1,000 applicants, they selected a diverse group of 21 people with various backgrounds

but little to no trading experience.

The group, which came to be known as the Turtles

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, was trained for two weeks.

146

The

experiment was a resounding success.

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After the experiment, several turtles went on to have

successful careers in trading, and some started their own trading firms, like Jerry Parker in

Chesapeake Capital Corporation. The methods and rules taught to the Turtles were eventually

made public, influencing generations of traders.

The experiment is a significant part of trading history, highlighting the potential of systematic,

rule-based trading strategies. It provided empirical evidence supporting the concept of trend

following and the idea that disciplined adherence to a set of rules could be more effective

than relying on intuition or fundamental analysis.

The story of the turtle traders remains a foundational lesson in trading circles. It illustrates the

importance of a disciplined, systematic approach to trading and risk management and the

potential for individuals to learn and succeed in the markets with the proper training and

mindset.

Today, trend-following strategies have become a global phenomenon, embraced by traders

and investors across different continents and markets. This widespread adoption is a

testament to the versatility and resilience of trend-following methodologies, which have been

effectively applied not only in traditional equity and commodity markets but also in

currencies, bonds, and emerging market assets. The approach's fundamental appeal lies in its

145

This is a nickname whose origin is a bit of a mystery, but some say it was because Dennis had recently returned

from a trip to Asia and likened the process to a Singapore turtle farm.

146

They were taught a simple trend-following system, which involved buying futures contracts during market

breakouts and selling during downturns. The system had specific rules for when to buy or sell, how much to buy

or sell (based on market volatility), and where to place stop-loss orders. The rules were designed to be

mechanical and emotion-free, focusing on following the market trends, managing risk, and preserving capital.

After training, each turtle was given a trading account. Dennis funded these accounts with his own money, with

initial amounts ranging from $500,000 to $2 million. He closely monitored their performance, ensuring they

adhered to the rules.

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Over the next four years, the turtle traders reportedly earned an aggregate profit of over $100 million, proving

Dennis's theory that trading could be taught.

simplicity and empirical basis: it relies on the observable momentum of market prices,

eschewing complex predictions about future events or economic conditions. As financial

markets have become increasingly interconnected and accessible through technological

advancements, trend-following principles have been adapted and refined to suit diverse

trading environments and instruments. Moreover, the proliferation of data analytics and

computing power has enabled the development of sophisticated trend-following models that

can analyze vast datasets to identify potential trends more accurately and swiftly.

Consequently, trend-following is not just a strategy limited to individual traders but has been

institutionalized by hedge funds, commodity trading advisors (CTAs), and quantitative

investment firms, further cementing its place as a fundamental component of modern

financial strategies on a global scale.

APPENDIX B

RISK AS POSSIBILITY OF LOSS VS. RISK AS VOLATILITY

Definition of Risk

A correct theoretical perspective on risk is crucial to deciding which measures are most

relevant for investment purposes. That, in turn, allows portfolio managers to assess risks and

risk-adjusted returns accurately, make better-informed investment decisions, manage

portfolios effectively, handle the behavioral aspects of investing, and adhere to regulatory and

ethical standards in terms of transparency and accountability.

One common perspective of risk among intellectuals and professionals is viewing it as

volatility. This viewpoint equates risk with unpredictability in the asset's price movements.

Volatility is often measured statistically, for example, through standard deviation or variance

of returns. From this perspective, an investment with high price fluctuations is considered

riskier than one with stable, predictable returns.

However, seeing risk solely in terms of volatility presents a partial and sometimes misleading

view. This approach focuses on price movements without considering the fundamental

reasons behind these fluctuations. Moreover, it implies a symmetric view of risk, where both

upward and downward portfolio movements are treated equally, overlooking that investors

typically view gains more favorably than losses. Consequently, this perspective might

misrepresent the risk involved, especially for long-term investors for whom short-term

volatility might be less relevant.

As Howard Marks pointed out: “Academicians settled on volatility as the proxy for risk as a

matter of convenience. They needed a number for their calculations that was objective and

could be ascertained historically and extrapolated into the future. Volatility fits the bill, and

most of the other types of risk do not. The problem with all of this, however, is that I just don’t

think volatility is the risk most investors care about. Rather than volatility, I think that people

decline to make investments primarily because they’re worried about a loss of capital or an

unacceptably low return. To me, “I need more upside potential because I’m afraid I could lose

money” makes an awful lot more sense than “I need more upside potential because I’m afraid

the price may fluctuate.” No, I’m sure “risk” is -first and foremost-the likelihood of losing

money.

Trend followers view risk from a different perspective than mainstream finance academia. For

them, volatility is just a partial and misleading method to view the risk of a market. This is

because volatility can work in the traders’ favor, not only against them. This is why trend

followers understand risk as the possibility of loss. This means that, as long as you own the

asset, you are at risk, so the best an investor can do is to manage that risk.

Risk Measures

Standard deviation is a widely used statistical measure in Finance to quantify the volatility of

an investment's return over a period of time. It estimates the variability of returns around the

mean (average) return. However, while it is a valuable tool, standard deviation has several

shortcomings

148

as a measure of risk.

All these shortcomings can be extrapolated to the risk-return measures that contain the

standard deviation within their formula, such as the Sharpe Ratio.

Semi-standard deviations and downside deviations only count the volatility on the downside,

which makes them more relevant for calculating the probability of loss. The Sortino Ratio

149

provides a much better picture of the risk of a portfolio, as it does not count the upside

volatility as risk.

148

The shortcomings are the following:

1. Assumption of Normal Distribution: Standard deviation is most effective when an investment's

returns follow a normal (Gaussian) distribution. However, financial market returns often exhibit 'fat tails'

and are not normally distributed. This means extreme price movements are more common than a

normal distribution would predict. Standard deviation may underestimate the likelihood of these

extreme events (like market crashes).

2. Symmetrical Measurement: Standard deviation treats all deviations from the mean above and

below as the same. For investors and traders, however, the concerns are more about downside

deviations (losses) than upside deviations (gains). This symmetry in measurement does not align well

with the asymmetrical nature of investment risks.

3. Focus on Past Data: Standard deviation is a backward-looking measure based on historical data.

It assumes that past volatility will continue, which may not always be accurate. Markets can change

rapidly, making historical volatility an unreliable predictor of future risk.

4. Does Not Account for Extreme Events: Standard deviation may not adequately capture the risk

of rare but catastrophic events, often called "Black Swan" events. These events can significantly impact

trading portfolios but occur so infrequently that they do not significantly affect the standard deviation.

5. Over-simplification of Risk: Risk in trading is multifaceted and can stem from various sources

like market risk, liquidity risk, credit risk, operational risk, etc. Standard deviation primarily measures

market risk and does not account for these other types of risks.

6. Ignores Investment Time Horizon: A trader or investor's perception of an investment's riskiness

can vary based on their investment horizon. Standard deviation does not differentiate between short-

term and long-term risk perspectives.

7. Non-linear Risks: Risks are not linear in some trading strategies, particularly those involving

options or other derivatives. As a linear measure, standard deviation may not accurately capture the

risks inherent in these non-linear instruments.

149

The Sortino Ratio uses the downside deviations of returns below a certain threshold called the minimum

acceptable return (MAR). The MAR depends on the specific requirements, preferences, or objectives of the

investor. Typically, MAR is set at 0%, but in some cases, investors might set the MAR according to their own rate

of return, which could be based on factors such as inflation, the risk-free rate, or a specific target return rate.

“Hedge fund researcher Nicola Meaden (…) found that although trend following arguably

experiences higher volatility, it is often concentrated on the upside (positive returns), not the

downside (negative returns). Trend following performance is thus unfairly penalized by

performance measures such as the Sharpe ratio. The Sharpe ratio ignores whether volatility is

on the plus or minus side because it does not account for the difference between the standard

deviation and the semi-standard deviation. The actual formula is identical, with one exception

-the semi-standard deviation looks only at observations below the mean.” (Covel, 2017).

Being on the right side of a volatile market is what ultimately makes trend followers excel.

Some could think that trend followers are long volatility traders. Although on many occasions

they benefit from a high volatility environment, this is not always the case, as high volatility

can also play against trend following strategies, depending on their positioning.

Because of these limitations aforementioned, traders and investors often complement

standard deviation with other risk measures, such as Value at Risk (VaR), Conditional Value at

Risk (CVaR), maximum drawdown, and skewness/kurtosis analysis, to get a more

comprehensive view of the risks involved in their trading strategies.

A typical trend-follower trader is less concerned about volatility than the average professional

investor. For them, saying that a trader is volatile and thus bad makes little sense if examined

through the lenses of absolute return performance (Covel, 2017). For trend-following,

volatility is the precursor to achieving profit. Without volatility, there is no opportunity for

profit.

An alternative perspective of risk, and often considered more comprehensive, is viewing it as

the possibility of loss. This approach, advocated by investors like Ed Seykota, shifts the focus

from the unpredictability of returns to the potential for an investment to result in a capital

loss. It considers risk in terms of the likelihood and magnitude of a loss rather than just price

fluctuations.

Viewing risk as the possibility of loss aligns more closely with the primary concern of most

investors: the preservation of capital. This perspective encourages investors to consider the

worst-case scenarios and the durability of their investments under adverse conditions. It also

facilitates a more strategic approach to risk management, such as setting stop-loss orders or

diversifying portfolios to mitigate potential losses.

Moreover, this view acknowledges that not all volatility is detrimental; for instance, upward

price movements (positive volatility) in a portfolio favor investors. This perspective provides a

more nuanced and investor-centric understanding of risk by differentiating between desirable

and undesirable market movements.

When considering risk as primarily the possibility of loss rather than just volatility, it's

important to use measures focusing on downside risks and potential losses. Here are some of

the best risk and risk-reward measures for this perspective:

▪ Maximum Drawdown: This is a measure of the largest single drop from peak to trough

in the value of a portfolio before a new peak is attained. Maximum drawdown is an

excellent measure of the worst-case scenario loss an investor might have faced during

a specific period.

▪ Value at Risk (VaR): VaR estimates the maximum potential loss in the value of a

portfolio over a defined period for a given confidence interval. For example, a 5% one-

month VaR of $1 million means there is a 5% chance that the portfolio will lose more

than $1 million over the next month.

▪ Conditional Value at Risk (CVaR): Also known as Expected Shortfall, CVaR goes a step

further than VaR. It looks at the average losses that could occur beyond the VaR

threshold, providing insight into the severity of losses in the worst-case scenarios.

▪ Calmar Ratio: This ratio measures the return of an investment compared to its

maximum drawdown risk. It is calculated by dividing the annualized return by the

maximum drawdown. A higher Calmar Ratio indicates a better risk-adjusted return,

emphasizing how well an investment has performed considering the potential for

significant losses.

▪ Sortino Ratio: Unlike the Sharpe Ratio, which considers overall volatility, the Sortino

Ratio specifically measures performance relative to downside risk. It's calculated by

dividing the portfolio's excess return over the risk-free rate by the downside deviation,

focusing only on negative returns.

▪ Tail Risk Measures: These include statistical measures like skewness and kurtosis,

which help understand the asymmetry and tail heaviness of the return distribution.

Negative skewness indicates a potential for significant negative returns, while high

kurtosis indicates a higher probability of extreme returns (both positive and negative).

▪ Stress Testing and Scenario Analysis: These involve assessing how a portfolio would

perform under various adverse market conditions or specific "stress" scenarios, like

market crashes, interest rate hikes, etc. This helps in understanding the portfolio's

resilience to potential market shocks.

▪ Omega Ratio: This measure compares the probability and size of gains versus losses. It

is defined as the ratio of the probability-weighted gain to the probability-weighted loss

for a given threshold level.

▪ Downside Beta: This beta variation focuses on how a portfolio moves in relation to a

benchmark index during periods when the benchmark's returns are negative, offering

insight into relative downside risk.

Each measure focuses on different aspects of downside risk and potential losses. The choice

of which to use can depend on the specific investment strategy, the type of portfolio being

assessed, and the investor's risk tolerance and objectives. Often, a combination of these

metrics provides a more comprehensive view of downside risks and the risk-reward profile of

an investment or portfolio. In this thesis, we introduced the Koljonen Ratio, which is a

combination of the Sortino Ratio and the Calmar Ratio, which provides an overall measure of

the downside risk of the asset, strategy or portfolio analyzed.

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Master's Degree Program in

Statistics and Information Management

TREND-FOLLOWING STRATEGIES IN CRYPTOCURRENCIES,

OPTIMIZED FOR DOWNSIDE RISK-ADJUSTED RETURNS

Exploring Successful Trend-Following Algorithmic Trading Strategies

with a Deleveraging Mechanism in the Cryptocurrency Markets

Carlos Sakarías Koljonen Caballos

Master Thesis

presented as a partial requirement for obtaining a master’s degree in Statistics and Information Management

NOVA Information Management School

Instituto Superior de Estatística e Gestão de Informação

Universidade Nova de Lisboa

MEGI

NOVA Information Management School

Instituto Superior de Estatística e Gestão de Informação

Universidade Nova de Lisboa

TREND-FOLLOWING STRATEGIES IN CRYPTOCURRENCIES, OPTIMIZED FOR DOWNSIDE

RISK-ADJUSTED RETURNS

Exploring Successful Trend-Following Algorithmic Trading Strategies with a Deleveraging

Mechanism in the Cryptocurrency Markets

Carlos Sakarías Koljonen Caballos

The master's thesis was presented as a partial requirement for obtaining the master’s

degree in Statistics and Information Management, with a specialization in Risk Management.

Supervised by

Prof. Doutor Jorge Miguel Ventura Bravo (PhD)

Universidade Nova de Lisboa & Université Paris-Dauphine PSL

July,

2024

STATEMENT OF INTEGRITY

I hereby declare having conducted this academic work with integrity. I confirm that I have not

used plagiarism or any form of undue use of information or falsification of results along the

process leading to its elaboration. I further declare that I have fully acknowledged the Rules

of Conduct and Code of Honor from the NOVA Information Management School.

In Lisbon, 15/07/2024

DEDICATION

To my future wife

For tirelessly striving to bring out the best in me,

For understanding the importance of freedom in the world.

iii

ACKNOWLEDGMENTS

I would like to extend my deepest gratitude to Professor Jorge M. Bravo for his invaluable

inputs and ideas over the past months. His guidance has been instrumental in shaping this

thesis.

I also wish to express my heartfelt thanks to my friend Clifford D. Roman. Our countless

conversations, whether willingly or unwillingly on his part, have significantly contributed to

the enhancement of this work.

To my future wife, Katia F. Ferreira, I owe a special debt of gratitude for discovering this

master’s program, encouraging me to pursue it, and supporting me every step of the way. I

cannot imagine a better partner to share my life with.

I want to thank my parents for their unwavering support throughout this journey. Their

encouragement and belief in me have been the foundation upon which I have built my

academic and personal successes.

Finally, I would like to acknowledge Javier Milei for reviving my motivation to give the cultural

battle for the libertarian ideas. As Ludwig von Mises used to say: Tu ne cede malis, sed contra

audentior ito.

ABSTRACT

Despite its popularity, trend-following lacks a cohesive theoretical framework, resulting in

fragmented understanding and application. This thesis addresses this gap by integrating

principles from the Austrian School of Economics to provide a structured foundation for trend-

following. It posits two key assumptions: the unpredictability of market movements and the

existence of trends, introducing the theorem of the impossibility of accurate market

predictions based on dispersed human knowledge.

Traditional risk-adjusted metrics like the Sharpe, Sortino, and Calmar Ratios have a different

set of limitations. This thesis proposes the Koljonen Ratio, a novel downside risk-adjusted

return metric that combines drawdown and downside volatility for a more nuanced

evaluation, particularly in cryptocurrency markets.

The study aims to: (1) consolidate trend-following philosophy with Austrian economic theory,

(2) develop a superior downside risk-adjusted return metric, (3) assess traditional trend-

following strategies in cryptocurrency trading, and (4) implement an innovative and

sophisticated trading strategy with a deleveraging mechanism to enhance downside risk-

adjusted returns.

Anticipated contributions include a robust theoretical framework for trend-following,

improved performance evaluation metrics, practical insights into cryptocurrency trading, and

an advanced strategy for better downside risk-adjusted returns. This thesis aspires to advance

both academic research and practical applications in trading strategies.

KEYWORDS

Trend-Following; Austrian School of Economics; Cryptocurrencies; Downside-Risk;

Algorithmic Trading; Koljonen Ratio

Sustainable Development Goals (SDG):

v 
 
TABLE OF CONTENTS 
Statement of Integrity ........................................................................................................ i 
Dedication ......................................................................................................................... ii 
Acknowledgments ............................................................................................................ iii 
Abstract ............................................................................................................................ iv 
List of Figures.................................................................................................................. viii 
List of Tables ..................................................................................................................... ix 
List of Abbreviations and Acronyms.................................................................................. x 
 Introduction .................................................................................................................. 1 
 Trend-Following ............................................................................................................ 3 
1. Foundational Assumptions .................................................................................... 3 
1.1. On the Future’s Unpredictability .................................................................... 4 
1.1.1.  The Theorem of the Impossibility of Socialism .................................... 4 
1.1.2.  The Theorem of the Impossibility of Making Accurate Predictions .... 6 
1.1.3.  Trend-Following as a Philosophy of Reaction and Adaptation ............ 7 
1.2. On the Existence of Trends in Prices .............................................................. 8 
1.2.1.  Static Efficiency vs Dynamic Efficiency ................................................ 9 
1.2.2.  Austrian School of Economics (ASE) .................................................. 11 
1.2.3.  Behavioral Finance ............................................................................. 17 
1.2.4.  Newton’s First Law of Motion............................................................ 18 
2. Principles ............................................................................................................. 19 
2.1. Follow the Trend .......................................................................................... 19 
2.2. Systematic .................................................................................................... 21 
2.3. Directional Flexibility .................................................................................... 23 
2.4. Risk Management ......................................................................................... 24 
2.4.1.  Diversification .................................................................................... 24 
2.4.2.  Portfolio Heat ..................................................................................... 26 
2.4.3.  Stop-Loss ............................................................................................ 26 
2.4.4.  Position Sizing .................................................................................... 27 
2.5. Absolute Returns .......................................................................................... 29 
2.6. Sophisticated Simplicity ............................................................................... 30 
2.7. Emotional Discipline ..................................................................................... 32 
3. Historical Perspectives and Portfolio Properties................................................. 33 
3.1. Historical Perspectives ................................................................................. 33 
3.2. Portfolio Properties ...................................................................................... 36 

vi 
 
3.2.1.  Crisis Alpha ......................................................................................... 36 
3.2.2.  Low Correlation with Traditional Assets ............................................ 37 
3.2.3.  Low Drawdowns ................................................................................. 37 
3.2.4.  Positive Skewness .............................................................................. 38 
3.2.5.  Good Risk-Adjusted Returns .............................................................. 38 
3.2.6.  Good Diversifier ................................................................................. 38 
 Introducing a New Measure of Downside Risk: the Koljonen Ratio .......................... 39 
1. The Sharpe Ratio as a Measure of Risk-Adjusted Returns .................................. 39 
2. The Sortino Ratio as a Measure of Downside Risk-Adjusted Returns ................. 39 
3. The Calmar Ratio as a Measure of Downside Risk-Adjusted Returns ................. 40 
4. Combining Sortino and Calmar Ratios: The Koljonen Ratio ................................ 41 
5. Interpretation ...................................................................................................... 41 
6. Limitations ........................................................................................................... 42 
7. Conclusion ........................................................................................................... 43 
 Methodology .............................................................................................................. 44 
1. General Methodology ......................................................................................... 44 
1.1. Data Sources and Python Libraries Used ..................................................... 44 
1.2. Time Frame and Window ............................................................................. 44 
1.3. Cryptocurrencies and Commissions ............................................................. 44 
1.4. Performance Evaluation ............................................................................... 45 
2. Traditional Trend-Following Strategies Applied to Cryptocurrencies ................. 45 
3. An Ensemble Trend-Following Strategy, Optimized for Downside Risk-Adjusted 
Returns ............................................................................................................................ 46 
3.1. Strategies ...................................................................................................... 46 
3.2. Ensemble Signal Generation ........................................................................ 46 
3.3. Optimization Without a Deleveraging Mechanism ...................................... 47 
3.4. Optimization with a Deleveraging Mechanism ............................................ 47 
3.1. Application of the Kelly Criterion ................................................................. 49 
 Results and Discussion................................................................................................ 50 
1. Traditional Trend-Following Strategies Applied to Cryptocurrencies ................. 50 
1.1. Results .......................................................................................................... 50 
1.1.1.  50/100 Days SMA Crossover Long-Only ............................................ 50 
1.1.2.  20 Days Donchian Channel Long-Only ............................................... 51 
1.1.3.  Daily Heikin-Ashi Candles Long-Only ................................................. 52 
1.1.4.  50/100 Days SMA Crossover Long-Short ........................................... 52 
1.1.5.  20 Days Donchian Channel Long-Short .............................................. 53 

vii 
 
1.1.6.  Daily Heikin-Ashi Candles Long-Short ................................................ 54 
1.2. Discussion ..................................................................................................... 55 
1.2.1.  General Performance Trends ............................................................. 55 
1.2.2.  Key Metrics Analysis .......................................................................... 56 
1.2.3.  Conclusion .......................................................................................... 57 
2. An Ensemble Trend-Following Strategy for Cryptocurrencies, Optimized for Downside 
Risk-Adjusted Returns ..................................................................................................... 57 
2.1. Results .......................................................................................................... 57 
2.1.1.  Ensemble Model Strategy Without a Deleveraging Mechanism ....... 57 
2.1.2.  Ensemble Model Strategy With a Deleveraging Mechanism ............ 58 
2.1.3.  Ensemble Model Strategy With a Deleveraging Mechanism, Including the 
Application of the Kelly Criterion ........................................................................ 59 
2.2. Discussion ..................................................................................................... 60 
2.2.1.  Risk-Adjusted Return Metrics ............................................................ 61 
2.2.2.  Drawdowns Metrics ........................................................................... 62 
2.2.3.  Overall Perspective ............................................................................ 63 
2.2.4.  Conclusion .......................................................................................... 63 
Conclusions and Future Works.................................................................................... 65 
Bibliographical References .............................................................................................. 67 
Appendix A ...................................................................................................................... 71 
Appendix B ...................................................................................................................... 78 
 
 
 
 
 
 
 
 
  