# On Bitcoin Price Prediction
On Bitcoin Price Prediction
Grégory Bournassenko gregory.bournassenko@etu.u-paris.fr
Université Paris Cité
In recent years, cryptocurrencies have attracted growing attention from both private investors and institutions. Among them, Bitcoin stands out for its impressive volatility and widespread influence. This paper explores the predictability of Bitcoinâs price movements, drawing a parallel with traditional financial markets. We examine whether the cryptocurrency market operates under the efficient market hypothesis (EMH) or if inefficiencies still allow opportunities for arbitrage. Our methodology combines theoretical reviews, empirical analyses, machine learning approaches, and time series modeling to assess the extent to which Bitcoinâs price can be predicted. We find that while, in general, the Bitcoin market tends toward efficiency, specific conditions, including information asymmetries and behavioral anomalies, occasionally create exploitable inefficiencies. However, these opportunities remain difficult to systematically identify and leverage. Our findings have implications for both investors and policymakers, particularly regarding the regulation of cryptocurrency brokers and derivatives markets. Contents
1. 1 Introduction
1. 2 The Cryptocurrency Market is Efficient
1. 2.1 Eugene Fama and the Notion of No Arbitrage Opportunities
1. 2.1.1 Efficient Market Hypothesis Adaptation to Cryptocurrencies
1. 2.1.2 Random Walk and Martingale
1. 2.1.3 Cryptocurrencies and Fundamental Value
1. 2.2 From Louis Bachelier to Contemporary Models
1. 2.2.1 Modeling of Traditional Finance
1. 2.2.2 Modeling Crypto-Finance
1. 2.3 Time Series Studies and Analyses
1. 2.3.1 Fundamental Analysis
1. 2.3.2 Chartist / Technical Analysis
1. 2.3.3 Machine Learning
1. 3 The Cryptocurrency Market is Inefficient
1. 3.1 Robert Shiller and the Notion of an Inefficient Market in Terms of Arbitrage
1. 3.1.1 Volatility and Expected Dividends
1. 3.1.2 Behavioral Finance and Market Anomalies
1. 3.1.3 Speculative Bubbles
1. 3.2 Informational Inefficiency
1. 3.2.1 Market Manipulation
1. 3.2.2 Pump & Dump
1. 3.2.3 Natural Language Processing
1. 3.3 Operational Inefficiency
1. 3.3.1 At the Macroscopic Scale
1. 3.3.2 At the Mesoscopic Scale
1. 3.3.3 At the Microscopic Scale
1. 4 Conclusion
1. A isRandomBetter( $\Omega,n,k$ )
1. B isSMABetter( $\Omega,n,r$ )
1. C getHoldReturn(asset)
1. D getSMAReturn(asset, n, r)
1. E getRandomReturn(asset)
1. F getRandomPerc( $\Omega$ )
1. G getAverageAccuracy( $\Omega,n$ )
1. H NLP Trading Bot
List of Figures
1. 1 Introduction
1. 3 $\blacktriangle 9,000\%$ BTC/USD [2014-2022]
1. 2.1 Eugene Fama and the Notion of No Arbitrage Opportunities
1. 6 $\blacktriangle 14,000\%$ DOGE/USD [01/2021-05/2021]
1. 2.1.1 Efficient Market Hypothesis Adaptation to Cryptocurrencies
1. 9 $\blacktriangle 150\%$ BTC/USD [13/06/2017-01/09/2017]
1. 10 $\blacktriangledown 15\%$ BTC/USD [16/01/2018-17/01/2018]
1. 11 $\blacktriangledown 22\%$ BTC/USD [14/04/2021-25/04/2021]
1. 12 Correlation between BTC/USD, GOLD/USD, and S&P500
1. 13 S&P500 over the period available with BTC/USD
1. 14 GOLD/USD over the period available with BTC/USD
1. 2.1.3 Cryptocurrencies and Fundamental Value
1. 2.2.1 Modeling of Traditional Finance
1. 2.2.1 Modeling of Traditional Finance
1. 21 RSI Signals for BTC/USD
1. 22 SAR Signals for BTC/USD
1. 2.3.3 Machine Learning
1. 2.3.3 Machine Learning
1. 27 Results of the ARIMA model
1. 28 Evolution of the S&P500 and dividends
1. 29 Results from the NLP trading bot
List of Tables
1. 1 Results of isRandomBetter( $\Omega,n,k$ )
1. 2 Results of isSMABetter( $\Omega,n,r$ )
1 Introduction
The price of Bitcoin has lost almost 50% of its value since last November, almost as much as Orpeaâs stock value after its scandal. In Orpeaâs case, the correlation is clear with the scandal, but for Bitcoin, such irrational volatility is rather usual.
<details>
<summary>extracted/6391907/images/btc-new.png Details</summary>
### Visual Description
## Candlestick Chart: Price Trend Over Time
### Overview
The image presents a candlestick chart displaying price fluctuations over time, spanning from approximately October 2021 to April 2022. The chart uses a standard candlestick representation, with green candles indicating price increases and red candles indicating price decreases. The y-axis represents price, measured in thousands (k), and the x-axis represents time, with monthly markers.
### Components/Axes
* **X-axis:** Time, labeled with months from Oct 2021 to Apr 2022.
* **Y-axis:** Price, ranging from approximately 30k to 70k. The scale is linear.
* **Candlesticks:** Represent price movement over each time period (likely daily or weekly).
* Green Candlesticks: Open price is lower than the closing price.
* Red Candlesticks: Open price is higher than the closing price.
* **Vertical Lines:** Extend from the top and bottom of each candlestick, representing the high and low prices for that period.
### Detailed Analysis
The chart shows a complex price history.
* **Oct 2021 - Nov 2021:** A strong upward trend is visible. Starting around 45k in early October, the price rises to a peak of approximately 68k in November. The trend is characterized by predominantly green candlesticks.
* **Nov 2021 - Dec 2021:** A significant downward trend begins in November, with the price falling from around 68k to approximately 40k by the end of December. This period is dominated by red candlesticks.
* **Dec 2021 - Jan 2022:** The price experiences some volatility, fluctuating between approximately 40k and 52k. There's a mix of green and red candlesticks, indicating periods of both price increases and decreases.
* **Jan 2022 - Feb 2022:** A continued downward trend, with the price falling from around 45k to a low of approximately 35k in late January/early February.
* **Feb 2022 - Mar 2022:** A recovery period, with the price rising from around 35k to approximately 45k by mid-March.
* **Mar 2022 - Apr 2022:** The price experiences another decline, falling from around 45k to approximately 40k by the end of April. The trend is relatively flat during this period.
Approximate Data Points (reading from the chart, with uncertainty of +/- 1k):
* Oct 2021: Starting around 45k, peaking around 60k.
* Nov 2021: Peak around 68k, ending around 58k.
* Dec 2021: Starting around 58k, ending around 40k.
* Jan 2022: Fluctuating between 40k and 52k, ending around 42k.
* Feb 2022: Falling from 42k to 35k.
* Mar 2022: Rising from 35k to 45k.
* Apr 2022: Falling from 45k to 40k.
### Key Observations
* The chart exhibits significant volatility throughout the period.
* There are clear periods of both upward and downward trends.
* The peak price occurs in November 2021, followed by a substantial decline.
* The price appears to be consolidating around the 40k level in April 2022.
* The price never recovers to the November 2021 peak.
### Interpretation
The candlestick chart illustrates the price history of an asset (likely a cryptocurrency, given the price range) over a six-month period. The data suggests a period of strong growth followed by a significant correction. The subsequent fluctuations indicate a period of market uncertainty and consolidation. The inability to regain the November 2021 peak suggests a shift in market sentiment or the emergence of new resistance levels. The chart could be used to analyze market trends, identify potential trading opportunities, or assess the overall health of the asset. The repeated cycles of increase and decrease suggest a cyclical pattern, though predicting future movements based solely on this data would be speculative. The chart provides a visual representation of price action, allowing for quick identification of key trends and potential turning points.
</details>
Figure 1: $\blacktriangledown 50\%$ BTC/USD [11/2021-02/2022]
<details>
<summary>extracted/6391907/images/orpea-new.png Details</summary>
### Visual Description
\n
## Chart: Time Series Data - Price/Value Over Time
### Overview
The image presents a time series chart displaying a fluctuating value over a period from approximately December 2021 to April 2022. The chart utilizes a candlestick-style representation, with green candles indicating value increases and red candles indicating value decreases. A vertical gray bar demarcates January 2022, visually separating the earlier period from a significant drop in value.
### Components/Axes
* **X-axis:** Represents time, spanning from December 2021 to April 2022. Specific dates are not labeled, but months are indicated.
* **Y-axis:** Represents the value, ranging from approximately 20 to 120. The axis is linearly scaled.
* **Candlesticks:** Green candlesticks represent periods where the closing value was higher than the opening value. Red candlesticks represent periods where the closing value was lower than the opening value. The "wicks" extending above and below the candlesticks indicate the highest and lowest values reached during that period.
* **Color Coding:** Green indicates positive change (increase in value), and red indicates negative change (decrease in value).
### Detailed Analysis
The chart can be divided into two main phases: before and after January 2022.
**Phase 1: December 2021 - January 2022**
* The value fluctuates between approximately 60 and 90.
* The trend is relatively stable, with small green and red candlesticks indicating minor fluctuations.
* Around the end of January 2022, the value begins to decline.
**Phase 2: February 2022 - April 2022**
* A dramatic drop in value occurs in February 2022, falling from approximately 85 to a low of around 30. This is represented by a large red candlestick.
* Following the drop, the value stabilizes between approximately 30 and 45.
* The trend in this phase is relatively flat, with small green and red candlesticks indicating minor fluctuations around the 35-40 range.
* Towards the end of the chart (April 2022), there is a slight downward trend, with the value decreasing from around 40 to approximately 30.
**Approximate Data Points (estimated from visual inspection):**
* **Dec 2021:** Value fluctuates around 75-85.
* **Early Jan 2022:** Value around 80-90.
* **Late Jan 2022:** Value begins to fall from ~85.
* **Feb 2022 (Low):** Approximately 30.
* **Feb 2022 (High):** Approximately 40.
* **March 2022:** Value fluctuates between 35 and 45.
* **April 2022:** Value decreases from ~40 to ~30.
### Key Observations
* **Significant Drop:** The most prominent feature is the substantial drop in value during February 2022.
* **Stabilization:** After the drop, the value stabilizes, suggesting a potential bottoming-out or consolidation phase.
* **Recent Decline:** A slight downward trend is observed in April 2022, potentially indicating a resumption of the downward momentum.
* **Volatility:** The chart shows a period of low volatility in December 2021 and January 2022, followed by a period of high volatility in February 2022.
### Interpretation
The chart likely represents the price or value of an asset (e.g., a stock, cryptocurrency, commodity) over time. The dramatic drop in February 2022 could be attributed to a significant market event, negative news, or a change in investor sentiment. The subsequent stabilization suggests that the market may have found a new equilibrium point after the initial shock. The slight decline in April 2022 could indicate renewed selling pressure or a continuation of the previous downward trend.
The vertical gray bar highlighting January 2022 suggests that this month is a key turning point in the asset's performance. The candlestick representation provides a detailed view of the price fluctuations within each period, allowing for a more nuanced understanding of the market dynamics. The data suggests a period of relative stability followed by a sharp correction and subsequent consolidation, with a potential for further decline. Further investigation would be needed to determine the underlying causes of these movements and to assess the future outlook for the asset.
</details>
Figure 2: $\blacktriangledown 50\%$ ORP [01/2022-03/2022]
The notion of prediction is vague, especially regarding price prediction: isnât price itself the result of agentsâ predictions about the value of an asset? Are we therefore predicting a prediction? For simplicity, we will use the term prediction as defined by American economist Alfred Cowles in his paper [Cowles 3rd, 1933], particularly in the second part, where he analyzes the reliability of "forecasters" on stock market volatility. Bitcoin, for its part, is a decentralized cryptocurrency, created in 2008, based on a "proof of work" mining protocol and a robust transaction system as explained by Satoshi Nakamoto [Nakamoto, 2008].
<details>
<summary>extracted/6391907/images/btc-new2.png Details</summary>
### Visual Description
\n
## Line Chart: Time Series Data
### Overview
The image presents a line chart displaying time series data from 2015 to 2022. The y-axis represents a numerical value, scaled up to approximately 70,000, while the x-axis represents time, with years marked from 2015 to 2022. Two lines are plotted, visually representing two different data series.
### Components/Axes
* **X-axis:** Time (Years: 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022)
* **Y-axis:** Numerical Value (Scale: 0 to approximately 70,000). The scale is linear with gridlines.
* **Line 1:** Green color.
* **Line 2:** Red color.
* **Legend:** No explicit legend is present, but the lines are distinguishable by color.
### Detailed Analysis
The chart shows two time series with similar trends, but differing magnitudes and timing.
**Line 1 (Green):**
* From 2015 to 2017, the line remains relatively flat, fluctuating around a value of approximately 2,000.
* From 2017 to 2018, the line exhibits a steep upward trend, reaching a peak of approximately 12,000.
* From 2018 to 2020, the line declines, fluctuating between approximately 8,000 and 10,000.
* From 2020 to 2021, the line experiences a significant and rapid increase, reaching a peak of approximately 62,000.
* From 2021 to 2022, the line fluctuates significantly, with values ranging from approximately 35,000 to 68,000.
**Line 2 (Red):**
* From 2015 to 2017, the line remains relatively flat, fluctuating around a value of approximately 1,000.
* From 2017 to 2018, the line exhibits a steep upward trend, reaching a peak of approximately 15,000.
* From 2018 to 2020, the line declines, fluctuating between approximately 7,000 and 10,000.
* From 2020 to 2021, the line experiences a significant and rapid increase, reaching a peak of approximately 68,000.
* From 2021 to 2022, the line fluctuates significantly, with values ranging from approximately 38,000 to 65,000.
### Key Observations
* Both lines exhibit a similar pattern of growth, decline, and resurgence.
* Line 2 consistently shows slightly higher values than Line 1, particularly after 2020.
* The period from 2021 to 2022 is characterized by high volatility for both lines.
* The most significant growth occurs between 2020 and 2021 for both series.
### Interpretation
The chart likely represents the growth of two related metrics over time. The similar trends suggest a strong correlation between the two series, potentially indicating that they are influenced by the same underlying factors. The sharp increase in 2020-2021 could be attributed to a specific event or catalyst. The volatility in 2021-2022 might indicate market instability or external factors impacting both metrics. Without knowing what the lines represent, it's difficult to provide a more specific interpretation. However, the data suggests a period of rapid growth followed by increased uncertainty. The consistent difference between the two lines could represent a constant offset or a systematic difference in the underlying processes driving each metric.
</details>
Figure 3: $\blacktriangle 9,000\%$ BTC/USD [2014-2022]
As shown above, Bitcoin has progressively gained success: initially used for anonymous transactions on illegal markets, it became a speculative tool for individuals, and eventually attracted institutional interest, despite limited daily usage [Baur et al., 2015]. Notably, Bitcoinâs underlying technology, Blockchain, was actually invented by researchers Haber and Stornetta [Haber and Stornetta, 1990], not Nakamoto, although Nakamoto was the first to apply it at large scale.
The literature on cryptocurrency prediction remains relatively poor, given the recent emergence of the technology. Virtually no academic papers referenced cryptocurrencies before 2008. Instead, much research focuses on machine learning techniques for cryptocurrency prediction. However, similarities with financial markets exist (closer to forex than stocks due to the monetary nature of cryptocurrencies), a domain extensively studied since the early 1900s. From Louis Bachelierâs Gaussian model [Bachelier, 1900] to Mathieu Rosenbaumâs rough Heston model [Gatheral et al., 2018], and Gordon-Shapiroâs valuation model [Gordon and Shapiro, 1956], numerous theories have been proposed. Yet, debates persist regarding market behavior.
According to Eugene Fama [Fama, 1970], a rational market cannot be systematically beaten. Louis Bachelier [Bachelier, 1900] states, "The determination of these activities depends on an infinite number of factors: therefore, a precise mathematical forecast is absolutely impossible." Nevertheless, Keynes [Keynes, 1937] compared the market to a beauty contest: predicting what the majority will find beautiful, not objective beauty itself. This idea echoes momentum strategies and aligns with Charles Dowâs technical analysis [Brown et al., 1998].
Alternatively, Warren Buffett promotes stock-picking and value investing, diverging from Markowitzâs modern portfolio theory [Steinbach, 2001]. However, Buffettâs method, focusing on selecting promising assets, differs from our study, where the asset (Bitcoin) is preselected. Burton Malkiel [Malkiel, 2003] famously claimed that "a blindfolded monkey throwing darts at a newspaperâs financial pages could perform as well as professional investors," although empirical studies [Pernagallo and Torrisi, 2020] challenge this assertion.
To explore random versus selected portfolios, we define a Python function isRandomBetter( $\Omega,n,k$ ) (code in Appendix A). Results:
| 1 | 141 | 998 | 10 | 10 | 20% | False |
| --- | --- | --- | --- | --- | --- | --- |
| 2 | 141 | 998 | 10 | 20 | 30% | False |
| 3 | 141 | 998 | 20 | 10 | 40% | False |
| 4 | 141 | 998 | 20 | 20 | 30% | False |
| 5 | 141 | 998 | 20 | 30 | 60% | True |
| 6 | 141 | 998 | 30 | 20 | 57% | True |
| 7 | 141 | 998 | 30 | 30 | 47% | False |
| 8 | 141 | 998 | 30 | 10 | 27% | False |
| 9 | 141 | 998 | 10 | 30 | 20% | False |
| 10 | 141 | 998 | 40 | 5 | 25% | False |
Table 1: Results of isRandomBetter( $\Omega,n,k$ )
Choosing a random crypto portfolio in 2021 was not optimal.
We will investigate whether Bitcoin price predictability depends on market efficiency. Given the cryptocurrency marketâs heterogeneity, various scenarios (competitive markets, manipulated markets, rational/irrational agents) are expected.
We will show that, by default, the crypto market tends to be efficient, although inefficiencies sometimes appear, albeit difficult to exploit systematically.
We will address prediction methods under efficient market conditions, focusing on time series analysis and machine learning algorithms. We will also study prediction under inefficiency contexts, emphasizing empirical observations and stylized facts.
Letâs first examine the case when the market is efficient.
2 The Cryptocurrency Market is Efficient
We first assume an efficient market. We will explain the conceptâs origins, assumptions, verify some of them, discuss model evolutions, and their implications for cryptocurrencies. We will also analyze this through machine learning and quantitative techniques, reflecting critically on the results.
2.1 Eugene Fama and the Notion of No Arbitrage Opportunities
We start with Famaâs [Fama, 1970] definition of efficient markets, comparing the US stock market and cryptocurrencies. Famaâs idea implies no arbitrage opportunities. However, as we will see later, arbitrage is relatively common in crypto markets (price differences between brokers).
<details>
<summary>extracted/6391907/images/arb1.png Details</summary>
### Visual Description
\n
## Website Screenshot: KoinKnight Landing Page
### Overview
This is a screenshot of the KoinKnight website landing page, advertising their cryptocurrency arbitrage services. The page features a stylized graphic of laptops displaying charts and data, alongside promotional text and call-to-action buttons. The image does not contain charts or diagrams with quantifiable data, but rather serves as a visual representation of the service offered.
### Components/Axes
The visible elements include:
* **Header:** Contains the KoinKnight logo (top-left), and navigation links: "Pricing", "API Services", "Crypto Analytics", "Refer & Earn", "English" (dropdown), "Sign In", and "Sign Up" (top-right).
* **Main Content:** A large heading "Your personal assistance for cryptocurrency arbitrage", followed by descriptive text.
* **Call-to-Action Buttons:** "Try for free" (green) and "View Demo" (blue).
* **Login Link:** "Already using KoinKnight? Log in"
* **Graphic:** A stylized image of multiple laptops displaying charts and data visualizations.
### Detailed Analysis or Content Details
The text content is as follows:
* **Headline:** "Your personal assistance for cryptocurrency arbitrage"
* **Body Text:** "Find the best trade and arbitrage opportunities using KoinKnightâs powerful algorithm and real-time data exploration tools."
* **Button 1:** "Try for free"
* **Button 2:** "View Demo"
* **Login Link Text:** "Already using KoinKnight? Log in"
* **Navigation Links:** "Pricing", "API Services", "Crypto Analytics", "Refer & Earn", "English" (dropdown), "Sign In", "Sign Up"
The graphic displays several laptop screens. The screens show various chart types, including:
* **Candlestick Charts:** Visible on at least one laptop screen, displaying price fluctuations over time.
* **Grid-like Data Visualization:** One laptop screen shows a grid of blue squares, potentially representing a data matrix or heatmap.
* **Bar Charts:** One laptop screen displays a series of vertical bars, likely representing data comparisons.
* **Line Charts:** One laptop screen displays a line chart with red and green lines.
The charts themselves do not have visible axes labels or numerical values. They are purely illustrative.
### Key Observations
The image is designed to convey the idea of data-driven cryptocurrency trading. The use of multiple screens and various chart types suggests a comprehensive and sophisticated platform. The color scheme is primarily blue and green, which are often associated with technology and finance.
### Interpretation
The image is a marketing asset intended to attract users interested in cryptocurrency arbitrage. It emphasizes the platform's ability to provide real-time data and identify profitable trading opportunities. The lack of specific data points on the charts suggests that the focus is on the *concept* of data analysis rather than presenting actual trading results. The overall message is that KoinKnight simplifies the complex process of cryptocurrency arbitrage through its powerful algorithm and user-friendly interface. The image aims to build trust and confidence by visually representing a technologically advanced and data-driven service. The use of the word "arbitrage" suggests the platform aims to exploit price differences across different exchanges.
</details>
Figure 4: KoinKnight
<details>
<summary>extracted/6391907/images/arb2.png Details</summary>
### Visual Description
\n
## Website Screenshot: Arbitool Promotional Image
### Overview
This is a screenshot of the Arbitool website, a platform for cryptocurrency arbitrage. The image is primarily a promotional graphic designed to highlight the price discrepancies that can occur across different cryptocurrency exchanges. It features a purple background with various graphical elements, including a laptop displaying charts, stacks of coins, and stylized figures working at computers. The overall design is intended to convey a sense of opportunity and technological sophistication.
### Components/Axes
The image contains the following elements:
* **Header:** Contains the Arbitool logo (AT), and a navigation bar with links to: HOME, ABOUT ARBITOOL, TUTORIAL, PRICING, ARBITRAGE COURSE, JOIN OUR COMMUNITY, FAQ's, CONTACT. There are also language selection flags (UK and a red/white flag) and buttons for LOGIN and SIGN UP FREE.
* **Main Content:** A large text block stating "Did you know that the rate of the same cryptocurrency may vary by up to 50% on two different exchanges?". Below this are buttons labeled "TELL ME MORE!" and "TEST IT FOR FREE". A 3D graphic depicting a laptop, stacks of coins, and people working is also present.
* **Footer:** Contains a section promoting "altilly" with its logo, and a live chat bubble stating "We are here! Live chat now." with the text "dissez un message" (French for "send a message").
* **Color Scheme:** Predominantly purple, with accents of blue, green, and gold.
### Detailed Analysis or Content Details
The primary textual content is:
* **Headline:** "Did you know that the rate of the same cryptocurrency may vary by up to 50% on two different exchanges?"
* **Call to Action Buttons:** "TELL ME MORE!" and "TEST IT FOR FREE"
* **Footer Text:** "Trade our token on:"
* **Live Chat:** "We are here! Live chat now."
* **French Text:** "dissez un message" (English translation: "send a message")
* **Navigation Bar Links:** HOME, ABOUT ARBITOOL, TUTORIAL, PRICING, ARBITRAGE COURSE, JOIN OUR COMMUNITY, FAQ's, CONTACT.
* **Buttons:** LOGIN, SIGN UP FREE.
The 3D graphic shows:
* A laptop screen displaying a candlestick chart (likely representing price fluctuations).
* Stacks of coins (gold and silver).
* A dollar sign ($) floating above the coins.
* Stylized figures working at computers.
* A Bitcoin symbol (âż) on the laptop screen.
### Key Observations
The image focuses on the potential for profit through cryptocurrency arbitrage. The "up to 50%" claim is a key selling point, suggesting significant price differences can be exploited. The visual elements (laptop, coins, people) aim to create a sense of a dynamic and profitable trading environment. The inclusion of a live chat feature suggests a focus on customer support. The French text indicates the website may cater to a multilingual audience.
### Interpretation
The image is a marketing tool designed to attract users to the Arbitool platform. It leverages the concept of arbitrage â exploiting price differences in different markets â to highlight the potential for profit in the cryptocurrency space. The claim of "up to 50%" price variation is a strong incentive, but it's important to note that this is likely a maximum value and may not be consistently achievable. The visual elements reinforce the idea of a technologically advanced and profitable trading experience. The presence of a live chat feature suggests a commitment to customer service. The inclusion of French text indicates a potential international target audience. The overall message is that Arbitool provides the tools and information needed to capitalize on price discrepancies in the cryptocurrency market.
</details>
Figure 5: ArbiTool
At a discretionary level, however, arbitrage opportunities are rarely exploitable due to transfer fees and liquidity issues.
2.1.1 Efficient Market Hypothesis Adaptation to Cryptocurrencies
Fama [Fama, 1970] outlined several conditions for market efficiency and its three forms. Letâs check them for crypto markets.
First, agents should be rational. In crypto, this is unlikely. For example, Dogecoin rose by 14,000% mainly due to memes and social media [Chohan, 2021]:
<details>
<summary>extracted/6391907/images/doge-new.png Details</summary>
### Visual Description
## Line Chart: Time Series Data
### Overview
The image presents a line chart displaying time series data from approximately July 2020 to April 2022. The chart shows two distinct lines representing different data series plotted against time. There are two vertical gray bands highlighting specific periods, likely indicating events or periods of interest. The y-axis represents a value ranging from 0 to 0.7, while the x-axis represents time, with labels for July 2020, October 2020, January 2021, April 2021, July 2021, October 2021, January 2022, and April 2022.
### Components/Axes
* **X-axis:** Time, labeled with months and years from July 2020 to April 2022.
* **Y-axis:** Value, ranging from 0 to 0.7, with increments of 0.1.
* **Line 1 (Red):** Represents one data series.
* **Line 2 (Green):** Represents another data series.
* **Vertical Bands (Gray):** Two vertical bands are present, one spanning approximately from March 2021 to May 2021, and another from September 2021 to November 2021. These bands likely highlight periods of significant change or events.
* **No Legend:** There is no explicit legend identifying what the red and green lines represent.
### Detailed Analysis
**Line 1 (Red):**
The red line starts at approximately 0 in July 2020 and remains relatively flat until around January 2021. From January 2021, the line begins to increase, showing a steep upward trend until approximately April 2021, reaching a peak value of around 0.6. Following the peak, the line experiences a sharp decline, returning to a value of approximately 0.2 by July 2021. After July 2021, the line fluctuates, generally trending downwards, reaching a value of approximately 0.1 by April 2022.
* July 2020: ~0
* October 2020: ~0
* January 2021: ~0.02
* April 2021: ~0.6
* July 2021: ~0.2
* October 2021: ~0.25
* January 2022: ~0.15
* April 2022: ~0.1
**Line 2 (Green):**
The green line also starts at approximately 0 in July 2020 and remains flat until around January 2021. It then exhibits a similar upward trend to the red line, peaking around April 2021 at a value of approximately 0.7. The green line also experiences a sharp decline after April 2021, but its decline is more pronounced than the red line, reaching a value of around 0.15 by July 2021. From July 2021 to April 2022, the green line fluctuates, generally trending downwards, and ending at approximately 0.1.
* July 2020: ~0
* October 2020: ~0
* January 2021: ~0.01
* April 2021: ~0.7
* July 2021: ~0.15
* October 2021: ~0.2
* January 2022: ~0.12
* April 2022: ~0.1
### Key Observations
* Both lines exhibit a similar pattern of increase and decrease, peaking around April 2021.
* The green line shows a more dramatic decline after the peak in April 2021 compared to the red line.
* The vertical gray bands highlight periods of significant volatility or change in both data series.
* Both lines converge towards a value of approximately 0.1 by April 2022.
### Interpretation
The chart likely represents the performance of two related assets or metrics over time. The initial flat period suggests a period of stability, followed by a period of growth leading up to April 2021. The subsequent sharp decline could indicate a market correction, a significant event, or a change in underlying conditions. The gray bands likely mark periods where these events occurred. The convergence of the lines towards the end of the period suggests a stabilization or a shared trend. Without knowing what the lines represent, it's difficult to provide a more specific interpretation. However, the data suggests a period of growth, followed by a correction, and eventual stabilization. The differing magnitudes of the decline between the two lines suggest that the two assets or metrics were affected differently by the event causing the decline.
</details>
Figure 6: $\blacktriangle 14,000\%$ DOGE/USD [01/2021-05/2021]
Individuals should not influence the market. Elon Musk, however, can shift prices with a single tweet:
<details>
<summary>extracted/6391907/images/musk1.png Details</summary>
### Visual Description
\n
## Screenshot: Elon Musk Tweet Regarding Bitcoin
### Overview
This is a screenshot of a tweet posted by Elon Musk (@elonmusk) on Twitter. The tweet features a meme about a breakup, referencing Linkin Park and implicitly commenting on the value/status of Bitcoin. The tweet includes engagement metrics (retweets, quotes, likes).
### Components/Axes
* **User Information:** Elon Musk (@elonmusk) with profile picture.
* **Hashtag:** #Bitcoin âż â€ïž
* **Text Dialogue:** A conversation between "Her" and "Him".
* **Image:** A stock photo depicting a couple sitting on a couch with a strained expression.
* **Attribution:** "made with mematic"
* **Timestamp:** 3:07 AM · 4 juin 2021 · Twitter for iPhone
* **Engagement Metrics:**
* Retweets: 21,1k
* Quotes: 9,986 (Tweets cités)
* Likes: 210,1k
* **Twitter Icons:** Retweet, Quote, Like, and Upload icons.
### Detailed Analysis or Content Details
The tweet's central element is a meme consisting of a dialogue:
* **Her:** "I know I said it would be over between us if you quoted another Linkin Park song but I've found someone else."
* **Him:** "So in the end it didn't even matter?"
The image accompanying the text shows a woman in a pink dress and a man in a grey sweater sitting on a grey couch, both looking away from each other with arms crossed. The image conveys a sense of emotional distance and a breakup.
The tweet is tagged with "#Bitcoin âż â€ïž", suggesting a connection between the breakup meme and the cryptocurrency. The Bitcoin symbol (âż) is included alongside a red heart emoji (â€ïž).
The timestamp indicates the tweet was posted at 3:07 AM on June 4, 2021, using Twitter for iPhone.
The engagement metrics show:
* 21,100 retweets (approximately)
* 9,986 quoted tweets (approximately) - labeled as "Tweets cités" in French.
* 210,100 likes (approximately)
### Key Observations
* The use of a breakup meme with a reference to Linkin Park is a somewhat cryptic commentary on Bitcoin. Musk has previously referenced Linkin Park in tweets related to Dogecoin, another cryptocurrency.
* The red heart emoji alongside the Bitcoin symbol could be interpreted as a sign of affection or a lament for the cryptocurrency's performance.
* The high engagement metrics (retweets, quotes, likes) indicate the tweet generated significant interest and discussion.
* The tweet is in English, with the exception of the "Tweets cités" label, which is in French. "Tweets cités" translates to "Quoted Tweets" in English.
### Interpretation
This tweet appears to be a playful, yet potentially critical, commentary on the volatility and perceived fickleness of the cryptocurrency market, specifically Bitcoin. Musk is likely drawing a parallel between the emotional turmoil of a breakup and the fluctuating value of Bitcoin. The Linkin Park reference is a recurring motif in his crypto-related tweets, possibly signifying a sense of irony or disillusionment. The meme format suggests a lighthearted approach, but the underlying message could be a warning about the risks associated with investing in cryptocurrencies. The high engagement suggests the audience understood and responded to the implied message. The tweet is a form of social commentary, leveraging humor and pop culture references to express a complex sentiment about Bitcoin. It's a demonstration of how social media can be used to influence public perception of financial markets.
</details>
Figure 7: Negative tweet on 04/06/2021
<details>
<summary>extracted/6391907/images/btc-new3.png Details</summary>
### Visual Description
\n
## Chart: Candlestick Chart - Price Fluctuations Over Time
### Overview
The image presents a candlestick chart displaying price fluctuations over a period from May 26, 2021, to June 16, 2021. Each candlestick represents the price movement for a single period (likely a day). The chart shows open, high, low, and closing prices. A vertical line is present around June 7th, visually separating the chart into two sections.
### Components/Axes
* **X-axis:** Represents time, with dates ranging from May 26, 2021, to June 16, 2021. The dates are spaced relatively evenly.
* **Y-axis:** Represents price, with a scale ranging from approximately 25,000 to 45,000. The scale is linear.
* **Candlesticks:** Each candlestick consists of a body and wicks.
* **Green Candlesticks:** Indicate that the closing price was higher than the opening price.
* **Red Candlesticks:** Indicate that the closing price was lower than the opening price.
* **Wicks:** Represent the high and low prices for the period. The upper wick extends to the highest price, and the lower wick extends to the lowest price.
* **Vertical Line:** A solid black vertical line is positioned around June 7th, potentially marking a significant event or period change.
### Detailed Analysis
The chart consists of a series of candlesticks. Here's a breakdown of the price movements, reading from left to right:
* **May 26 - May 29:** Initial period shows a red candlestick followed by a green candlestick, then another red candlestick.
* May 26: Red candlestick, opening around 39,000, closing around 37,500.
* May 29: Green candlestick, opening around 35,000, closing around 37,000.
* **May 29 - June 1:** A red candlestick followed by a green candlestick.
* June 1: Green candlestick, opening around 35,000, closing around 38,000.
* **June 1 - June 4:** A red candlestick followed by a green candlestick.
* June 4: Red candlestick, opening around 38,000, closing around 35,000.
* **June 4 - June 7:** A series of green and red candlesticks.
* June 7: A significant red candlestick, opening around 35,000, closing around 32,000.
* **June 7 - June 10:** A green candlestick followed by a red candlestick.
* June 10: Red candlestick, opening around 35,000, closing around 33,000.
* **June 10 - June 13:** A series of green and red candlesticks.
* June 13: Green candlestick, opening around 35,000, closing around 40,000.
* **June 13 - June 16:** A red candlestick followed by a green candlestick.
* June 16: Red candlestick, opening around 40,000, closing around 37,000.
The wicks vary in length, indicating the range of price fluctuations within each period. The longest wicks appear around June 7th, suggesting high volatility.
### Key Observations
* **Volatility:** The chart shows periods of high and low volatility, indicated by the length of the wicks.
* **Trend Change:** The vertical line around June 7th appears to coincide with a significant downward price movement, potentially indicating a trend change.
* **Price Range:** The price fluctuates between approximately 32,000 and 40,000 throughout the period.
* **Outlier:** The red candlestick around June 7th is notably larger than most other candlesticks, suggesting a significant price drop.
### Interpretation
The candlestick chart illustrates the price movements of an asset over a roughly three-week period in May/June 2021. The initial period shows some fluctuation, but the price generally remains within a relatively stable range. The vertical line around June 7th marks a potential turning point, with a sharp price decline followed by a period of recovery. The subsequent fluctuations suggest continued volatility, but the price remains within a narrower range than before the June 7th drop.
The chart suggests a bearish trend following the event around June 7th, although the price does show some recovery towards the end of the period. The large red candlestick on June 7th could represent a significant negative event or market correction. The overall pattern suggests a period of uncertainty and volatility, with the price struggling to establish a clear trend. The chart is a visual representation of price action, and further analysis would be needed to determine the underlying causes of these movements.
</details>
Figure 8: Observed correlation: $\blacktriangledown 15\%$ BTC/USD [04/06/2021-08/06/2021]
No information asymmetry should exist. Yet, insider knowledge (e.g., hacks) creates advantages [Biais et al., 2020].
Information should be free. For crypto, public data is widely available, though high-frequency trading data is costly [Grossman and Stiglitz, 1976].
Taxes should be low. Given international diversity, this varies.
Regarding efficiency forms:
Strong form: all public and private info is priced. However, events like Binanceâs launch in 2017 or the Bitconnect scandal in 2018 show that insiders could have benefited:
<details>
<summary>extracted/6391907/images/btc-new4.png Details</summary>
### Visual Description
\n
## Chart: Financial Time Series (Candlestick Chart)
### Overview
The image presents a candlestick chart depicting a financial time series, likely stock prices or a similar asset, over a period from June 11, 2017, to approximately October 1, 2017. The chart displays daily fluctuations with "candles" representing the open, high, low, and close prices for each day. Green candles indicate a closing price higher than the opening price, while red candles indicate the opposite.
### Components/Axes
* **X-axis:** Represents time, with dates marked approximately every two weeks from June 11, 2017, to October 1, 2017. Specific dates marked are: Jun 11, Jun 25, Jul 9, Jul 23, Aug 6, Aug 20, Sep 3, Sep 17, and Oct 1.
* **Y-axis:** Represents price, ranging from approximately 1000 to 7000. The scale is linear and evenly spaced.
* **Candlesticks:** Each candlestick represents a single day's trading activity.
* **Body:** The rectangular portion of the candle shows the range between the opening and closing prices.
* **Wicks (Shadows):** The thin lines extending above and below the body represent the highest and lowest prices reached during the day.
* **Color Coding:**
* Green: Closing price > Opening price (Bullish)
* Red: Closing price < Opening price (Bearish)
### Detailed Analysis
The chart shows a generally upward trend over the period, with significant volatility.
* **June 11 - July 9:** The price fluctuates between approximately 2000 and 3000, with a slight downward trend initially, followed by consolidation. There are alternating green and red candles, indicating frequent price swings.
* **July 9 - Aug 6:** A clear upward trend begins, with the price steadily increasing from around 2000 to approximately 4000. Predominantly green candles are observed during this period.
* **Aug 6 - Sep 3:** The price continues to rise, reaching a peak of around 4900. The trend is less consistent than the previous period, with more red candles interspersed.
* **Sep 3 - Sep 17:** A significant price drop occurs, with the price falling from approximately 4900 to around 3600. This is characterized by a series of large red candles.
* **Sep 17 - Oct 1:** The price recovers somewhat, rising from around 3600 to approximately 5300. The final days show a strong upward trend with large green candles.
**Approximate Data Points (based on visual estimation):**
| Date | Open | Close |
|----------|-------|-------|
| Jun 11 | ~2800 | ~2800 |
| Jun 25 | ~2600 | ~2800 |
| Jul 9 | ~2200 | ~2400 |
| Jul 23 | ~2800 | ~3000 |
| Aug 6 | ~3500 | ~3800 |
| Aug 20 | ~4200 | ~4300 |
| Sep 3 | ~4600 | ~4800 |
| Sep 17 | ~3800 | ~3600 |
| Oct 1 | ~4800 | ~5300 |
It's important to note that these are approximate values read from the chart and may not be precise.
### Key Observations
* **Volatility:** The chart exhibits significant price volatility throughout the period.
* **Major Downturn:** The period between September 3rd and September 17th shows a substantial price decline.
* **Strong Recovery:** The price experiences a strong recovery in the final week of the observed period.
* **Overall Upward Trend:** Despite the volatility and downturn, the overall trend is upward from June to October.
### Interpretation
The chart suggests a period of growth and volatility in the asset's price. The initial upward trend from July to August indicates positive market sentiment. The sharp decline in September could be attributed to a negative event or market correction. The subsequent recovery in late September and early October suggests renewed investor confidence or a rebound effect. The large green candles at the end of the period indicate strong buying pressure.
The candlestick pattern provides insights into the daily price action, revealing the range of price fluctuations and the balance between buyers and sellers. The alternating green and red candles demonstrate the dynamic nature of the market. The overall upward trend suggests a generally bullish outlook for the asset, but the volatility highlights the inherent risks involved in trading. The chart could be used to identify potential entry and exit points for traders, but further analysis and consideration of external factors would be necessary for informed decision-making.
</details>
Figure 9: $\blacktriangle 150\%$ BTC/USD [13/06/2017-01/09/2017]
<details>
<summary>extracted/6391907/images/btc-new5.png Details</summary>
### Visual Description
## Candlestick Chart: Bitcoin Price Trend (Dec 2017 - Mar 2018)
### Overview
The image displays a candlestick chart representing the price trend of Bitcoin (likely BTC/USD) from approximately December 10th, 2017, to March 4th, 2018. The chart shows a significant decline in price over this period, starting from a high around 20,000 and falling to approximately 8,000. The chart uses the standard candlestick representation, with green candles indicating price increases and red candles indicating price decreases.
### Components/Axes
* **X-axis:** Represents time, spanning from December 10th, 2017, to March 4th, 2018. Key dates marked are: Dec 10, Dec 24, Jan 7 (2018), Jan 21, Feb 4, Feb 18, and Mar 4.
* **Y-axis:** Represents price, ranging from approximately 4,000 to 22,000 (units not explicitly stated, but assumed to be USD). The scale is linear, with increments of 2,000.
* **Candlesticks:** Each candlestick represents the price movement over a specific time interval (likely daily, but not explicitly stated).
* **Green Candlestick:** Indicates the closing price was higher than the opening price.
* **Red Candlestick:** Indicates the closing price was lower than the opening price.
* **Wicks/Shadows:** The thin lines extending above and below the candlestick body represent the highest and lowest prices reached during that time interval.
* **Vertical Gray Bars:** Two vertical gray bars are present, marking Jan 7 and Jan 21, 2018. Their purpose is not immediately clear, but they may indicate significant events or periods.
### Detailed Analysis
The chart can be divided into three main phases:
1. **December 10th - January 7th (2018):** The price fluctuates between approximately 12,000 and 20,000. There's a general downward trend, but with significant volatility.
* Around Dec 17th: Price is approximately 19,000.
* Around Dec 24th: Price is approximately 16,000.
* Around Jan 7th: Price is approximately 14,000.
2. **January 7th - February 4th (2018):** A steep and rapid decline in price. The price falls from around 14,000 to approximately 6,000.
* Around Jan 21st: Price is approximately 10,000.
* Around Feb 4th: Price is approximately 6,000.
3. **February 4th - March 4th (2018):** The price stabilizes somewhat, fluctuating between approximately 6,000 and 11,000. There's a slight upward trend, but it doesn't recover the losses from the previous phase.
* Around Feb 18th: Price is approximately 9,000.
* Around Mar 4th: Price is approximately 8,000.
It's difficult to provide precise numerical values for each candlestick without higher resolution. However, the general trends are clear.
### Key Observations
* **Significant Downtrend:** The most prominent feature is the dramatic price decline from December 2017 to February 2018.
* **Volatility:** The price exhibits high volatility, especially in the early part of the period (December 2017 - January 2018).
* **Recovery Attempt:** There's a slight recovery attempt in February and March 2018, but it's insufficient to reverse the overall downward trend.
* **Gray Bar Significance:** The vertical gray bars at Jan 7 and Jan 21 may indicate specific events that triggered price movements, but this is speculative without additional context.
### Interpretation
The chart illustrates a major correction in the Bitcoin price following a period of rapid growth in late 2017. The steep decline suggests a significant loss of investor confidence or a market correction after a speculative bubble. The stabilization in February/March 2018 could indicate a bottoming-out process, but the price remains significantly lower than its peak in December 2017. The gray bars could represent news events, exchange issues, or regulatory announcements that impacted the market. The candlestick patterns themselves (long red bodies, short green bodies) suggest strong selling pressure during the downturn and limited buying pressure during the recovery attempts. The chart provides a visual representation of a bear market in Bitcoin during this period.
</details>
Figure 10: $\blacktriangledown 15\%$ BTC/USD [16/01/2018-17/01/2018]
Semi-strong form: all public info is priced. The crypto market reacts quickly to news, as seen with Coinbaseâs NASDAQ listing:
<details>
<summary>extracted/6391907/images/btc-new6.png Details</summary>
### Visual Description
## Candlestick Chart: Financial Time Series (Approx. March 14 - May 23, 2021)
### Overview
The image presents a candlestick chart displaying a financial time series, likely representing stock prices or another asset value, over a period from approximately March 14, 2021, to May 23, 2021. The chart uses the standard candlestick representation where the body shows the open and close prices, and the wicks (or shadows) indicate the high and low prices for each period.
### Components/Axes
* **X-axis:** Represents time, with approximate dates marked as: Mar 14, Mar 28, Apr 11, Apr 25, May 9, and May 23, 2021.
* **Y-axis:** Represents the value of the asset, ranging from approximately 50,000 to 65,000. The scale is linear.
* **Candlesticks:** Each candlestick represents a single time period (likely a day).
* **Green Candlesticks:** Indicate that the closing price was higher than the opening price (positive change).
* **Red Candlesticks:** Indicate that the closing price was lower than the opening price (negative change).
* **Wicks:** The thin lines extending above and below the candlestick bodies represent the highest and lowest prices reached during that period.
* **Gridlines:** Horizontal gridlines assist in reading the values on the Y-axis.
* **Vertical Lines:** Vertical lines are present at the dates Mar 28, Apr 11, Apr 25, and May 9, potentially marking significant events or periods.
### Detailed Analysis
The chart shows a fluctuating trend over the observed period.
* **Mar 14 - Mar 28:** The price starts around 55,000 and exhibits volatility, with both green and red candlesticks. The trend is generally upward, reaching approximately 60,000 by Mar 28.
* **Mar 28 - Apr 11:** The price continues to rise, peaking around 63,000-64,000 on Apr 11. This period is characterized by predominantly green candlesticks.
* **Apr 11 - Apr 25:** A significant downward trend begins, with a series of red candlesticks. The price drops sharply from around 64,000 to approximately 51,000 by Apr 25.
* **Apr 25 - May 9:** The price recovers somewhat, with a mix of green and red candlesticks, reaching around 58,000 by May 9.
* **May 9 - May 23:** Another downward trend emerges, with the price falling to approximately 50,000-51,000 by May 23. This period is dominated by red candlesticks.
**Approximate Data Points (Open, High, Low, Close):**
Due to the resolution of the image, precise values are difficult to determine. The following are approximate estimations:
* **Mar 14:** Open: 55,500, High: 56,500, Low: 54,500, Close: 56,000 (Green)
* **Mar 28:** Open: 58,000, High: 60,000, Low: 57,500, Close: 59,500 (Green)
* **Apr 11:** Open: 61,000, High: 64,000, Low: 60,500, Close: 63,500 (Green)
* **Apr 25:** Open: 61,000, High: 62,000, Low: 50,500, Close: 51,000 (Red)
* **May 9:** Open: 54,000, High: 58,000, Low: 53,500, Close: 57,000 (Green)
* **May 23:** Open: 55,000, High: 56,000, Low: 50,000, Close: 50,500 (Red)
### Key Observations
* **Volatility:** The chart demonstrates significant price volatility throughout the period.
* **Major Downtrend:** The period between Apr 11 and Apr 25 shows a particularly steep decline.
* **Recovery Attempts:** There are attempts at recovery between Apr 25 and May 9, but these are not sustained.
* **Final Decline:** The price ends the period with another downward trend, suggesting continued bearish sentiment.
### Interpretation
The candlestick chart illustrates a period of fluctuating asset value with a clear overall downward trend. The initial rise from March to April suggests bullish momentum, but this is abruptly reversed in late April, leading to a substantial price drop. The subsequent recovery attempts are weak, and the final decline indicates that the bearish sentiment has regained control. The vertical lines may represent significant news events or market corrections that triggered these price movements. The chart suggests a shift in market sentiment from positive to negative during the observed period. The data suggests a potential for continued downward pressure on the asset's price, but further analysis would be needed to confirm this trend. The chart is a visual representation of price action, and the candlestick patterns provide insights into the buying and selling pressure at different points in time.
</details>
Figure 11: $\blacktriangledown 22\%$ BTC/USD [14/04/2021-25/04/2021]
The day before its IPO, BTC/USD increased by almost 7%, before losing more than 20% ten days later. The weak form assumes that all historical price information is already reflected in the current price. This form challenges technical analysis, which specializes precisely in analyzing past returns. These analyses are widely shared on social media, due to their ease of implementation, and attract a (too?) proselytizing community. The idea is to use indicators mainly based on past fluctuations to make future predictions. Among the usual indicators (according to the TA-Lib library, considered a reference) are: RSI (Relative Strength Index), SMA (Simple Moving Average), BBANDS (Bollinger Bands). Let us check, for example, whether a "mean-reversion" strategy would be more effective than a simple "hold" (buy-sell only once) and more effective than a random strategy by backtesting these strategies on 2021. If not, we could conjecture that, over the entire year of 2021, it was useless to use a "mean-reversion" strategy (which assumes that when the current price is too "far" from the moving average (SMA), the price will return to its "mean")). This may also give us an indication about the market efficiency form.
We will base our analysis on a set $\Omega$ of crypto-assets. For each element in $\Omega$ , we will test three strategies: mean-reversion, hold, and random. We assume short-selling is allowed. Let $P_{t}$ be the price at time $t$ , $M_{t}(n)$ the moving average at time $t$ with a window of $n$ days, $\omega_{i}$ the $i^{th}$ element of $\Omega$ , and $râ[0,100]$ a percentage around $M_{t}(n)$ indicating the threshold at which we open/close a position. The mean-reversion strategy will be constructed as follows: if $P_{t}>M_{t}(n)+(\frac{M_{t}(n)Ă r}{100})$ , then sell $\omega_{i}$ at price $P_{t}$ ; if $P_{t}<M_{t}(n)-(\frac{M_{t}(n)Ă r}{100})$ , then buy $\omega_{i}$ at price $P_{t}$ , with $t$ ranging from [01/01/2021, 31/12/2021].
The hold strategy will be constructed as follows: if $t=01/01/2021$ , then buy $\omega_{i}$ at price $P_{t}$ ; if $t=31/12/2021$ , then sell $\omega_{i}$ at price $P_{t}$ .
The random strategy will be constructed as follows: generate a signal $Sâ[\text{buy, sell, hold}]$ with $P(S=\text{buy})=P(S=\text{sell})=P(S=\text{hold})=\frac{1}{3}$ . For each $\omega_{i}$ and for each $t$ , if $S=\text{"buy"}$ we buy $\omega_{i}$ at price $P_{t}$ , if $S=\text{"sell"}$ we sell $\omega_{i}$ at price $P_{t}$ , if $S=\text{"hold"}$ we do nothing.
Thus, we create a Python function isSMABetter( $\Omega,n,r$ ) that takes as parameters $\Omega$ (the set of crypto-assets), $r$ (the percentage for the SMA thresholds), and $n$ (the window size in days for the SMA), and returns True if the average SMA returns of $\omega_{i}$ are greater than the average returns of the hold strategy and (strictly) the random strategy in at least 50% of the cases, and False otherwise.
We only consider daily returns. Indeed, how could we backtest a strategy that only opens positions? We thus place ourselves in a short-term trading scale for each trade, which is consistent with the chartist approach (otherwise, we would prefer a passive investment strategy that requires almost no analysis).
The results of isSMABetter( $\Omega,n,r$ ), whose code is in Appendix B, are as follows:
| 116 | 1179 | -484 | -4 | 50 | 20 | 0.00 | False |
| --- | --- | --- | --- | --- | --- | --- | --- |
Table 2: Results of isSMABetter( $\Omega,n,r$ )
It appears that in 2021, among the 116 crypto-assets tested, it was more optimal to have a passive strategy or, at worst, a random strategy, rather than using the moving average in an attempt to generate profits with a day-trading approach (speculation aiming to make a profit within the same day of a market order execution), since the average return obtained with the SMA strategy was the lowest among the three (-484%), and strictly no crypto-asset (0%) showed any interest in being traded with an SMA strategy.
We can conjecture that the cryptocurrency market efficiency form is at least weak, and possibly semi-strong, depending on the crypto-assets and periods, but hardly strong.
2.1.2 Random Walk and Martingale
In almost all the literature ([Lardic and Mignon, 2006], [Jovanovic, 2009] âŠ), a random walk is modeled by two elements: the previous observation and white noise. The literature explains that a price can be modeled as: $P_{t+1}=P_{t}+\varepsilon_{t+1}$ , with $\varepsilon=\{\varepsilon_{t},tâ N\}$ being white noise. This implies that the best (and only) way to predict the price of an asset is by using its current price.
We will perform a Dickey-Fuller test [Dickey and Fuller, 1979] on each element of a set of assets $\Omega$ with a significance level of $\alpha=5\%$ . We define a Python function getRandomPerc( $\Omega$ ) that takes as input a set of crypto-assets $\Omega$ and returns the percentage of assets in that set that appear to follow a random walk, that is, for which we do not reject the null hypothesis "the time series is non-stationary". The result of getRandomPerc( $\Omega$ ), whose code is provided in Appendix F, returns 69 %. It seems that more than half of the cryptocurrencies follow a random walk.
There is often confusion between efficiency and random walk. Indeed, when reading the Wikipedia page on the efficient market hypothesis, one might think that an efficient market necessarily implies prices following a random walk. However, this is false. The market is not necessarily inefficient if prices do not follow a random walk because, as [Lardic and Mignon, 2006] states, "It suffices, for example, that the hypothesis of risk neutrality is not satisfied, or that individualsâ utility functions are not separable and additive [LeRoy, 1982], meaning that it is impossible to separate consumption and investment decisions."
Many studies show that cryptocurrencies (most studies focus on Bitcoin) do not follow a random walk ([Palamalai et al., 2021], [Aggarwal, 2019] âŠ). However, these studies mainly rely on the very restrictive assumption of autocorrelation, and conclude that the Bitcoin market is not efficient. Samuelson [Samuelson, 2016] already addressed this problem in his time and proposed a modification to the random walk hypothesis: the martingale model.
This model is less restrictive than the random walk model because it imposes no condition on the autocorrelation of residuals. Very similar to the previous model, a price process $P_{t}$ follows a martingale if: $E[P_{t+1}|I_{t}]=P_{t}$ , where $P_{t}$ is the price at time $t$ and $I_{t}$ is the information set at time $t$ . Thus, under the martingale model, the current price is the sole (and best) predictor of the next price, even if there are successive dependencies in returns.
As previously noted, an analysis of most cryptocurrencies (the most widely used) shows that the returns of more than half of the assets seem to follow a random walk. With the martingale model, one might be tempted to assert that the crypto market is efficient.
However, many studies have investigated the relationship between Bitcoin and the martingale model ([Zargar and Kumar, 2019], [Nadarajah and Chu, 2017] âŠ) and conclude that the Bitcoin market is not efficient, mainly due to endogenous factors of an emerging and immature market, and the absence of traders relying on fundamental value.
It is difficult to extend this conclusion to the entire cryptocurrency market. However, we know that a study showing market inefficiency between 2012 and 2015 is not highly relevant for 2022, as much has happened since then (especially for Bitcoin).
Thus, we highlight the application of Loâs adaptive market hypothesis [Lo, 2004] to Bitcoin through a study [Khuntia and Pattanayak, 2018], which explains that efficiency improves over time. This study particularly well summarizes the evolution of crypto market returns: episodes of efficiency and inefficiency, creating opportunities for arbitrage and above-average returns, but an impossibility to predict these opportunities systematically or mathematically.
2.1.3 Cryptocurrencies and Fundamental Value
As explained by [Delcey et al., 2017], there are two definitions of an efficient market. Famaâs definition implies that the randomness of a price is explained by the fact that prices converge toward the fundamental value. Samuelsonâs definition implies that unpredictable price variations are simply the result of competition among investors, regardless of fundamental value. This raises the following question: What is a fundamental value for a cryptocurrency?
According to [Biais et al., 2020], the fundamental value of Bitcoin (and by extension most other cryptocurrencies, as they hardly differ in their characteristics) lies in its stream of net transactional benefits, which depend on its future prices. These transactional benefits may, for instance, represent the ability to exchange money in an unstable economic and financial system (such as in Venezuela or Zimbabwe), or when exchanges are blocked or heavily taxed.
To determine the net value, [Biais et al., 2020] consider various costs: limited convertibility, transaction fees from brokers, mining costs, and crash risk. They thus provide a definition of Bitcoinâs fundamental value (and technically of other cryptocurrencies) and answer the question of whether a cryptocurrency can have a fundamental value.
Obviously, this value differs depending on the cryptocurrency. For instance, if there is a strong demand for privacy in transactions, Monero (XMR) would dominate in volume, since it uses a private blockchain by default (making transactions untraceable, unlike Bitcoin where the blockchain is public and all transactions are identifiable).
However, the very idea that Bitcoin has a fundamental value is debated both in the media and academic literature. According to [Yermack, 2013], cryptocurrencies have no fundamental value because, if they did, there would be no incentive to mine cryptocurrency. According to [Hanley, 2013], Bitcoinâs value merely floats relative to other currencies as a market estimate without any fundamental value to support it. [Woo et al., 2013] suggests Bitcoin may have a certain fair value because of its features similar to fiat currencies (means of exchange and store of value), but without any other underlying basis.
[Hayes, 2015] links the importance of Bitcoinâs mining network to the dependency of altcoin holders on Bitcoin, given that most altcoins must be exchanged into Bitcoin before being converted into fiat currency for real-world use. Furthermore, [Garcia et al., 2014] highlights the importance of mining production costs in the fundamental value of cryptocurrencies, as it provides a kind of âfloor valueâ.
Cryptocurrencies are often criticized for being "backed by nothing", a misconception regarding the role of money in an economy. For example, according to the U.S. Federal Reserve, â Federal Reserve notes are not redeemable in gold, silver, or any other commodity. Federal Reserve notes have not been redeemable in gold since January 30, 1934, when the Congress amended Section 16 of the Federal Reserve Act to read: "The said [Federal Reserve] notes shall be obligations of the United StatesâŠ.They shall be redeemed in lawful money on demand at the Treasury Department of the United States, in the city of Washington, District of Columbia, or at any Federal Reserve bank." â
Beyond the purely economic definition of value (utility and scarcity), for which Bitcoin qualifies (its utility lying in being an alternative to the centralized financial system, and its scarcity from the 21 million unit limit and diminishing accessibility over time), there is also a subjective characteristic to this value.
We highlight two relevant elements: network value and safe-haven value. According to Metcalfeâs law [Metcalfe, 1995], although nuanced [Odlyzko and Tilly, 2005], the value of a network is proportional to the square of the number of its users: a single fax machine is useless, but the value of each fax increases with the total number of machines in the network. One could thus infer a similar characteristic for cryptocurrencies.
According to [Baur and McDermott, 2010], a safe-haven asset can be defined as one that is negatively correlated with equities during crises. Gold is often a reference point. Let us verify this. We cannot directly compare superimposed charts due to vastly different magnitudes:
<details>
<summary>extracted/6391907/images/cor1.png Details</summary>
### Visual Description
\n
## Line Chart: Asset Price Comparison (2015-2022)
### Overview
This image presents a line chart comparing the price trends of three assets â Gold (GOLD/USD), Bitcoin (BTC/USD), and the S&P 500 (S&P500) â over the period from 2015 to 2022. The chart displays price on the y-axis and time (years) on the x-axis.
### Components/Axes
* **X-axis:** Represents time, spanning from 2015 to 2022. Markers are present for each year.
* **Y-axis:** Represents price, scaled from 0 to 70,000. The scale is linear.
* **Legend:** Located in the top-right corner, identifying each line:
* GOLD/USD (Blue)
* BTC/USD (Red)
* S&P500 (Teal/Green)
### Detailed Analysis
The chart displays three distinct price trends.
* **GOLD/USD (Blue Line):** The blue line representing Gold exhibits a relatively flat trend throughout the period. It starts at approximately 1,100 in 2015 and ends around 1,800 in 2022. There is a slight upward slope, but the overall change is modest.
* **BTC/USD (Red Line):** The red line representing Bitcoin shows a dramatic increase in price. Starting near 200 in 2015, it experiences periods of growth and decline. A significant surge occurs around 2017, peaking at approximately 20,000. After a correction, it rises sharply again in 2021, reaching a peak of around 69,000. The price then declines to approximately 40,000 by the end of 2022.
* **S&P500 (Teal/Green Line):** The teal line representing the S&P 500 shows a consistent upward trend, though less volatile than Bitcoin. It begins around 2,000 in 2015 and rises to approximately 4,000 by the end of 2022. There is a dip in early 2020, likely corresponding to the start of the COVID-19 pandemic, followed by a strong recovery.
**Approximate Data Points (extracted visually):**
| Year | GOLD/USD | BTC/USD | S&P500 |
|---|---|---|---|
| 2015 | 1,100 | 200 | 2,000 |
| 2016 | 1,200 | 900 | 2,200 |
| 2017 | 1,300 | 20,000 | 2,400 |
| 2018 | 1,250 | 13,000 | 2,700 |
| 2019 | 1,350 | 7,000 | 3,100 |
| 2020 | 1,900 | 9,000 | 3,200 (dip to ~2,200) |
| 2021 | 1,800 | 69,000 | 4,700 |
| 2022 | 1,800 | 40,000 | 4,000 |
### Key Observations
* Bitcoin exhibits significantly higher volatility compared to Gold and the S&P 500.
* The S&P 500 demonstrates a steady, long-term growth trend.
* Gold's price remains relatively stable throughout the period, acting as a potential safe-haven asset.
* The most significant price surge for Bitcoin occurred between 2020 and 2021.
* The S&P 500 experienced a temporary decline in early 2020, but quickly recovered.
### Interpretation
The chart illustrates the differing risk-reward profiles of these three assets. Bitcoin, while offering the potential for substantial gains, also carries a high degree of risk due to its volatility. Gold, on the other hand, provides relative stability but with limited growth potential. The S&P 500 represents a more balanced approach, offering steady growth with moderate risk.
The data suggests a period of increased risk appetite in the market, particularly during 2020-2021, as evidenced by the surge in Bitcoin's price. The dip in the S&P 500 in early 2020 likely reflects the initial uncertainty surrounding the COVID-19 pandemic, while the subsequent recovery indicates a return to investor confidence. Gold's stable performance throughout the period suggests its role as a hedge against economic uncertainty.
The chart provides a snapshot of asset performance over a specific timeframe and should not be interpreted as a prediction of future trends. Market conditions can change rapidly, and past performance is not necessarily indicative of future results.
</details>
Figure 12: Correlation between BTC/USD, GOLD/USD, and S&P500
Thus, we will separately analyze the correlation between S&P500 crashes and BTC/USD prices:
<details>
<summary>extracted/6391907/images/sp.png Details</summary>
### Visual Description
\n
## Line Chart: Time Series Data
### Overview
The image presents a line chart depicting a time series. The chart shows a single data series fluctuating over time, with a clear upward trend overall. The x-axis represents time, spanning from 2015 to 2022, and the y-axis represents a numerical value, ranging from approximately 1800 to 4700.
### Components/Axes
* **X-axis:** Time, labeled with years from 2015 to 2022. The axis is evenly spaced.
* **Y-axis:** Numerical value, ranging from approximately 1800 to 4700. The axis is linearly scaled with gridlines.
* **Data Series:** A single blue line representing the time series data.
* **No Legend:** There is no explicit legend provided.
### Detailed Analysis
The data series begins around 2015 at approximately 2000. From 2015 to 2018, the line exhibits relatively stable fluctuations, generally trending upwards but with several dips and peaks.
* **2015:** Starts around 2000, fluctuates between approximately 1900 and 2200.
* **2016:** Fluctuates between approximately 1900 and 2300.
* **2017:** Shows a more consistent upward trend, reaching approximately 2500 by the end of the year.
* **2018:** Continues the upward trend, reaching approximately 2800.
* **2019:** Exhibits more volatility, fluctuating between approximately 2700 and 3100.
* **2020:** A significant drop occurs around the beginning of 2020, reaching a low of approximately 2400. The line then recovers sharply, reaching approximately 3500 by the end of the year.
* **2021:** A strong upward trend is observed, with the line increasing from approximately 3500 to 4000.
* **2022:** Continues the upward trend, reaching a peak of approximately 4700, followed by some fluctuations towards the end of the year. The line ends around 4500.
### Key Observations
* **Overall Trend:** The dominant trend is upward, indicating a general increase in the value represented by the y-axis over time.
* **Volatility:** The data exhibits volatility, particularly in 2019 and 2022.
* **Significant Drop in 2020:** The sharp drop in early 2020 is a notable anomaly, potentially indicating a significant event or disruption.
* **Rapid Recovery in 2020:** The subsequent rapid recovery in 2020 suggests resilience or a strong rebound effect.
### Interpretation
The chart likely represents the value of an asset, an index, or a key performance indicator (KPI) over time. The upward trend suggests growth or positive performance. The drop in 2020 could be attributed to a global event, such as the COVID-19 pandemic, which caused market disruptions. The rapid recovery indicates a strong response to the event. The volatility in 2019 and 2022 could be due to various factors, such as economic uncertainty, geopolitical events, or market speculation. Without further context, it is difficult to determine the exact nature of the data, but the chart clearly demonstrates a positive long-term trend with periods of volatility and a significant disruption in 2020.
</details>
Figure 13: S&P500 over the period available with BTC/USD
We notice graphical correlations during several crash periods:
- Early 2018
- Late 2019
- Early 2020
- Early 2022
These correlations are weaker, or even negative, with gold:
<details>
<summary>extracted/6391907/images/gold.png Details</summary>
### Visual Description
\n
## Line Chart: Time Series Data
### Overview
The image presents a line chart depicting a time series. The chart shows a single data series fluctuating over time, with a clear upward trend beginning around 2020. The x-axis represents time, and the y-axis represents a numerical value.
### Components/Axes
* **X-axis:** Represents time, spanning from approximately 2015 to 2022. The axis is labeled with year markers.
* **Y-axis:** Represents a numerical value, ranging from approximately 1000 to 2000. The axis is labeled with numerical markers in increments of 200.
* **Data Series:** A single blue line representing the time series data.
* **Grid:** A light gray grid is present in the background to aid in reading values.
### Detailed Analysis
The data series exhibits the following behavior:
* **2015-2019:** The line fluctuates within a relatively narrow range, generally between 1200 and 1400. There are several peaks and troughs, but no significant overall trend.
* **2019-2020:** A gradual upward trend begins around late 2019, accelerating into 2020.
* **2020-2021:** A steep increase occurs in early 2020, reaching a peak of approximately 2000. The line then experiences a significant drop, followed by fluctuations between 1700 and 1900.
* **2021-2022:** The line continues to fluctuate, with a slight upward trend towards the end of the period, reaching approximately 1850-1900 by 2022.
Approximate data points (with uncertainty of +/- 25):
* **2015:** ~1250
* **2016:** Fluctuates between ~1150 and ~1350
* **2017:** Fluctuates between ~1250 and ~1400
* **2018:** Fluctuates between ~1200 and ~1450
* **2019:** Fluctuates between ~1250 and ~1450
* **Early 2020:** ~1400, rapidly increasing to ~1900
* **Mid 2020:** Peak of ~2000
* **Late 2020:** Drop to ~1700
* **2021:** Fluctuates between ~1700 and ~1900
* **2022:** ~1850-1900
### Key Observations
* The most significant feature of the chart is the dramatic increase in the data series starting in 2020.
* The period from 2015 to 2019 shows relatively stable data with minor fluctuations.
* The data after 2020 is more volatile, with larger swings in value.
### Interpretation
The chart likely represents a time series of some quantifiable metric. The initial stability from 2015-2019 suggests a consistent state or process. The sharp increase in 2020 could indicate a significant event or change that dramatically impacted the metric. The subsequent fluctuations suggest ongoing adjustments or responses to the initial change.
Without knowing what the y-axis represents, it's difficult to provide a more specific interpretation. However, the pattern suggests a system that experienced a major disruption around 2020, followed by a period of adaptation and ongoing variability. The upward trend at the end of 2022 could indicate a recovery or stabilization, but further data would be needed to confirm this. The data suggests a non-linear relationship, with a period of relative stability followed by a period of rapid change and then continued, but less dramatic, fluctuation.
</details>
Figure 14: GOLD/USD over the period available with BTC/USD
Let us graphically check the correlation of daily returns:
<details>
<summary>extracted/6391907/images/cor-btc-sp.png Details</summary>
### Visual Description
\n
## Line Chart: BTC/USD and S&P500 Daily Returns
### Overview
This image presents a line chart comparing the daily returns of Bitcoin (BTC/USD) and the S&P 500 index over a period from approximately 2015 to 2022. The chart displays fluctuations in returns, with the y-axis representing the return value and the x-axis representing time.
### Components/Axes
* **X-axis:** Time, ranging from approximately 2015 to 2022. The axis is labeled with year markers.
* **Y-axis:** Daily Return, ranging from -0.4 to 0.2. The axis is linearly scaled.
* **Legend:** Located in the top-right corner.
* **Blue Line:** BTC/USD
* **Red Line:** S&P 500
* **Gridlines:** Horizontal gridlines are present to aid in reading the return values.
### Detailed Analysis
The chart shows two time series: BTC/USD daily returns (blue line) and S&P 500 daily returns (red line).
**BTC/USD (Blue Line):**
The BTC/USD line exhibits significantly higher volatility than the S&P 500 line. The line fluctuates wildly, with frequent and large positive and negative swings.
* **2015-2016:** The line fluctuates around 0, with some negative excursions.
* **2017:** A period of increasing volatility and generally positive returns.
* **2018:** A significant downturn, with returns dropping to approximately -0.3.
* **2019-2020:** Moderate volatility, fluctuating around 0.
* **2020:** A large negative spike, dropping to approximately -0.35, followed by a recovery.
* **2021:** High volatility with both positive and negative excursions.
* **2022:** Generally negative returns, with fluctuations around -0.1.
**S&P 500 (Red Line):**
The S&P 500 line is much smoother and less volatile than the BTC/USD line. It generally fluctuates within a narrower range.
* **2015-2017:** Relatively stable, fluctuating around 0.
* **2018:** A moderate downturn, with returns dropping to approximately -0.1.
* **2019-2020:** Generally positive returns, with fluctuations around 0.05.
* **2020:** A sharp negative spike, dropping to approximately -0.2, followed by a rapid recovery.
* **2021:** Moderate positive returns, fluctuating around 0.02.
* **2022:** Generally negative returns, fluctuating around -0.05.
It is difficult to extract precise numerical values from the chart due to its resolution. However, approximate values can be estimated.
### Key Observations
* **Volatility:** BTC/USD is significantly more volatile than the S&P 500.
* **Correlation:** There appears to be limited correlation between the two assets. While both experienced a downturn in 2018 and 2020, the magnitude and timing of the fluctuations differ.
* **Outliers:** The large negative spike in BTC/USD in 2020 is a notable outlier.
* **Trend:** Both assets show a general trend of fluctuating around 0, indicating that daily returns are often small.
### Interpretation
The chart demonstrates the substantial difference in volatility between Bitcoin and the S&P 500. Bitcoin exhibits much larger price swings, suggesting it is a riskier asset. The limited correlation between the two assets suggests that Bitcoin does not consistently move in the same direction as the broader stock market. The 2020 events show that both assets can experience significant downturns simultaneously, but the recovery patterns differ. The chart highlights the potential for both gains and losses in Bitcoin, while the S&P 500 offers a more stable, albeit potentially lower, return. The data suggests that Bitcoin may not be an effective hedge against broader market downturns, as both assets experienced declines in 2020.
</details>
Figure 15: Correlation between BTC/USD and S&P500 (daily returns)
<details>
<summary>extracted/6391907/images/cor-gold-sp.png Details</summary>
### Visual Description
## Line Chart: Correlation of GOLD/USD and S&P500
### Overview
The image presents a line chart comparing the fluctuations of GOLD/USD and S&P500 over time, from approximately 2015 to 2022. The chart displays the data as a time series, with the y-axis representing a value ranging from approximately -0.1 to 0.1, and the x-axis representing the years from 2015 to 2022.
### Components/Axes
* **X-axis:** Represents time, labeled with years from 2015 to 2022. The scale is linear and evenly spaced.
* **Y-axis:** Represents a numerical value, ranging from approximately -0.1 to 0.1. The axis is not explicitly labeled, but appears to represent a rate of change or normalized value. The scale is linear.
* **Legend:** Located in the top-right corner, identifies the two data series:
* **GOLD/USD:** Represented by a blue line.
* **S&P500:** Represented by a red line.
* **Gridlines:** Horizontal and vertical gridlines are present to aid in reading values.
### Detailed Analysis
The chart shows two fluctuating lines over the specified time period.
* **GOLD/USD (Blue Line):** The line exhibits high-frequency fluctuations throughout the period. The trend is generally around the zero line, with periods of positive and negative values. There is a significant spike upwards around 2020, reaching a peak value of approximately 0.08. After 2020, the line returns to its previous fluctuating pattern.
* **S&P500 (Red Line):** Similar to GOLD/USD, the S&P500 line also shows high-frequency fluctuations. It generally oscillates around the zero line. However, there is a dramatic negative spike in early 2020, dropping to approximately -0.1. This is a much larger drop than any observed in the GOLD/USD line. After the drop, the S&P500 line recovers and continues to fluctuate around the zero line.
Approximate Data Points (extracted visually):
| Year | GOLD/USD (approx.) | S&P500 (approx.) |
|---|---|---|
| 2015 | 0.01 | 0.005 |
| 2016 | -0.02 | 0.01 |
| 2017 | 0.005 | 0.02 |
| 2018 | -0.01 | 0.005 |
| 2019 | 0.01 | 0.015 |
| 2020 (Jan-Feb) | 0.02 | 0.02 |
| 2020 (March) | 0.08 | -0.1 |
| 2021 | 0.01 | 0.01 |
| 2022 | -0.01 | 0.005 |
### Key Observations
* **Inverse Correlation in 2020:** The most striking observation is the inverse correlation between the two assets in early 2020. While the S&P500 experienced a significant drop, GOLD/USD spiked upwards. This suggests a flight to safety during that period, with investors moving funds from stocks to gold.
* **Similar Fluctuations:** Outside of the 2020 event, both assets exhibit similar fluctuating patterns, suggesting a degree of correlation or shared underlying factors influencing their movements.
* **Magnitude of Change:** The S&P500 experienced a much larger single-point drop in 2020 than any fluctuation observed in GOLD/USD.
### Interpretation
The chart demonstrates the relationship between GOLD/USD and the S&P500 over a period of economic uncertainty. The inverse correlation observed in early 2020 is a classic example of a "safe haven" asset (gold) performing well during a stock market downturn (S&P500). This suggests that investors perceived increased risk in the stock market and sought the relative safety of gold. The subsequent recovery of the S&P500 and the return of GOLD/USD to its previous fluctuations indicate a stabilization of market conditions. The chart highlights the potential for gold to act as a hedge against market volatility, but also shows that its performance is not always directly opposite to that of stocks. The data suggests that while there is some correlation, the two assets are influenced by a complex interplay of factors.
</details>
Figure 16: Correlation between GOLD/USD and S&P500 (daily returns)
A numerical analysis of the correlation of daily returns over the entire period shows 16% for Bitcoin with the S&P500 and 5% for gold with the S&P500. Bitcoin does not appear to be a better safe-haven asset than gold, which is confirmed by other studies ([Smales, 2019], [Bouri et al., 2017]).
2.2 From Louis Bachelier to Contemporary Models
EugĂšne Fama is not the inventor of the idea of a random market. We can trace it back to 1863, when Jules Regnault [Regnault, 1863] proposed a model of randomly volatile markets. Then, in 1900, Bachelier [Bachelier, 1900] formalized it. It was only from the 1930s that the random aspect of the market began to be considered, notably in the United States with the emergence of econometrics, and then, from the 1960s, financial economics in the United States started to connect the model to economic theory, giving rise to the theory of informational efficiency of financial markets. However, this theory, although constituting the foundation of the random walk model, would never achieve unanimous acceptance. In this subsection, we will present the theoretical models that have explained the variations of financial assets since 1900, from Louis Bachelierâs theory of speculation to the present day.
2.2.1 Modeling of Traditional Finance
It is important to understand that the cryptocurrency market is not disconnected from traditional financial markets in its creation.
- The Louis Bachelier Model Bachelier is a pioneer of modern finance in the sense that he was the first to use Brownian motion in modeling stock prices, five years before [Einstein, 1956]. From his model, the Wiener process [Wiener, 1976] would later be formalized. The model simply explains that the stock market follows a Gaussian distribution. Of course, such a model today would not be considered rigorous, but for its time, it was already remarkably close to a correct model. Indeed, Brownian motion applied to stock price fluctuations is based on questionable assumptions: Markov chain (memoryless process), stationarity (constant mean and standard deviation), and normal distribution. We can clearly see, for example, for the four largest cryptocurrencies, that the distribution of daily returns is not really Gaussian:
<details>
<summary>extracted/6391907/images/dist-btc.png Details</summary>
### Visual Description
\n
## Chart: Histogram with Density Curve
### Overview
The image displays a histogram representing the distribution of a dataset, overlaid with a smooth density curve. The histogram shows the frequency of values within specific bins, while the density curve provides a continuous estimate of the distribution's shape.
### Components/Axes
* **X-axis:** Ranges from approximately -0.3 to 0.2, with markings at -0.3, -0.2, -0.1, 0, 0.1, and 0.2. Represents the values of the dataset.
* **Y-axis:** Ranges from 0 to approximately 0.004, with markings at 0, 0.0005, 0.001, 0.0015, 0.002, 0.0025, 0.003, 0.0035, and 0.004. Represents the frequency or density of values.
* **Histogram:** Composed of vertical bars representing the frequency of values within each bin.
* **Density Curve:** A smooth, black line overlaid on the histogram, estimating the probability density function of the data.
### Detailed Analysis
The histogram is heavily concentrated around the value of 0. The density curve confirms this, peaking sharply at 0. The distribution appears to be approximately symmetric, with tails extending to both the left and right, but with a much more pronounced tail on the left side.
Here's an approximate breakdown of the histogram's height (Y-axis value) for different ranges of X-axis values:
* **X = -0.3 to -0.2:** Y â 0
* **X = -0.2 to -0.1:** Y â 0.0002
* **X = -0.1 to 0:** Y increases rapidly from 0 to approximately 0.0035 at X = 0.
* **X = 0 to 0.05:** Y decreases rapidly from 0.0035 to approximately 0.001.
* **X = 0.05 to 0.1:** Y continues to decrease to approximately 0.0002.
* **X = 0.1 to 0.2:** Y â 0
The density curve closely follows the shape of the histogram, peaking at approximately 0.0035 at X = 0. The curve gradually descends on both sides of the peak, approaching 0 as X moves away from 0.
### Key Observations
* The distribution is unimodal, with a single prominent peak at 0.
* The distribution is not perfectly symmetric; it exhibits a slight left skew.
* The data is highly concentrated around 0, with frequencies decreasing rapidly as you move away from 0.
* There are no significant outliers visible in the histogram.
### Interpretation
The data suggests a distribution centered around zero, potentially representing errors, differences, or changes relative to a baseline. The concentration of values near zero indicates that most observations are close to the baseline. The slight left skew suggests that there are more smaller negative values than larger positive values. This could indicate a systematic bias or a process that tends to produce slightly negative results more often. The density curve provides a smoothed representation of this distribution, allowing for a clearer understanding of its overall shape and characteristics. Without knowing the context of the data, it's difficult to draw more specific conclusions, but the distribution's characteristics suggest a relatively stable process with a tendency towards values near zero.
</details>
Figure 17: Distribution of daily returns for BTC/USD
<details>
<summary>extracted/6391907/images/dist-eth.png Details</summary>
### Visual Description
\n
## Chart: Density Plot
### Overview
The image presents a density plot, visually representing the distribution of a dataset. The plot shows a large number of vertical lines (likely representing individual data points) overlaid on a smooth curve, which is an estimation of the probability density function. The x-axis represents the values of the data, and the y-axis represents the density.
### Components/Axes
* **X-axis:** Ranges from approximately -0.4 to 0.2, with markings at -0.4, -0.3, -0.2, -0.1, 0, 0.1, and 0.2.
* **Y-axis:** Ranges from 0 to 0.005, with markings at 0, 0.001, 0.002, 0.003, 0.004, and 0.005.
* **Vertical Lines:** Numerous thin, gray vertical lines are distributed along the x-axis, representing individual data points.
* **Curve:** A black, smooth curve overlays the vertical lines, representing the estimated probability density function.
### Detailed Analysis
The density is highest around x = 0, and decreases as you move away from 0 in either direction. The curve is approximately symmetrical around x = 0.
* **Peak Density:** The maximum density appears to be around 0.0035, occurring at approximately x = 0.
* **Density at x = 0:** The density at x = 0 is approximately 0.0015.
* **Density at x = -0.1:** The density at x = -0.1 is approximately 0.001.
* **Density at x = 0.1:** The density at x = 0.1 is approximately 0.001.
* **Density at x = -0.2:** The density at x = -0.2 is approximately 0.0005.
* **Density at x = 0.2:** The density at x = 0.2 is approximately 0.0002.
* **Vertical Line Distribution:** The vertical lines are most densely packed around x = 0, and become sparser as you move away from 0. There is a noticeable cluster of vertical lines around x = 0.05.
### Key Observations
* The distribution is approximately bell-shaped, suggesting a normal or Gaussian distribution.
* The data is concentrated around x = 0.
* There is a slight asymmetry, with a longer tail extending towards the positive x-axis.
* The vertical lines reveal the individual data points, showing the underlying distribution that the smooth curve is estimating.
### Interpretation
The data suggests a central tendency around 0, with values becoming less frequent as they deviate from this central point. The smooth curve provides a generalized representation of this distribution, while the vertical lines offer a more granular view of the individual data points. The slight asymmetry indicates that values greater than 0 are slightly more common than values less than 0. This type of plot is commonly used to visualize the distribution of continuous data and identify potential patterns or anomalies. The density plot indicates that the data is not perfectly normally distributed, but is close to it. The cluster of vertical lines around x = 0.05 suggests a potential sub-grouping or mode within the data.
</details>
Figure 18: Distribution of daily returns for ETH/USD
<details>
<summary>extracted/6391907/images/dist-ltc.png Details</summary>
### Visual Description
\n
## Histogram: Distribution of Values
### Overview
The image presents a histogram displaying the distribution of a single variable. The x-axis represents the range of values, and the y-axis represents the frequency or density of those values. A smooth curve is overlaid on the histogram, likely representing a density estimate of the underlying distribution.
### Components/Axes
* **X-axis:** Ranges from approximately -0.4 to 0.6. The axis is labeled with numerical values, incrementing by 0.1.
* **Y-axis:** Ranges from 0 to approximately 0.004. The axis represents the frequency or density.
* **Histogram Bars:** Vertical bars representing the frequency of values within specific bins.
* **Density Curve:** A smooth, black curve overlaid on the histogram, approximating the probability density function of the data.
### Detailed Analysis
The histogram shows a highly skewed distribution. The majority of the data points are clustered around 0. The distribution exhibits a sharp peak near 0, with a rapid decline in frequency as values move away from 0 in either direction.
* **Peak:** The highest frequency occurs at approximately x = 0, with a y-value of around 0.0028.
* **Left Tail:** The distribution extends to the left (negative values) with a relatively slow decay. The frequency decreases gradually from x = 0 to x = -0.4.
* **Right Tail:** The distribution extends to the right (positive values) with a much faster decay. The frequency drops off rapidly from x = 0 to x = 0.2, and then continues to decrease more slowly to x = 0.6.
* **Density Curve:** The curve closely follows the shape of the histogram, indicating a good fit. The curve is highest at x = 0, mirroring the peak in the histogram.
### Key Observations
* The distribution is strongly concentrated around 0.
* The distribution is not symmetrical; it is skewed to the right (positive values).
* There are very few data points with values greater than 0.3.
* The density curve suggests a unimodal distribution.
### Interpretation
The data suggests a variable where values are predominantly close to zero, with a decreasing probability of observing larger positive or negative values. This could represent a variety of phenomena, such as:
* **Residuals from a regression model:** If this is a histogram of residuals, it suggests the model fits the data reasonably well, but there might be some slight skewness.
* **Changes or differences:** The variable could represent changes in a quantity over time, where most changes are small and infrequent.
* **Errors:** The variable could represent measurement errors, where most errors are small and close to zero.
The sharp peak at zero and the rapid decay in frequency indicate that extreme values are rare. The skewness suggests that positive values are more common than negative values, although both are relatively infrequent compared to values near zero. The density curve provides a smoothed representation of the distribution, allowing for a better understanding of the underlying probability density.
</details>
Figure 19: Distribution of daily returns for LTC/USD
<details>
<summary>extracted/6391907/images/dist-xrp.png Details</summary>
### Visual Description
\n
## Chart: Histogram with Density Curve
### Overview
The image displays a histogram with an overlaid density curve. The histogram represents the distribution of a single variable, with values ranging approximately from -0.4 to 0.8. The density curve provides a smoothed estimate of the underlying probability distribution.
### Components/Axes
* **X-axis:** Ranges from -0.4 to 0.8, with tick marks at intervals of 0.2. The axis is labeled, but the label is not visible in the image.
* **Y-axis:** Ranges from 0 to 0.005, with tick marks at intervals of 0.001. The axis is labeled, but the label is not visible in the image. The Y-axis represents frequency or density.
* **Histogram:** Composed of numerous vertical bars representing the frequency of values within specific bins.
* **Density Curve:** A smooth, black curve overlaid on the histogram, estimating the probability density function of the data.
### Detailed Analysis
The histogram shows a highly skewed distribution. The majority of the data is concentrated around 0, with a sharp peak. There is a long tail extending towards the right (positive values).
* **Peak:** The highest frequency occurs around x = 0, with a density of approximately 0.0045.
* **Left Side:** From -0.4 to approximately -0.1, the density is very low, close to 0.
* **Right Side:** From approximately 0.1 to 0.8, the density decreases gradually, with some minor fluctuations.
* **Density Curve Trend:** The density curve closely follows the shape of the histogram, peaking at x = 0 and decreasing as it moves away from 0. The curve is smooth and provides a general representation of the distribution.
### Key Observations
* The distribution is strongly right-skewed.
* There is a high concentration of data points near 0.
* The density decreases rapidly as the values move away from 0 in both directions, but more slowly towards positive values.
* The histogram has a large number of narrow bins, providing a detailed view of the distribution.
### Interpretation
The data suggests a variable where values are predominantly close to zero, with a smaller number of significantly positive values. This could represent a variety of phenomena, such as:
* **Residuals from a regression model:** If this is a histogram of residuals, it suggests the model may not be perfectly capturing the relationship between variables, as the residuals are not normally distributed.
* **Changes or differences:** The variable could represent changes or differences between two measurements, where most changes are small and close to zero, but some are larger and positive.
* **Rates or proportions:** The variable could represent a rate or proportion, where most values are small, but some are larger.
The density curve provides a smoothed representation of the distribution, highlighting the overall shape and central tendency. The skewness indicates that the mean and median of the distribution are likely to be different, with the mean being greater than the median. The presence of a long tail suggests that there may be outliers or extreme values in the data. Without knowing the context of the variable, it is difficult to draw more specific conclusions.
</details>
Figure 20: Distribution of daily returns for XRP/USD
It might be more appropriate to refer to a LĂ©vy law or an $\alpha$ -stable distribution.
- The Gordon-Shapiro Model The Gordon-Shapiro model [Gordon and Shapiro, 1956] is very well-known in finance and provides a very simple formula to model the price of a stock:
$$
P_{0}=\frac{D_{1}}{k-g} \tag{1}
$$
where $P_{0}$ is the theoretical value of the stock, $D_{1}$ the anticipated dividend for the first period, $k$ the expected return rate for the shareholder, and $g$ the growth rate of the gross earnings per share. The first thing to note is that this model is useless for the crypto market: there are no dividends. Therefore, this model can be dismissed, even though it is attractive.
- Contemporary Models With the development of quantitative finance and derivative pricing, many models have emerged, one of the most famous being the Black & Scholes model [Black and Scholes, 2019]. However, as with the binomial model (Cox, Ross & Rubinstein model), the problem of constant volatility of the underlying assets appeared. Indeed, in the Black & Scholes formula:
$$
C=S_{t}N(d_{1})-Ke^{-rt}N(d_{2}) \tag{2}
$$
where:
$$
d_{1}=\frac{\ln\frac{S_{t}}{K}+(r+\frac{\sigma^{2}}{2})t}{\sigma\sqrt{t}} \tag{3}
$$
$$
d_{2}=d_{1}-\sigma\sqrt{t} \tag{4}
$$
with: $C$ the price of the call option $P$ the stock price $K$ the strike price $r$ the risk-free interest rate $t$ the time in years to maturity $N$ a normal distribution $\sigma$ the volatility of the underlying asset We notice that volatility is considered constant. This led to the development of stochastic volatility models, treating the volatility of the underlying as a random process. As explained, for instance, by [Mantegna and Stanley, 1999], the price of an asset can be characterized by a standard geometric Brownian motion:
$$
dS_{t}=\mu S_{t}dt+\sigma S_{t}dW_{t} \tag{5}
$$
with: $\mu$ the drift (often negligible) $\sigma$ constant volatility $dW_{t}\hookrightarrow N(0,1)$ an increment of Brownian motion then replacing $\sigma$ by a process $\nu_{t}$ . This is indeed how the Heston model [Heston, 1993] is built, one of the most well-known stochastic volatility models. Its formulas are:
$$
dS_{t}=rS_{t}dt+\sqrt{V_{t}}S_{t}dW_{1t} \tag{6}
$$
with $V_{t}$ the instantaneous variance:
$$
dV_{t}=\kappa(\theta-V_{t})dt+\sigma\sqrt{V_{t}}dW_{2t} \tag{7}
$$
where: $S_{t}$ the asset price at time $t$ $r$ the risk-free interest rate $\sqrt{V_{t}}$ the volatility (standard deviation) of the price $\sigma$ the volatility of the volatility (i.e., of $\sqrt{V_{t}}$ ) $\theta$ the long-term variance $\kappa$ the reversion rate to $\theta$ $dt$ an infinitesimally small time increment $W_{1t}$ the Brownian motion for the asset price $W_{2t}$ the Brownian motion for the variance of the asset price with the property that, for Brownian motions, $W_{0}=0$ , the $W_{t}$ are independent, and $W_{t}$ is continuous in $t$ . This model seems well suited for modeling the price of cryptocurrencies. Indeed, [Kachnowski, 2020] explains that an adaptation of the Heston model to Bitcoin improves the accuracy of predictions over time windows ranging from 7 days to 2 months. However, as shown by [Gatheral et al., 2018], the log-volatility is not actually a classic Brownian motion but rather a fractional Brownian motion, as in the Fractional Stochastic Volatility Model by [Comte et al., 2012], but with a Hurst exponent of 0.1 (and not 0.5 as in [Comte et al., 2012], who did not take into account the rough aspect of volatility).
2.2.2 Modeling Crypto-Finance
- Quantitative Theory of (Crypto)Currency As we know [Fisher, 2006],
$$
MV=PY \tag{8}
$$
where: $M$ is the money supply $V$ is the velocity of money $P$ is the price level $Y$ is the output of the economy Letâs adapt this model to cryptocurrencies. For $M$ , it is simple: it is constant at 21 million. However, we can already anticipate that $M$ tends towards 0. Indeed, 21 million is the maximum number of Bitcoins that can be mined. Once mined, Bitcoins can disappear for several reasons: lost passwords, hacking, computer errors, etc. For $V$ , it is more complicated. We would need to differentiate between economically meaningful transactions and meaningless ones. And this is very difficult, even though all transactions are listed on the Blockchain, the reasons behind them are not. Thus, we cannot distinguish "real" transactions from "fake" ones. For $P$ , it refers to the goods and services that can be purchased with Bitcoin. In November 2020, the Venezuelan branch of Pizza Hut accepted Bitcoin. On that day, you could buy around 1,800 pizzas (worth approximately 10 USD each) with one Bitcoin. Today, you could buy around 4,000 pizzas with one Bitcoin. Thus, $P$ has been continuously falling for BTC/USD. For $Y$ , it represents the amount of goods and services available for purchase and sale. We can admit that very few goods and services are currently bought and sold with cryptocurrencies. Thus, over time, cryptocurrencies are expected to depreciate. Indeed, we know that the number of Bitcoins in circulation initially increases (then will decrease), which should induce inflation. However, the opposite is observed. If $Y$ is exogenous to Bitcoin (goods and services offered are not really dependent on Bitcoinâs price), and $M$ is constant, then $V$ will influence $P$ . In this case, two scenarios arise: if Bitcoin (same reasoning for other cryptocurrencies) is merely a means of exchange without any fundamental value, $V$ will increase, as it will become just another payment option for households. If Bitcoin is rather seen as a store of value, with a fundamental value, then households will invest and hold their Bitcoins, causing $V$ to decrease, which will raise $P$ . Studies, including [Pernice et al., 2020], show a link between price and velocity in cryptocurrencies.
- Other Models of the Crypto Market [Cretarola and FigĂ -Talamanca, 2018] propose modeling the crypto market by the interest it generates. They explore the link between Bitcoinâs price behavior and investor attention in the network. They conclude that the attention index impacts Bitcoinâs price through dependence of the drift and diffusion coefficients and potential correlation between the sources of randomness represented by Brownian motions. [Hou et al., 2020] propose a model for pricing crypto options, SVCJ (stochastic volatility with a correlated jump), similar to [Pascucci and Palomba,], and compare it with the cojump model of [Bandi and Reno, 2016]. It is very likely that the future of cryptocurrency price modeling will develop towards derivative products.
2.3 Time Series Studies and Analyses
We are still considering the case where the crypto market is efficient. Thus, it is impossible to predict its price movements, regardless of the methods employed. However, these methods are still widely used by both retail and professional investors. Therefore, we will examine these methods to understand whether they can be effective in prediction. Nevertheless, we will see that it is sometimes difficult to answer this question with a simple yes or no.
2.3.1 Fundamental Analysis
To perform fundamental analysis on a company, there are a number of well-established methods (financial ratios, EBITDA, cash flows, etc.). For cryptocurrencies, there are not really established methods. We have therefore chosen 5 themes. We cannot develop a full analysis due to the lack of data, but these indicators can, in our opinion, allow a good fundamental analysis:
- Supply Measures:
- Is the number of coins fixed in advance?
- How many coins have been mined, and how many remain?
- What is the inflation rate?
- What is the coin-to-flow ratio?
- What is the granularity of the coins?
- Value Measures:
- What is the current price?
- What is the current gross market capitalization?
- What is the current net market capitalization (excluding lost coins)?
- What is the interest rate (borrowing cryptocurrencies)?
- What are the yearly high and low points?
- What are the returns by day, week, month, year, and overall?
- Network Activity Measures:
- How many active addresses are there?
- How many new addresses are there?
- How many transactions are there?
- What is the average transaction size?
- Broker Activity Measures:
- What is the total traded volume?
- On how many brokers is the cryptocurrency listed?
- What is the broker flow?
- In which geographical areas do the flows occur?
- Mining Measures:
- What is the consensus mechanism (Proof of Work, Proof of Stake, etc.)?
- What is the governance of the mining network?
- How long does it take to mine a block?
- How are miners rewarded?
- What are the median fees?
- What is the hash rate?
2.3.2 Chartist / Technical Analysis
Technical analysis aims to predict a price using future prices, and more precisely through repetitive patterns or technical indicators. Beyond the SMA tested previously, letâs simply perform a graphical analysis. Letâs take the RSI on BTC/USD:
<details>
<summary>x1.png Details</summary>
### Visual Description
\n
## Chart: Bitcoin/Dollar (Weekly)
### Overview
The image displays a weekly candlestick chart of the Bitcoin/Dollar exchange rate, along with two indicator lines below it. The chart spans a significant period, showing substantial price fluctuations over time. The top portion shows the price action, while the bottom portion displays two oscillating indicator lines.
### Components/Axes
* **Title:** Bitcoin / Dollar 1W COINBASE - TradingView
* **Y-axis (Price):** Ranges from 0.00 to 70000.00 (USD). The scale is linear.
* **X-axis (Time):** Represents weekly intervals. The exact dates are not visible, but the chart covers a long period.
* **Candlestick Chart:** Displays open, high, low, and close prices for each week.
* **Indicator 1 (Purple Line):** Oscillates between approximately 30.00 and 90.00.
* **Indicator 2 (Yellow Line):** Oscillates between approximately 40.00 and 70.00.
* **Top-Left Box:** Contains three numerical values: 37607.87, 2087.16, 39695.03. These likely represent current price, low, and high values respectively.
* **Horizontal Lines:** Several horizontal lines are present across the price chart, potentially indicating support or resistance levels.
### Detailed Analysis or Content Details
**Price Chart:**
The price chart shows a generally upward trend over the long term, with significant volatility.
* **Early Period (Left Side):** The price fluctuates between approximately 2,000 and 10,000 USD.
* **Mid-Period:** A substantial price increase occurs, reaching a peak of approximately 69,000 USD.
* **Recent Period (Right Side):** A significant price decline follows the peak, with the price currently around 38,682.55 USD.
* **Candlestick Patterns:** Numerous candlestick patterns are visible, indicating bullish and bearish sentiment at different times.
**Indicator 1 (Purple Line):**
* The purple line exhibits a cyclical pattern, oscillating between approximately 30 and 90.
* The line generally peaks and troughs in sync with major price movements.
* The line is currently around 50.
**Indicator 2 (Yellow Line):**
* The yellow line also exhibits a cyclical pattern, oscillating between approximately 40 and 70.
* The line shows a more muted oscillation compared to the purple line.
* The line is currently around 60.
**Numerical Values (Top-Left):**
* 37607.87: Likely the current Bitcoin price.
* 2087.16: Likely the lowest price observed.
* 39695.03: Likely the highest price observed.
### Key Observations
* **Strong Correlation:** The purple indicator line appears to have a stronger correlation with price movements than the yellow line.
* **Recent Downtrend:** The price has experienced a significant downtrend in the recent period, falling from a peak of around 69,000 USD to approximately 38,682.55 USD.
* **Volatility:** The chart demonstrates high volatility in the Bitcoin/Dollar exchange rate.
* **Indicator Divergence:** There are instances where the indicators diverge from the price action, potentially signaling a change in trend.
### Interpretation
The chart illustrates the historical price performance of Bitcoin against the US Dollar. The long-term trend is upward, but the price is subject to significant volatility. The indicators (purple and yellow lines) are likely momentum oscillators, designed to identify overbought and oversold conditions. The purple line's stronger correlation with price suggests it may be a more reliable indicator. The recent downtrend, coupled with the current indicator values, could suggest a potential for further price declines, but this is not definitive. The horizontal lines on the chart likely represent key support and resistance levels that traders monitor. The top-left box provides a snapshot of the current price and recent price range.
The chart provides a visual representation of the risk and reward associated with investing in Bitcoin. The potential for high returns is evident in the price increase from the early period to the peak, but the recent decline highlights the inherent risks. The indicators can be used to help identify potential entry and exit points, but they are not foolproof.
</details>
Figure 21: RSI Signals for BTC/USD
This indicator tells us that when it is below 30, we should buy, and above 70, we should sell. It is clearly seen that the RSI is useless for a long-term vision: what is the use of selling at 10,000 in 2018 when one could simply buy, hold, and sell at 60,000 in 2022? Now, letâs take another very famous technical indicator: the SAR.
<details>
<summary>x2.png Details</summary>
### Visual Description
\n
## Chart: Bitcoin / Dollar (1W)
### Overview
The image displays a weekly (1W) candlestick chart of the Bitcoin/Dollar exchange rate, sourced from COINBASE. The chart spans from July 2018 to April 2022, visualizing the price fluctuations of Bitcoin against the US Dollar. The chart includes candlestick patterns representing open, high, low, and close prices for each week. A highlighted region indicates a significant price surge in late 2020/early 2021.
### Components/Axes
* **Title:** Bitcoin / Dollar 1W COINBASE. TradingView
* **X-axis:** Time (Weekly intervals from July 2018 to April 2022) - Marked with month/year labels (Jul, Oct, Jan, Apr, Jul, Oct, Jan, Apr, Jul, Oct, Jan, Apr)
* **Y-axis:** Price (USD) - Scale ranges from -4000.00 to 70000.00.
* **Candlesticks:** Green candlesticks indicate price increases (close > open), while red candlesticks indicate price decreases (close < open).
* **Top-Left Corner:** Current price indicators: 38506.93 (Red), 3510.20 (Red), 38763.05 (Green).
* **Highlighted Region:** A light-grey shaded area covering a significant price increase from approximately October 2020 to February 2021.
* **Bottom-Left Corner:** TradingView logo.
### Detailed Analysis
The chart shows several distinct phases in Bitcoin's price history:
* **July 2018 - Early 2020:** A period of significant price decline and consolidation. The price fluctuates between approximately $3,000 and $13,000. The candlesticks are relatively small, indicating low volatility.
* **Late 2020 - Early 2021:** A massive bull run. The price increases exponentially from around $7,000 to nearly $65,000. This is the highlighted region. The candlesticks are large and predominantly green.
* **April 2021 - April 2022:** A period of high volatility and price correction. The price initially falls from around $65,000 to approximately $30,000, then recovers to around $48,000 before falling again to around $38,500. The candlesticks are large and alternate between green and red.
**Approximate Data Points (Extracted from visual inspection):**
* **July 2018:** Price around $7,000 - $8,000.
* **December 2018:** Price around $3,500.
* **July 2019:** Price around $10,000.
* **October 2020:** Price around $12,000.
* **December 2020:** Price around $23,000.
* **February 2021:** Price peaks around $58,000.
* **April 2021:** Price peaks around $64,000.
* **July 2021:** Price around $30,000.
* **November 2021:** Price around $68,000.
* **January 2022:** Price around $42,000.
* **April 2022:** Price around $38,500.
The current price indicators at the top-left show:
* 38506.93 (Red) - Likely the current price.
* 3510.20 (Red) - Possibly a low price point.
* 38763.05 (Green) - Possibly a high price point.
### Key Observations
* The most significant trend is the exponential price increase between late 2020 and early 2021.
* The price has experienced significant volatility since April 2021, with large swings in both directions.
* The price in April 2022 is significantly lower than the peak in November 2021, indicating a substantial correction.
* The highlighted region clearly demonstrates a period of rapid growth and investor interest.
### Interpretation
The chart illustrates the highly volatile nature of Bitcoin. The dramatic price surge in 2020/2021 likely reflects increased institutional adoption, media attention, and speculative investment. The subsequent correction in 2021/2022 suggests a maturing market and a potential shift in investor sentiment. The chart demonstrates the cyclical nature of Bitcoin's price, with periods of rapid growth followed by corrections. The current price (April 2022) is still significantly higher than the price in July 2018, indicating a long-term upward trend despite the recent volatility. The highlighted region is a key indicator of a major market event, and its size and shape suggest a period of intense buying pressure. The red and green candlesticks provide a visual representation of the ongoing battle between buyers and sellers, and their relative sizes indicate the strength of each side. The data suggests that Bitcoin remains a high-risk, high-reward investment.
</details>
Figure 22: SAR Signals for BTC/USD
This indicator tells us that when the blue dots are below the candlesticks, we should buy, and when they are above, we should sell (first appearance of dots per sequence). The same reasoning applies: what is the point of selling in 2018? These indicators are ultimately only signals for day-trading, with the aim of making quick profits. However, statistics show that more than 70% of day-traders lose money. Yet, they all have access to all available indicators. Technical analysis would therefore seem useless both in the long term and in the short term, a priori. According to [Park and Irwin, 2007], the literature on the subject is inconclusive: some studies are positive, others negative, and others mixed.
2.3.3 Machine Learning
Letâs now check the effectiveness of Machine Learning in predicting cryptocurrency prices. We will not test all algorithms, but only two. The first, Support Vector Machine classification, was introduced by [Cortes and Vapnik, 1995]. It consists of classifying "good" trades from "bad" trades. For this, we create a Python function getAverageAccuracy( $\Omega,n$ ), which takes as parameters $\Omega$ and $n$ the window for technical indicators and returns the average accuracy percentage of our model across all tested cryptocurrencies (over 100). The features considered are: price (OHLC), previous prices, previous returns, SAR, RSI, SMA, ADX, ATR, and 80% training dataset. The function, whose code is in Appendix G, returns 38%. This is low. Here are the confusion matrices for the 4 largest cryptocurrencies (read as "Perfect prediction on the top-left/bottom-right diagonal, inverse prediction on the bottom-left/top-right"):
<details>
<summary>extracted/6391907/images/btc-ml.png Details</summary>
### Visual Description
\n
## Heatmap: Numerical Grid
### Overview
The image presents a 3x3 heatmap displaying numerical values within a grid of colored cells. Each cell is colored based on its corresponding numerical value, with a gradient from yellow (high values) to purple (low values). The values are directly displayed within each cell.
### Components/Axes
The image lacks explicit axes labels or a legend. The data is presented as a grid with 3 rows and 3 columns. The values range from 3 to 13.
### Detailed Analysis or Content Details
The heatmap contains the following data points:
* **Row 1, Column 1:** Value = 9, Color = Red-Orange
* **Row 1, Column 2:** Value = 10, Color = Orange
* **Row 1, Column 3:** Value = 4, Color = Dark Purple
* **Row 2, Column 1:** Value = 12, Color = Yellow
* **Row 2, Column 2:** Value = 8, Color = Pink-Purple
* **Row 2, Column 3:** Value = 3, Color = Dark Blue
* **Row 3, Column 1:** Value = 13, Color = Yellow
* **Row 3, Column 2:** Value = 9, Color = Red-Orange
* **Row 3, Column 3:** Value = 3, Color = Dark Blue
The color gradient appears to be roughly linear, with yellow representing the highest values and purple/blue representing the lowest.
### Key Observations
* The highest values (12 and 13) are located in the first column.
* The lowest values (3 and 4) are located in the third column.
* There is a noticeable difference in values between the left and right sides of the grid.
* The center cell in the second row (value 8) is a relatively low value compared to its neighbors.
### Interpretation
The heatmap suggests a correlation between position within the grid and the numerical value. The data indicates a higher concentration of larger values on the left side of the grid and smaller values on the right. This could represent a spatial distribution of some quantity, where the left side exhibits higher intensity or concentration. The relatively low value in the center of the second row (8) could be an anomaly or represent a localized minimum within the data. Without context, it is difficult to determine the meaning of these values, but the heatmap clearly visualizes a pattern of variation across the grid. The data suggests a gradient or trend from left to right.
</details>
Figure 23: Confusion matrix for BTC/USD
<details>
<summary>extracted/6391907/images/eth-ml.png Details</summary>
### Visual Description
\n
## Heatmap: Numerical Grid
### Overview
The image presents a 3x3 heatmap displaying numerical values within a color-coded grid. The color gradient ranges from dark purple (low values) to yellow (high values). Each cell in the grid contains a single numerical value.
### Components/Axes
The image lacks explicit axis labels or a legend. However, the grid structure implies a two-dimensional arrangement of data. The color scheme serves as a visual representation of the data's magnitude.
### Detailed Analysis
The grid contains the following numerical values, mapped to their corresponding colors:
* **Top-Left:** 9 (Orange-Purple)
* **Top-Center:** 11 (Orange)
* **Top-Right:** 1 (Dark Purple)
* **Middle-Left:** 12 (Orange)
* **Middle-Center:** 17 (Yellow)
* **Middle-Right:** 3 (Dark Purple)
* **Bottom-Left:** 4 (Purple)
* **Bottom-Center:** 9 (Pink-Purple)
* **Bottom-Right:** 5 (Purple)
The color gradient suggests that the value 17 is the highest, while 1 and 3 are the lowest. The values generally increase from the dark purple areas towards the yellow center.
### Key Observations
* The highest value (17) is located in the center of the grid.
* The lowest values (1 and 3) are located in the top-right and middle-right cells, respectively.
* There is a noticeable color contrast between the center cell (17) and the surrounding cells.
* The value 9 appears twice, once in the top-left and once in the bottom-center.
### Interpretation
The heatmap likely represents a correlation or distribution of some underlying data. The central high value (17) could indicate a point of maximum concentration or intensity. The lower values on the right side might represent areas of lower concentration or weaker correlation. Without knowing the context of the data, it's difficult to draw definitive conclusions. However, the pattern suggests a potential peak in the center and a gradual decrease towards the right. The repetition of the value 9 could indicate a consistent factor or relationship within the dataset. The image is a simple visualization of numerical data, and its meaning is dependent on the variables it represents.
</details>
Figure 24: Confusion matrix for ETH/USD
<details>
<summary>extracted/6391907/images/ltc-ml.png Details</summary>
### Visual Description
\n
## Heatmap: Numerical Grid
### Overview
The image presents a 3x3 heatmap displaying numerical values within a grid of colored cells. The color intensity appears to correlate with the magnitude of the numerical value, ranging from deep blue (low values) to bright yellow (high values). There are no explicit axis labels or a legend provided.
### Components/Axes
The image consists of a 3x3 grid. Each cell contains a numerical value. The color scheme transitions from red/pink to orange to yellow to purple to dark blue. There are no axis titles or labels.
### Detailed Analysis or Content Details
The grid contains the following numerical values, with associated color observations:
* **Top-Left:** 8 (Reddish-Pink)
* **Top-Center:** 10 (Orange)
* **Top-Right:** 2 (Dark Blue)
* **Middle-Left:** 12 (Yellow)
* **Middle-Center:** 13 (Bright Yellow) - This is the highest value in the grid.
* **Middle-Right:** 5 (Purple)
* **Bottom-Left:** 8 (Reddish-Pink)
* **Bottom-Center:** 8 (Orange)
* **Bottom-Right:** 5 (Purple)
The values appear to be integers. The color gradient suggests a mapping where lower numbers are represented by darker, cooler colors (blue/purple) and higher numbers by brighter, warmer colors (yellow/orange/red).
### Key Observations
* The highest value (13) is located in the center of the grid.
* The lowest value (2) is located in the top-right corner.
* The values 8 and 5 appear multiple times.
* There is a symmetrical pattern in the values, with 8 appearing in the bottom-left and top-left, and 5 appearing in the bottom-right and middle-right.
### Interpretation
Without context, it's difficult to definitively interpret the meaning of this heatmap. However, the arrangement of values suggests a potential correlation or relationship between the grid positions. The central position having the highest value could indicate a focal point or maximum intensity. The symmetrical pattern of values might suggest a balanced or repeating phenomenon.
The data could represent various things, such as:
* **Sensor readings:** Values could represent temperature, pressure, or other sensor data at different locations.
* **Correlation matrix:** Values could represent the correlation between different variables.
* **Game board:** Values could represent scores or states in a game.
* **Image processing:** Values could represent pixel intensities in an image.
Further information about the source and meaning of the data is needed to draw more specific conclusions. The lack of axis labels and a legend limits the interpretability of the data.
</details>
Figure 25: Confusion matrix for LTC/USD
<details>
<summary>extracted/6391907/images/xrp-ml.png Details</summary>
### Visual Description
\n
## Heatmap: Numerical Grid
### Overview
The image presents a 3x3 heatmap displaying numerical values within a grid of colored cells. Each cell is colored differently, presumably representing the magnitude of the number it contains. There are no explicit axis labels or a legend, but the values are directly embedded within each cell.
### Components/Axes
The image consists of a 3x3 grid. There are no visible axes or legends. The data is represented by numerical values displayed within each cell.
### Detailed Analysis or Content Details
The grid contains the following numerical values:
* **Row 1, Column 1:** 10
* **Row 1, Column 2:** 5
* **Row 1, Column 3:** 9
* **Row 2, Column 1:** 10
* **Row 2, Column 2:** 8
* **Row 2, Column 3:** 13
* **Row 3, Column 1:** 3
* **Row 3, Column 2:** 6
* **Row 3, Column 3:** 7
The color scheme appears to be:
* Dark Blue: 3
* Orange: 10 (appears twice)
* Purple: 5, 6, 8
* Salmon/Coral: 9
* Yellow: 13
* Magenta/Pink: 7
### Key Observations
The highest value (13) is located in the bottom-right corner of the grid. The lowest value (3) is located in the bottom-left corner. The values 10 appear twice, in the top-left and middle-left cells. The values are not evenly distributed, with a concentration of lower values in the bottom row.
### Interpretation
Without context, it's difficult to determine the meaning of this heatmap. However, the varying colors and numerical values suggest a representation of some underlying data where magnitude is important. It could represent anything from sensor readings to survey responses to game state information. The spatial arrangement of the values might indicate correlations or patterns within the data. For example, the high value in the bottom-right and low value in the bottom-left could suggest a gradient or directional trend. The repetition of the value 10 could indicate a common occurrence or baseline level. The lack of labels makes it impossible to draw definitive conclusions, but the heatmap clearly visualizes differences in magnitude across the grid.
</details>
Figure 26: Confusion matrix for XRP/USD
The second model is ARIMA, introduced by [Box et al., 2015], and it aims to predict future trends. The results of our model are as follows:
<details>
<summary>extracted/6391907/images/arima.png Details</summary>
### Visual Description
\n
## Statistical Output: ARIMA Model Results
### Overview
This image presents the results of an ARIMA (Autoregressive Integrated Moving Average) model applied to time series data. The output details model parameters, statistical tests, and root analysis. The data appears to be financial, specifically "D.Close" (presumably Daily Close price).
### Components/Axes
The output is structured into several sections:
* **Model Information:** Includes dependent variable, model specification (ARIMA(4,1,0)), method (css-mle), date, time, and sample period.
* **Model Fit Statistics:** Provides metrics like No. Observations, Log Likelihood, S.D. of innovations, AIC, BIC, and HQIC.
* **Parameter Estimates:** A table displaying coefficients (coef), standard errors (std err), z-statistics (z), p-values (P>|z|), and confidence intervals ([0.025, 0.975]) for each model parameter.
* **Root Analysis:** A table showing the real, imaginary, modulus, and frequency components of the roots of the characteristic polynomial.
### Detailed Analysis or Content Details
**Model Information:**
* Dependent Variable: D.Close
* Model: ARIMA(4, 1, 0)
* Method: css-mle
* Date: Mon, 02 May 2022
* Time: 03:16:01
* Sample: 05-03-2021 - 02-17-2022
* No. Observations: 291
* Log Likelihood: -2586.480
* S.D. of innovations: 1753.258
* AIC: 5184.959
* BIC: 5206.999
* HQIC: 5193.789
**Parameter Estimates:**
| Parameter | coef | std err | z | P>|z| | [0.025 | 0.975 |
|-----------|---------|---------|--------|-------|-------|----------|----------|
| const | -55.2311| 101.025 | -0.547 | 0.585 | -253.236| 142.774 |
| ar.L1.D.Close | -0.0541 | 0.059 | -0.923 | 0.357 | -0.169 | 0.061 |
| ar.L2.D.Close | -0.0278 | 0.059 | -0.470 | 0.638 | -0.143 | 0.088 |
| ar.L3.D.Close | -0.0297 | 0.060 | -0.499 | 0.618 | -0.147 | 0.087 |
| ar.L4.D.Close | 0.0947 | 0.060 | 1.592 | 0.113 | -0.022 | 0.211 |
**Root Analysis:**
| Root | Real | Imaginary | Modulus | Frequency |
|-------|---------|-----------|---------|-----------|
| AR.1 | -1.7241 | -0.0000j | 1.7241 | -0.5000 |
| AR.2 | 0.0309 | -1.7600j | 1.7603 | -0.2472 |
| AR.3 | 0.0309 | +1.7600j | 1.7603 | 0.2472 |
| AR.4 | 1.9763 | -0.0000j | 1.9763 | -0.0000 |
*Note: 'j' denotes the imaginary unit.*
### Key Observations
* The p-values for all AR coefficients are relatively high (greater than 0.05), suggesting that these coefficients are not statistically significant at the 5% level.
* The constant term also has a high p-value, indicating it's not statistically significant.
* The roots of the characteristic polynomial have moduli greater than 1, indicating that the ARIMA model is stationary.
* The imaginary components of AR.2 and AR.3 roots are non-zero, indicating oscillatory behavior.
### Interpretation
The ARIMA(4,1,0) model was fitted to the daily closing price (D.Close) time series data from March 5, 2021, to February 17, 2022. The model attempts to capture the autocorrelation structure in the data using four autoregressive (AR) terms. However, the statistical significance of the estimated coefficients is questionable, as indicated by the high p-values. This suggests that the model may not be a good fit for the data, or that a simpler model might be sufficient.
The root analysis confirms the stationarity of the model, which is a necessary condition for valid inference. The presence of complex roots (AR.2 and AR.3) indicates that the time series exhibits some oscillatory behavior. The relatively large standard errors of the coefficients suggest that the estimates are imprecise, potentially due to a limited sample size or high noise in the data. The AIC, BIC, and HQIC values provide measures of model fit, but their interpretation requires comparison with other potential models. The negative log-likelihood suggests the model is attempting to fit the data, but the high AIC/BIC/HQIC values suggest it may not be doing so efficiently.
</details>
Figure 27: Results of the ARIMA model
3 The Cryptocurrency Market is Inefficient
In 1981, Robert Shiller [Shiller, 1980] showed a higher volatility than that predicted by the rational behavior of agents. Shiller concluded that no rationality could explain the observed volatility, which ultimately had no link with dividend expectations. Thus, if the market is inefficient, it is possible to achieve performances superior to the market.
3.1 Robert Shiller and the Notion of an Inefficient Market in Terms of Arbitrage
This section deals with elements that prove that the Bitcoin market admits arbitrage opportunities. For example, we observe that the price of Bitcoin varies from one exchange to another. This is even more true for the altcoin market. Intuitively, we can imagine that the price will tend to move closer to the average price across exchanges.
3.1.1 Volatility and Expected Dividends
In his book, [Shiller, 2015], Shiller shows the difference between stock price volatility and expected dividends:
<details>
<summary>extracted/6391907/images/shiller-plot.png Details</summary>
### Visual Description
\n
## Line Chart: Real S&P Stock Price Index, Earnings, Dividends, and Interest Rates (1871=100)
### Overview
The image presents a line chart depicting the historical trends of the Real S&P Stock Price Index, Earnings, Dividends, and Interest Rates from 1870 to 2010. The chart aims to visually compare the fluctuations of these four financial indicators over time. The Price and Earnings are plotted on the primary y-axis (left), while Dividends and Interest Rates are plotted on the secondary y-axis (right).
### Components/Axes
* **X-axis:** Year, ranging from 1870 to 2010, with major tick marks at 1870, 1890, 1910, 1930, 1950, 1970, 1990, and 2010.
* **Primary Y-axis (left):** Real S&P Stock Price Index and Earnings (1871=100), ranging from 0 to 2500.
* **Secondary Y-axis (right):** Interest Rate (%), ranging from 0 to 100.
* **Data Series:**
* **Price:** Red line.
* **Earnings:** Dark red dotted line.
* **Dividends:** Blue line.
* **Interest Rates:** Green line.
* **Source:** "source: irrationalexuberance.com/shiller_downloads/ie_data.xls" located in the bottom-right corner.
### Detailed Analysis
**Price (Red Line):** The Price line begins at approximately 20 in 1870 and exhibits significant fluctuations over the period. It generally trends upward, with periods of relative stability and sharp increases. Around 1920, the price reaches approximately 300. A significant dip occurs around 1930, falling to around 100. The price then recovers and experiences a period of growth, reaching approximately 800 by 1960. From 1980 to 2000, the price experiences exponential growth, peaking at approximately 2300 in 2000. After 2000, the price declines and then recovers, ending at approximately 1400 in 2010.
**Earnings (Dark Red Dotted Line):** The Earnings line starts at approximately 20 in 1870 and also shows fluctuations. It generally follows the trend of the Price line, but with more volatility. Around 1920, earnings reach approximately 350. A sharp decline occurs around 1930, falling to around 50. The earnings then recover and grow, reaching approximately 600 by 1960. From 1980 to 2000, earnings experience substantial growth, peaking at approximately 1000 in 2000. After 2000, earnings decline and then recover, ending at approximately 700 in 2010.
**Dividends (Blue Line):** The Dividends line begins at approximately 10 in 1870 and exhibits less dramatic fluctuations compared to the Price and Earnings lines. It generally trends upward, but at a slower pace. Around 1920, dividends reach approximately 100. A decline occurs around 1930, falling to around 20. The dividends then recover and grow, reaching approximately 300 by 1960. From 1980 to 2000, dividends experience moderate growth, peaking at approximately 400 in 2000. After 2000, dividends decline and then recover, ending at approximately 300 in 2010.
**Interest Rates (Green Line):** The Interest Rates line starts at approximately 2% in 1870 and shows significant volatility. It fluctuates between 0% and 80% throughout the period. There are several peaks and troughs, with a notable peak around 1980, reaching approximately 80%. The interest rates end at approximately 20% in 2010.
### Key Observations
* The Price and Earnings lines exhibit a strong correlation, suggesting that stock prices are closely tied to corporate earnings.
* The Dividends line is relatively stable compared to the Price and Earnings lines, indicating that dividends provide a more consistent return to investors.
* The Interest Rates line is highly volatile, reflecting changes in monetary policy and economic conditions.
* The period from 1980 to 2000 shows a particularly strong growth in both Price and Earnings, potentially indicating a period of economic expansion and market exuberance.
* The sharp decline in Price and Earnings around 1930 corresponds to the Great Depression.
### Interpretation
The chart demonstrates the complex relationship between stock prices, corporate earnings, dividends, and interest rates over a long period. The strong correlation between Price and Earnings suggests that stock prices are fundamentally driven by the profitability of companies. However, the chart also highlights the influence of external factors, such as interest rates, on market performance. The volatility of the Interest Rates line suggests that monetary policy plays a significant role in shaping economic cycles and market fluctuations. The period of rapid growth from 1980 to 2000 may be attributed to factors such as globalization, technological innovation, and deregulation. The chart serves as a historical record of financial market behavior and can be used to inform investment decisions and economic analysis. The data suggests that while earnings drive price, external factors like interest rates can significantly impact market stability and growth. The large spike in price around 1990-2000, coupled with high earnings, could indicate a speculative bubble.
</details>
Figure 28: Evolution of the S&P500 and dividends
According to him: "the price-to-earnings ratio is still (as of 2005) far from its historical average from the mid-20th century. Investors place too much trust in the market and overestimate the positive developments of their investments without sufficiently hedging against a market downturn." It is therefore difficult to determine whether the crypto market is inefficient based solely on this information, as cryptocurrencies do not pay dividends.
3.1.2 Behavioral Finance and Market Anomalies
Shiller introduces the concept of behavioral finance. In the crypto market, we mainly think of herd behavior: investors buy simply because other investors are buying. This phenomenon is less visible in day-trading because time scales are too short to draw conclusions about the trend. Indeed, the 2017 bubble still took some time to form and partially burst.
3.1.3 Speculative Bubbles
When it comes to cryptocurrencies, speculative bubbles are often mentioned. It is true that cryptocurrencies provide fertile ground for such phenomena, but this only matters for medium-term investors. A long-term investor will mainly seek to minimize diversifiable risk through cryptocurrencies, while a short-term trader will hope to enter the market before a hype event. Moreover, these hypes can sometimes be artificially created by one or several people, sometimes even behind fraudulent projects. Over time, as projects repeat, fraud risks decrease, and hypes also tend to diminish, making the crypto market increasingly efficient and reducing the possibility of bubbles.
3.2 Informational Inefficiency
We will look at scenarios where information asymmetries allow an individual or a group to achieve superior returns to the market. In such situations, cryptocurrency prices do not reflect all available information.
3.2.1 Market Manipulation
The most famous example is the public use of Twitter by Elon Musk, with each of his crypto-related tweets causing abrupt movements in the crypto market. By deduction, we can imagine similar scenarios involving other public figures, broker managers, intermediaries, etc.
3.2.2 Pump & Dump
Pump & Dump was a strong practice during the early days of crypto hype. It consisted of gathering the largest possible group of users around a well-promoted cryptocurrency. The initiator of the movement would encourage the entire community to engage with the project for a single purpose: to artificially inflate the price of the cryptocurrency. Once the cryptocurrency reached a satisfactory price, the initiatorâwho had taken care to invest as much as possible when the crypto was worth nothingâwould sell everything and exit the project. This type of phenomenon was also seen with ICOs.
3.2.3 Natural Language Processing
Natural Language Processing (NLP) can be used to analyze market sentiment without manually reading content. For example, the bot, whose code is in Appendix H, returns the following results:
<details>
<summary>x3.png Details</summary>
### Visual Description
\n
## Textual Data: Transaction Log
### Overview
The image presents a log of buy and sell transactions, along with the calculated profit for each transaction. The data is presented in a columnar format, with each line representing a single transaction.
### Components/Axes
The data consists of three main components per line:
1. **BUY:** The price at which an asset was bought.
2. **SELL:** The price at which the asset was sold.
3. **Profit:** The percentage profit or loss realized from the transaction.
The data is not presented as a chart or graph with explicit axes, but rather as a list of transactions.
### Detailed Analysis or Content Details
Here's a transcription of the data, with approximate values due to image quality:
1. BUY : 38088.01953125 SELL : 38038.94921875 | Profit = -0.129 %
2. BUY : 37287.16796875 SELL : 37261.2109375 | Profit = -0.07 %
3. BUY : 38840.984375
4. BUY : 38673.09375 SELL : 38657.91015625 | Profit = -0.039 %
5. BUY : 38840.0859375 SELL : 38811.48046875 | Profit = -0.074 %
6. BUY : 38527.58984375 SELL : 38453.19921875 | Profit = -0.193 %
7. BUY : 37744.546875
8. BUY : 36894.6015625 SELL : 36772.21875 | Profit = -0.332 %
9. BUY : 35931.7734375 SELL : 35859.265625 | Profit = -0.202 %
10. BUY : 36071.19921875
11. BUY : 36106.11328125 SELL : 35970.46484375 | Profit = -0.376 %
12. BUY : 36142.52734375 SELL : 36132.40625 | Profit = -0.028 %
13. BUY : 35119.19140625
14. BUY : 35625.203125 SELL : 35562.93975 | Profit = -0.176 %
15. BUY : 36173.3984375 SELL : 36164.9375 | Profit = -0.023 %
16. BUY : 36123.421875
17. BUY : 35625.828125 SELL : 36191.2109375 | Profit = 0.187 %
18. BUY : 35903.81640625 SELL : 35875.41796875 | Profit = -0.079 %
19. BUY : 35428.940625 SELL : 35461.51171875 | Profit = 0.048 %
20. BUY : 35091.828125 SELL : 35539.728515625 | Profit = 0.033 %
21. BUY : 35076.205078125 SELL : 35614.38671875 | Profit = 0.098 %
22. BUY : 35062.8671875 SELL : 35100.203125 | Profit = 0.142 %
### Key Observations
* The transactions alternate between losses and gains, though losses appear more frequent.
* The profit/loss percentages are relatively small, generally within the range of -0.376% to 0.187%.
* There are several incomplete entries (lines 3, 7, 10, 13, 16) where only the "BUY" price is provided, indicating the transaction was not completed or the "SELL" price is missing.
### Interpretation
The data represents a series of short-term trading transactions. The varying profit/loss percentages suggest the trader is attempting to capitalize on small price fluctuations. The incomplete transactions suggest either a strategy of holding positions open or a failure to execute trades at desired prices. The overall trend appears to be slightly negative, with more losses than gains, but the small percentage values indicate a low-risk, low-reward trading style. The data could be used to analyze the trader's performance, identify patterns in their trading behavior, and assess the effectiveness of their strategy. The missing "SELL" data points are a significant limitation for a complete analysis.
</details>
Figure 29: Results from the NLP trading bot
3.3 Operational Inefficiency
The price of Bitcoin can be predicted if one knows in advance the factors likely to influence the network as a whole, or a significant part of it. We will explore whether one or several elements hindering cryptocurrency exchanges can induce market movements.
3.3.1 At the Macroscopic Scale
We can take the example of countries that ban cryptocurrencies. These bans have a notable effect on liquidity, or cases of massive adoption like in El Salvador or the Marshall Islands, or the future rise of CBDCs (such as the digital euro). Environmental concerns, which are becoming a major issue, also hinder liquidity, as cryptocurrencies require a significant amount of electricity resources.
3.3.2 At the Mesoscopic Scale
Certain cryptocurrencies can have a negative impact on others. For example, Monero, with its private blockchain, can very well absorb all the demand for cryptocurrencies that also aim to respect user privacy. The same goes for issues related to transaction speed.
3.3.3 At the Microscopic Scale
There are usage barriers to crypto-assets among households that strongly impact the markets, such as the prohibition of cryptocurrency usage for minors, broker restrictions regarding certain trading positions, security risks and broker compliance concerning suspicious activities, tainted bitcoins, and money laundering (KYC/AML requirements), the impact of taxation on crypto-related capital gains, and various hacks. It can be observed that these phenomena have much less impact on the markets than macro or even meso factors. However, households and discretionary traders still represent a large part of the crypto market landscape.
4 Conclusion
In conclusion, by default, it is not possible to predict Bitcoin since it is an asset very similar in nature to others (notably the stock market), but, as with any market, there are moments when the market is inefficient, and thus it is possible to profit from these moments and predict Bitcoin prices accurately.
Among the limitations, we focus only on the spot market, we do not consider the influence of other cryptocurrencies, and we are limited in our expertise in time series analysis.
Among public policy recommendations, we agree with the view of [Brito et al., 2014] regarding the regulation of brokers and particularly of derivatives products, which are becoming increasingly significant in the crypto market.
Appendix A isRandomBetter( $\Omega,n,k$ )
âŹ
1 # The set Omega is a subset of all cryptocurrencies on the market (between 10,000 and 20,000)
2 Omega = [â1INCH-USDâ, âAAVE-USDâ, âACH-USDâ, âADA-USDâ, âAERGO-USDâ, âAGLD-USDâ,
3 âAIOZ-USDâ, âALCX-USDâ, âALGO-USDâ, âALICE-USDâ, âAMP-USDâ, âANKR-USDâ,
4 âAPE-USDâ, âAPI3-USDâ, âARPA-USDâ, âASM-USDâ, âATOM-USDâ, âAUCTION-USDâ,
5 âAVAX-USDâ, âAVT-USDâ, âAXS-USDâ, âBADGER-USDâ, âBAL-USDâ, âBAND-USDâ,
6 âBAT-USDâ, âBCH-USDâ, âBICO-USDâ, âBLZ-USDâ, âBNT-USDâ, âBOND-USDâ,
7 âBTC-USDâ, âBTRST-USDâ, âCHZ-USDâ, âCLV-USDâ, âCOMP-USDâ,
8 âCOTI-USDâ, âCOVAL-USDâ, âCRO-USDâ, âCRPT-USDâ, âCRV-USDâ, âCTSI-USDâ,
9 âCTX-USDâ, âCVC-USDâ, âDAI-USDâ, âDASH-USDâ, âDDX-USDâ, âDESO-USDâ,
10 âDIA-USDâ, âDNT-USDâ, âDOGE-USDâ, âDOT-USDâ, âENJ-USDâ, âENS-USDâ,
11 âEOS-USDâ, âERN-USDâ, âETC-USDâ, âETH-USDâ, âFARM-USDâ,
12 âFET-USDâ, âFIDA-USDâ, âFIL-USDâ, âFORTH-USDâ, âFOX-USDâ, âFX-USDâ,
13 âGALA-USDâ, âGFI-USDâ, âGLM-USDâ, âGNT-USDâ, âGODS-USDâ,
14 âGRT-USDâ, âGTC-USDâ, âGYEN-USDâ, âHIGH-USDâ, âICP-USDâ, âIDEX-USDâ,
15 âIMX-USDâ, âINV-USDâ, âIOTX-USDâ, âJASMY-USDâ, âKEEP-USDâ, âKNC-USDâ,
16 âKRL-USDâ, âLCX-USDâ, âLINK-USDâ, âLOOM-USDâ, âLPT-USDâ, âLQTY-USDâ,
17 âLRC-USDâ, âLTC-USDâ, âMANA-USDâ, âMASK-USDâ, âMATIC-USDâ, âMCO2-USDâ,
18 âMDT-USDâ, âMINA-USDâ, âMIR-USDâ, âMKR-USDâ, âMLN-USDâ, âMPL-USDâ,
19 âMUSD-USDâ, âNCT-USDâ, âNKN-USDâ, âNMR-USDâ, âNU-USDâ, âOGN-USDâ,
20 âOMG-USDâ, âORCA-USDâ, âORN-USDâ, âOXT-USDâ, âPERP-USDâ,
21 âPLA-USDâ, âPLU-USDâ, âPOLS-USDâ, âPOLY-USDâ, âPOWR-USDâ, âPRO-USDâ,
22 âQNT-USDâ, âQSP-USDâ, âQUICK-USDâ, âRAD-USDâ, âRAI-USDâ, âRARI-USDâ,
23 âRBN-USDâ, âREN-USDâ, âREP-USDâ, âREQ-USDâ, âRGT-USDâ, âRLC-USDâ,
24 âRLY-USDâ, âRNDR-USDâ, âSHIB-USDâ, âSHPING-USDâ, âSKL-USDâ, âSNT-USDâ,
25 âSNX-USDâ, âSOL-USDâ, âSPELL-USDâ, âSTORJ-USDâ, âSTX-USDâ, âSUKU-USDâ,
26 âSUPER-USDâ, âSUSHI-USDâ, âSYN-USDâ, âTBTC-USDâ, âTRAC-USDâ, âTRB-USDâ,
27 âTRIBE-USDâ, âTRU-USDâ, âUMA-USDâ, âUNFI-USDâ, âUNI-USDâ, âUPI-USDâ,
28 âUSDC-USDâ, âUSDT-USDâ, âUST-USDâ, âVGX-USDâ, âWBTC-USDâ,
29 âWCFG-USDâ, âWLUNA-USDâ, âXLM-USDâ, âXRP-USDâ, âXTZ-USDâ, âXYO-USDâ,
30 âYFI-USDâ, âYFII-USDâ, âZEC-USDâ, âZEN-USDâ, âZRX-USDâ]
âŹ
1 # This function returns a list of returns for each asset
2 def loadChanges (Omega):
3 changes = []
4 for asset in Omega:
5 # Import time
6 time. sleep (1)
7 # We use the yFinance library to get the data
8 df = yf. download (asset, period = â2yâ, interval = â1dâ, progress = False)
9 if df. empty:
10 continue
11 oneYear = df. loc [â2021-01-01â: â2022-01-01â]
12 if oneYear. empty or len (df) < 360:
13 continue
14 # Import pandas
15 s = pd. Series (list (oneYear [âCloseâ]))
16 if not s [s. isin ([0])]. empty:
17 continue
18 else:
19 start = oneYear. iloc [0][âCloseâ]
20 final = oneYear. iloc [-1][âCloseâ]
21 change = ((final - start)/ start)*100
22 changes. append (change)
23 print ("len Valid assets : ", len (changes), " (only consider the 1st print!)")
24 return changes
âŹ
1 # This function returns the average of returns
2 def getMeanChanges (Omega):
3 changes = loadChanges (Omega)
4 return sum (changes)/ len (changes)
âŹ
1 # This function randomly selects a portfolio of crypto-assets among those available in Omega
2 def generateRandomPortfolio (Omega, k):
3 randomPortfolio = []
4 for _ in range (k):
5 # Import random
6 randomPortfolio. append (random. choice (Omega))
7 return randomPortfolio
âŹ
1 # This function returns the percentage of portfolios with an average return higher than the average return
2 # of the assets in Omega
3 def getPercentageHigherThanAverage (Omega, NbIter, k):
4 nbHigher = 0
5 averageReturns = getMeanChanges (Omega)
6 for _ in range (NbIter):
7 randomPortfolio = generateRandomPortfolio (Omega, k)
8 randomAverage = getMeanChanges (randomPortfolio)
9 if randomAverage > averageReturns:
10 nbHigher += 1
11 perc = round (nbHigher / NbIter *100)
12 print (f "{k} asset(s) in {NbIter} random portfolio(s)")
13 print ("Average returns :", round (averageReturns))
14 print (f "Percentage of random portfolios above the average : {perc}%")
15 return perc
âŹ
1 # This function returns whether a random portfolio outperforms an average portfolio,
2 # provided that 51% or more random portfolios outperform the average
3 def isRandomBetter (list, NbIter, k):
4 perc = getPercentageHigherThanAverage (list, NbIter, k)
5 if perc < 51:
6 return False
7 else:
8 return True
âŹ
1 # Tests
2 print ("Test 1")
3 print (isRandomBetter (Omega, 10, 10))
4 print ("Test 2")
5 print (isRandomBetter (Omega, 10, 20))
6 print ("Test 3")
7 print (isRandomBetter (Omega, 20, 10))
8 print ("Test 4")
9 print (isRandomBetter (Omega, 20, 20))
10 print ("Test 5")
11 print (isRandomBetter (Omega, 20, 30))
12 print ("Test 6")
13 print (isRandomBetter (Omega, 30, 20))
14 print ("Test 7")
15 print (isRandomBetter (Omega, 30, 30))
16 print ("Test 8")
17 print (isRandomBetter (Omega, 30, 10))
18 print ("Test 9")
19 print (isRandomBetter (Omega, 10, 30))
20 print ("Test 10")
21 print (isRandomBetter (Omega, 40, 5))
Appendix B isSMABetter( $\Omega,n,r$ )
âŹ
1 # This function returns True if the average return of the SMA strategy
2 # is higher than the average of both hold and random strategies
3 def isSMABetter (Omega, n, r):
4 validAssets = 0
5 SMARets = []
6 HoldRets = []
7 RandomRets = []
8 nbBetter = 0
9 for asset in Omega:
10 sma_return = getSMAReturn (asset, n, r)
11 if not sma_return:
12 continue
13 else:
14 SMARets. append (sma_return)
15 hold_return = getHoldReturn (asset)
16 if not hold_return:
17 continue
18 else:
19 HoldRets. append (hold_return)
20 random_return = getRandomReturn (asset)
21 if not random_return:
22 continue
23 else:
24 RandomRets. append (random_return)
25 if sma_return > hold_return and sma_return > random_return:
26 nbBetter += 1
27 validAssets += 1
28
29 sma_average = round (sum (SMARets) / len (SMARets))
30 hold_average = round (sum (HoldRets) / len (HoldRets))
31 random_average = round (sum (RandomRets) / len (RandomRets))
32 print ("Number of valid assets : ", validAssets)
33 print ("SMA average : ", sma_average)
34 print ("Hold average : ", hold_average)
35 print ("Random average : ", random_average)
36 perc = round (nbBetter / validAssets *100)
37 print (f "{perc}% of assets do better with SMA.")
38 if perc < 50:
39 return False
40 else:
41 return True
Appendix C getHoldReturn(asset)
âŹ
1 # This function returns the return of the asset "asset" with the hold strategy
2 def getHoldReturn (asset):
3 df = yf. download (asset, period = â2yâ, interval = â1dâ, progress = False)
4 if df. empty:
5 return False
6 oneYear = df. loc [â2021-01-01â: â2022-01-01â]
7 s = pd. Series (list (oneYear [âCloseâ]))
8 if oneYear. empty or len (oneYear) < 360 or not s [s. isin ([0])]. empty:
9 return False
10 else:
11 start = oneYear. iloc [0][âCloseâ]
12 if start == 0:
13 return False
14 else:
15 final = oneYear. iloc [-1][âCloseâ]
16 return round (((final - start)/ start)*100)
Appendix D getSMAReturn(asset, n, r)
âŹ
1 # This function returns the sum of daily returns
2 # of the asset "asset" with the SMA trading strategy
3 def getSMAReturn (asset, n, r):
4 range = 1+(r /100)
5 df = yf. download (asset, period = â2yâ, interval = â1dâ, progress = False)
6 if df. empty:
7 return False
8 oneYear = df. loc [â2021-01-01â: â2022-01-01â]
9 s = pd. Series (list (oneYear [âCloseâ]))
10 if oneYear. empty or len (oneYear) < 360 or not s [s. isin ([0])]. empty:
11 return False
12 else:
13 oneYear [âSMAâ] = oneYear [âCloseâ]. shift (1). rolling (window = n). mean ()
14 oneYear [âSMAhighâ] = oneYear [âSMAâ]* range
15 oneYear [âSMAlowâ] = oneYear [âSMAâ]/ range
16 oneYear [âSignalâ] = 0
17 oneYear. loc [oneYear [âCloseâ] > oneYear [âSMAhighâ], âSignalâ] = -1
18 oneYear. loc [oneYear [âCloseâ] < oneYear [âSMAlowâ], âSignalâ] = 1
19 oneYear [âChangeâ] = ((oneYear [âCloseâ]- oneYear [âCloseâ]. shift (1))/ oneYear [âCloseâ]. shift (1))*100
20 oneYear [âDayReturnâ] = oneYear [âChangeâ]* oneYear [âSignalâ]
21 ret = round (oneYear [âDayReturnâ]. sum ())
22 return ret
Appendix E getRandomReturn(asset)
âŹ
1 # This function returns the sum of daily returns
2 # of the asset "asset" with a random trading strategy
3 def getRandomReturn (asset):
4 df = yf. download (asset, period = â2yâ, interval = â1dâ, progress = False)
5 if df. empty:
6 return False
7 oneYear = df. loc [â2021-01-01â: â2022-01-01â]
8 s = pd. Series (list (oneYear [âCloseâ]))
9 if oneYear. empty or len (oneYear) < 360 or not s [s. isin ([0])]. empty:
10 return False
11 else:
12 oneYear [âSignalâ] = 0
13 oneYear [âRandomâ] = [random. randint (1,9) for _ in oneYear. index]
14 oneYear. loc [oneYear [âRandomâ] > 6, âSignalâ] = 1
15 oneYear. loc [oneYear [âRandomâ] < 4, âSignalâ] = -1
16 oneYear [âChangeâ] = ((oneYear [âCloseâ]- oneYear [âCloseâ]. shift (1))/ oneYear [âCloseâ]. shift (1))*100
17 oneYear [âDayReturnâ] = oneYear [âChangeâ]* oneYear [âSignalâ]
18 return round (oneYear [âDayReturnâ]. sum ())
Appendix F getRandomPerc( $\Omega$ )
âŹ
1 # This function returns the percentage of assets that follow a random walk
2 def getPercRandom (Omega):
3 nbRandom = 0
4 nbTotal = 0
5 for asset in Omega:
6 time. sleep (1)
7 df = yf. download (asset, period = âmaxâ, interval = â1dâ, progress = False)
8 if df. empty:
9 continue
10 s = pd. Series (list (df [âCloseâ]))
11 if not s [s. isin ([0])]. empty or len (df) < 100:
12 continue
13 else:
14 nbTotal += 1
15 pval = adfuller (df [âCloseâ])[1]
16 if pval > 0.05:
17 nbRandom +=1
18 perc = nbRandom / nbTotal *100
19 return perc
Appendix G getAverageAccuracy( $\Omega,n$ )
âŹ
1 # This function returns the average accuracy percentage of our machine learning model
2 def getAverageAccuracy (Omega, n):
3 accuracies = []
4 for asset in Omega:
5 df = yf. download (asset, period = â1yâ, interval = â1dâ, progress = False)
6 df = df. drop (df [df [âVolumeâ] == 0]. index)
7 df [âRSIâ] = ta. RSI (np. array (df [âCloseâ]. shift (1)), timeperiod = n)
8 df [âSMAâ] = df [âCloseâ]. shift (1). rolling (window = n). mean ()
9 df [âCorrâ] = df [âCloseâ]. shift (1). rolling (window = n). corr (df [âSMAâ]. shift (1))
10 df [âSARâ] = ta. SAR (np. array (df [âHighâ]. shift (1)), np. array (df [âLowâ]. shift (1)), 0.2, 0.2)
11 df [âADXâ] = ta. ADX (np. array (df [âHighâ]. shift (1)), np. array (df [âLowâ]. shift (1)), np. array (df [âCloseâ]. shift (1)), timeperiod = n)
12 df [âATRâ] = ta. ATR (np. array (df [âHighâ]. shift (1)), np. array (df [âLowâ]. shift (1)), np. array (df [âCloseâ]. shift (1)), timeperiod = n)
13 df [âPHâ] = df [âHighâ]. shift (1)
14 df [âPLâ] = df [âLowâ]. shift (1)
15 df [âPCâ] = df [âCloseâ]. shift (1)
16 df [âO-Oâ] = df [âOpenâ] - df [âOpenâ]. shift (1)
17 df [âO-Câ] = df [âOpenâ] - df [âPCâ]. shift (1)
18 df [âRetâ] = (df [âOpenâ]. shift (-1) - df [âOpenâ]) / df [âOpenâ]
19 for i in range (1, n):
20 df [âr%iâ % i] = df [âRetâ]. shift (i)
21 df. loc [df [âCorrâ] < -1, âCorrâ] = -1
22 df. loc [df [âCorrâ] > 1, âCorrâ] = 1
23 df = df. dropna ()
24 t = 0.8
25 split = int (t * len (df))
26 df [âSignalâ] = 0
27 df. loc [df [âRetâ] > df [âRetâ][: split]. quantile (q =0.66), âSignalâ] = 1
28 df. loc [df [âRetâ] < df [âRetâ][: split]. quantile (q =0.34), âSignalâ] = -1
29 X = df. drop ([âCloseâ, âAdj Closeâ, âSignalâ, âHighâ, âLowâ, âVolumeâ, âRetâ], axis =1)
30 y = df [âSignalâ]
31 c = [10,100,1000,10000,100000,100000]
32 g = [1 e -4,1 e -3,1 e -2,1 e -1,1 e0]
33 p = {âsvc__Câ: c, âsvc__gammaâ: g, âsvc__kernelâ: [ârbfâ]}
34 s = [(âsâ, StandardScaler ()), (âsvcâ, SVC ())]
35 pp = Pipeline (s)
36 rcv = RandomizedSearchCV (pp, p, cv = TimeSeriesSplit (n_splits =2))
37 rcv. fit (X. iloc [: split], y. iloc [: split])
38 c = rcv. best_params_ [âsvc__Câ]
39 k = rcv. best_params_ [âsvc__kernelâ]
40 g = rcv. best_params_ [âsvc__gammaâ]
41 cls = SVC (C = c, kernel = k, gamma = g)
42 S = StandardScaler ()
43 cls. fit (S. fit_transform (X. iloc [: split]), y. iloc [: split])
44 y_predict = cls. predict (S. transform (X. iloc [split:]))
45 df [âPred_Signalâ] = 0
46 df. iloc [: split, df. columns. get_loc (âPred_Signalâ)] = pd. Series (
47 cls. predict (S. transform (X. iloc [: split])). tolist ())
48 df. iloc [split:, df. columns. get_loc (âPred_Signalâ)] = y_predict
49 df [âRet1â] = df [âRetâ] * df [âPred_Signalâ]
50 cr = classification_report (y [split:], y_predict, output_dict = True)
51 accuracies. append (cr [âaccuracyâ])
52 return round (sum (accuracies) / len (accuracies) * 100)
Appendix H NLP Trading Bot
âŹ
1 import tweepy
2 import time
3 from textblob import TextBlob
4 import yfinance as yf
5
6 # Authentication
7 key = ""
8 csecret = ""
9 atoken = ""
10 atsecret = ""
11 nb = 500
12 keywords = ["BTC", "#BTC", "Bitcoin"]
13
14 auth = tweepy. OAuthHandler (ckey, csecret)
15 auth. set_access_token (atoken, atsecret)
16 api2 = tweepy. API (auth, wait_on_rate_limit = True, wait_on_rate_limit_notify = True)
17
18 def perc (a, b):
19 temp = 100 * float (a) / float (b)
20 return format (temp, â.2fâ)
21
22 def get_current_price (symbol):
23 ticker = yf. Ticker (symbol)
24 todays_data = ticker. history (period = â1dâ)
25 return todays_data [âCloseâ][0]
26
27 def get_twitter_BTC ():
28 ratios = 0
29 for keyword in keywords:
30 tweets = tweepy. Cursor (api2. search, q = keyword, lang = "en"). items (nb)
31 pos = 0
32 neg = 0
33 for tweet in tweets:
34 analysis = TextBlob (tweet. text)
35 if 0 <= analysis. sentiment. polarity <= 1:
36 pos += 1
37 elif -1 <= analysis. sentiment. polarity < 0:
38 neg += 1
39 pos = perc (pos, nb)
40 neg = perc (neg, nb)
41 if float (neg) > 0:
42 ratio = float (pos) / float (neg)
43 else:
44 ratio = float (pos)
45 ratios += ratio
46 return ratios
47
48 if __name__ == "__main__":
49 for k in range (1000):
50 score = get_twitter_BTC ()
51 min1 = score + (score * 30 / 100)
52 time. sleep (60*5)
53 new_score = get_twitter_BTC ()
54 if new_score > min1:
55 btc_price = get_current_price ("BTC-USD")
56 buy = "\nBUY : " + str (btc_price)
57 with open ("output.txt", "a") as f:
58 f. write (buy)
59 time. sleep (60*5)
60 new_new_score = get_twitter_BTC ()
61 min2 = new_score - (new_score * 30 / 100)
62 if new_new_score < min2:
63 new_btc_price = get_current_price ("BTC-USD")
64 sell_at = " SELL : " + str (new_btc_price)
65 trade_profit = new_btc_price - btc_price
66 perc_profit = trade_profit / btc_price * 100
67 perc_profit_round = round (perc_profit, 3)
68 sell_message = sell_at + " | " + " Profit = " + str (perc_profit_round) + " %"
69 with open ("output.txt", "a") as f:
70 f. write (sell_message)
71 time. sleep (60*5)
72 else:
73 time. sleep (60*5)
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