M. Klinczak and E. Wildauer,

“A Comparative Study Between the Brazilian Stock Market and Cryptocurrencies”,

Latin-American Journal of Computing (LAJC), vol. 11, no. 2, 2024.

A Comparative Study

Between the Brazilian

Stock Market and

Cryptocurrencies

ARTICLE HISTORY

Received 01 April 2024

Accepted 21 May 2024

Marjori Klinczak

UFPR, Unifatec-PR

Curitiba, Brazil

marjori.klinczak@unifatecpr.com.br

ORCID: 0009-0009-2028-8359

Egon Wildauer

UFPR, Unifatec-PR

Curitiba, Brazil

egon@ufpr.br

ORCID: 0000-0003-2340-8984

ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

A Comparative Study Between the Brazilian Stock

Market and Cryptocurrencies

Marjori Klinczak

Information Management

UFPR, Unifatec-PR

Curitiba, Brazil

marjori.klinczak@unifatecpr.com.br

ORCID: 0009-0009-2028-8359

Egon Wildauer

Information Management

UFPR, Unifatec-PR

Curitiba, Brazil

egon@ufpr.br

ORCID: 0000-0003-2340-8984

Abstract—The Brazilian Stock Market has been experiencing an

increase in trading volume, and this shows an improvement in

indices. This phenomenon is due to the adoption of Corporate

Governance practices, improvement in institutional environments,

and greater liquidity in national markets. In this scenario, blockchain

technology has become popular in recent years, with various

applications, ensuring transaction identification, authenticity,

reliability, transparency, equity, and interoperability, along with the

emergence of smart contracts. However, the most well-known

cryptocurrency is Bitcoin, followed by Ethereum, which was the

first to allow the use of smart contracts, and Solana, created in 2018,

already holds the fourth position, with great expectations for future

growth. The popularization of this asset class may represent an

investment opportunity; on the other hand, there is research on its

possible relationship with other markets and assets, such as gold, the

dollar, or even the Dow Jones index. However, the literature on this

subject lacks broader research regarding the Brazilian economy,

which, being less stable than those markets known as strong, may

present different results. This is the aim of the research to compare

three cryptocurrencies (Bitcoin, Ethereum, and Solana) with the

Brazilian stock market by means of the non-parametric statistical

test Kolmogorov-Smirnov.

Keywords—Bitcoin, Kolmogorov-Smirnov, Brazilian Stock

Market, Cryptocurrencies

I. INTRODUCTION

According to [2012], blockchain technology has become

popular in recent years due to its potential applications in

various areas. It offers the advantage of being a decentralized

method, what allows transactions to be made directly between

parties, eliminating central banks or intermediaries, and this

method ensures data integrity, anonymity, and immutability.

Among these applications, digital currencies or

cryptocurrencies have gained massive popularity due to their

market values (volatility), ongoing regulatory efforts by some

countries, and the proliferation of new currencies.

These digital currencies are encrypted, operate on a peer-

to-peer network to facilitate digital exchange, and were

developed in 2008, and propose a digital revolution in the

payment system, as stated by [5]. Transactions can be

completed in minutes, which aid in emergency responses, for

example.

Bitcoin, the most well-known and first-created

cryptocurrency, proposes a shift from a centralized to a

decentralized payment system, with no backing from any

central bank. This eliminates territorial barriers and

transaction fees, allowing people without bank accounts to

conduct transactions with just a mobile device and internet

connection.

Indeed, Ethereum allowed the idea of Bitcoin to be

extended to other sectors of the economy through the creation

of smart contracts, making it the second largest cryptocurrency

today [23]. Smart contracts consist of a series of rules that run

on the blockchain [24], and through them, it is possible to

reduce intermediaries and bureaucracy, as they allow the

execution of contracts that were previously done physically, in

a digital form, which ensures transparency and immutability.

Some areas where these smart contracts have already been

successfully applied include: healthcare, the Internet of

Things, the insurance industry, notary and registry offices, the

financial system, reduction in operacional costs, among others

[24, 25], what allows for significant gains in sustainability and

efficiency is the monitoring of data, as it enables the reduction

of operational costs, minimizes environmental impact, and

fosters the development of innovative applications and

services [25].

On the other hand, this rapid growth has created some

scalability issues, such as the transaction execution time, the

block size limit of transactions that can be created, a potential

increase in transaction fees, and the increasing complexity of

mining as the number of transactions grows, which leads to a

higher demand for resources and specialized hardware for

processing. To address some of these problems, Solana was

launched in 2018, and compared to older cryptocurrencies and

its short period of existence, it is already the fourth largest

cryptocurrency in the world, with great potential for growth

and appreciation in the coming years [22].

As they are not a physical product, their value are

generated as users engage in various transactions, such as

trading or store of value. Examples include the situation in

Argentina when the population faced limitations on converting

currency to dollars [9], or during the Brexit vote for the exit

of the UK from the European Union [3]. This ease of

exchange, without the need to visit authorized agents or

research exchange rates, coupled with the ability to use digital

currencies online, makes them a faster and more agile solution

[5].

Research has been conducted on whether Bitcoin

correlates with other indices or currencies. For instance, [10]

investigate correlations between Bitcoin value fluctuations

ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

M. Klinczak and E. Wildauer,

“A Comparative Study Between the Brazilian Stock Market and Cryptocurrencies”,

Latin-American Journal of Computing (LAJC), vol. 11, no. 2, 2024.

and the indices of G7 (Germany, Canada, France, Italy, United

States, Japan, and United Kingdom) and BRICS (Brazil,

Russia, India, China, and South Africa) stock exchanges. [15]

examine cryptocurrency efficiency by creating an index of the

30 largest digital currencies and comparing it with the

American Dow Jones index. [14] study risk propagation

between the Bitcoin market, crude oil, and six other traditional

markets (American stocks, Chinese currency, US Treasury

bonds, gold, bonds, and US currency).

Thus, the general objective of this study is to compare

Bitcoin, Ethereum and Solana volatility and correlation with

the Brazilian stock market and its local currency, the real, by

means of the Kolmogorov-Smirnov non-parametric statistical

test, a statistical method where the data or population lacks

characteristic structures or parameters.

This research is relevant because most existing studies

compare cryptocurrencies with already strong and established

economies, while the Brazilian economy, like that of many

other countries, it is still under development, and it faces

internal issues such as corruption, social problems, and low

education levels in many regions, which are not commonly

present in already developed countries. Consequently, the

country tends to feel changes in the macro and microeconomic

scenario more intensely, bringing greater volatility to the local

currency and stock market. Cryptocurrencies could represent

an opportunity for store of value during times of high

instability if they were to demonstrate greater stability.

Additionally, few studies analyze cryptocurrency market

behavior in relation to other parts of the economy.

One key difference between comparing the cryptocurrency

market with the traditional stock market is that the traditional

market operates within a specific schedule and operating days,

as well as having regulatory bodies and central banks, some of

the major traditional stock markets are: New York Stock

Exchange (NYSE), Nasdaq, Shanghai Stock Exchange,

EuroNext, Japan Exchange Group, Shenzhen, Hong Kong,

Bombay Stock Exchange, London Stock Exchange, and

Toronto Stock Exchange. On the other hand, cryptocurrencies

can trade 24/7 and there are no regulatory bodies or central

banks. This continuous operation leads to greater volatility

with regard to events, which may be reflected in quotes on

days when the traditional market is closed.

The methodology used is exploratory, where data

extraction from the Ibovespa is performed through the Python

library yfinance, and its grouping with the data of the

cryptocurrencies Bitcoin, Ethereum, and Solana. It is

necessary to preprocess these data, as they do not have

opening and closing times, making it possible to trade every

day, unlike stock markets which have specific days and times

for trading. After grouping and filtering the data to only

include those with movements on the same days, the

Kolmogorov-Smirnov test is performed for each

cryptocurrency in relation to the Brazilian index Ibovespa.

The choice of cryptocurrencies was made considering

Bitcoin as the largest and most famous, Ethereum as the

second largest, and Solana due to its rapid growth and future

potential.

II. L

ITERATURE REVIEW

The theoretical framework addresses the particularities of

the Brazilian stock market, Bitcoin, Ethereum e Solana and

probability distributions using the Kolmogorov-Smirnov (KS)

test. Thus, the section on the Brazilian stock market addresses

its growth since its inception, making a comparison with the

cryptocurrencies discussed. The parts related to each

cryptocurrency cover their particularities, creation, and

purpose. Finally, the part about the KS test explains its

functioning and usage.

A. Brazilian Stock Market

The Brazilian stock market, also known as B3 (B3 Brasil

Bolsa Balcão S.A.), is the main financial exchange in Brazil.

The establishment of the stock market and shares in Brazil

dates back to 1817, as referenced in [17], and in the 1990s,

there were several exchanges in the country, gradually unified

into a single one to facilitate transactions and regulations.

Today, it counts with more than 400 listed companies, that

represents various sectors of the economy such as finance,

education, healthcare, agribusiness, among others.

It plays a crucial role in the economy of the country,

facilitating the trading of stocks, commodities, and other

financial instruments. To understand the dynamics,

regulations, and trends of the Brazilian stock market is

essential for evaluating its performance and interactions with

other financial assets [17].

[8] mentions that economic development is fundamental

for the growth of any country, as it creates liquidity and

enables the financing of companies and businesses. According

to [4], the capital market in Brazil experienced expansion in

the 1990s, and the number of investors has been growing every

year due to the ease of investing, reduced brokerage fees, and

the possibility of higher gains compared to savings accounts,

for example. In 2023, the number of investors in B3 reached

19 million, an increase of 46% compared to 2021 [16], with

daily transactions amounting to approximately R$ 36.981

billion in January [22], which demonstrates a significant year-

on-year increase in transactions due to the influx of new

investors. To facilitate investment in a basket of assets and

also to track daily trading volume in the Brazilian market, an

index called Ibovespa (Ibov) was created, which currently

consists

of the 91 main Brazilian stocks, used to demonstrate the

overall market volatility. There are some rules for companies

to be included, such as transaction volume, market value, level

of corporate governance, and each one has a weight, with the

index being updated from time to time.

According to [20], the Ibovespa is calculated in real-time

and represents approximately 80% of the trading volume on

the Brazilian stock exchange, which reflects not only the daily

fluctuations in buying and selling of stocks, but also reflects

the local macroeconomic and political scenario.

In order to compare with the proposed cryptocurrencies,

Table I shows how much the Ibovespa index has risen since

its inception, as well as Bitcoin, Ethereum, and Solana, where

it can be observed that Ibovespa took more than 50 years to

double in value, whereas the cryptocurrencies, in a much

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DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

shorter time, have doubled their value by approximately 50

times, as is the case with Bitcoin.

TABLE I. % APPRECIATION OF ASSETS SINCE THEIR INCEPTION

Year of Creation

Ibovespa 1968 +200.59

Bitcoin 2008 +30,684.82

Ethereum 2013 +52,403.27

Solana 2018 +479,40

B. Bitcoin

According to [10], Bitcoin is a liberal decentralized

financial system that allows financial transactions to be carried

out without the intermediary of banks, brokers or regulatory

entities such as the Central Bank. It was created by [11], a

name that to this day is unknown whether it belongs to a

company, a person or a group of programmers, who presented

the idea as a payment system based on cryptography where

transactions would be made based on the trust of network

nodes.

Its value is then based on the number of available coins

(which are created as transactions and blocks are made),

within a finite limit, and on the digital transactions that are

being executed. This is carried out within a blockchain

network, similar to a ledger, keeping all transactions

transparent and immutable, according to [1].

Since then, several other currencies have emerged, with

Bitcoin having established itself as the largest, with the highest

volume of transactions and which has already reached the

highest market value, above 65 thousand dollars in 2021.

C. Ethereum

Ethereum was created in 2015 and is considered the

second largest cryptocurrency in the world, right behind

Bitcoin [23]. Its prominence stems from the possibility of

creating smart contracts, which allow two or more parties

make agreements digitally and without intermediaries,

extending the function of Bitcoin to other sectors.

It also enables the creation of other decentralized

applications (dApps), and its transaction completion time is

much shorter than with Bitcoin, which takes about 10 minutes,

while Ethereum takes about 20 seconds.

On the other hand, it faces scalability issues and often

charges high fees during periods of high demand, a problem

that has been investigated for the launch of future versions

[23].

D. Solana

According to [21], Solana is a public blockchain platform

that was launched in April 2018, aiming to increase scalability

compared to other cryptocurrencies without compromising

their security and decentralization. Like Ethereum, it supports

smart contracts. Unlike Ethereum, smart contracts on Solana

can be written in any programming language, which also

contributes to its rapid growth.

1 https://docs.scipy.org/doc/scipy/reference/generated/scipy.tats.kstest.html

Thus, despite being created relatively recently (compared

to other cryptocurrencies), it is seen as the fourth largest

cryptocurrency with a great potential for appreciation, having

appreciated by more than 34% in just one week [22].

Therefore, this cryptocurrency was chosen for analysis to

determine if the launch time has any influence on the proposed

tests.

E. Probability Distribution

According to [13], a probability distribution can be

understood as a function that indicates the possibility of

different events occurring within a set of observations, and it

can be either discrete or continuous. Discrete distributions can

be counted, while continuous distributions occur within a

certain range and cannot be presented in a tabular form.

They can also be of the normal or non-parametric type,

with normal distributions generally having a bell-shaped curve

and being more commonly found in nature. As [13] state, they

are typically defined by a mean and a standard deviation. On

the other hand, non-parametric distributions are often

encountered, for example, in the financial market, such as the

application of the Kolmogorov-Smirnov test.

Based on this, the correct identification of distributions

allows for the selection of the best analysis according to the

objective of the study, as applying the wrong method to a data

set can yield unsatisfactory and unreliable results.

Probability distributions are also used to try to predict asset

prices using time series and linear equations, as well as for

portfolio modeling and decision-making, where data mining

or artificial intelligence techniques can also be employed.

F. Kolmogorov-Smirnov Test (KS)

The Kolmogorov-Smirnov test (or KS test, named after the

Russian mathematicians Andrei Kolmogorov and Nikolai

Smirnov) is used to test the equality of probability

distributions, being employed for comparison of 2 samples

(bivariate) or of a sample with a reference value (univariate)

[6].

Thus, the objective of the test is to quantify the distance

between the distributions, with the null hypothesis (H0) being

that the sample is drawn from the distribution, in the case of

the univariate, or that both are part of the same distribution, in

the case of the bivariate [6]. This test can be applied in various

software packages or by developing routines by means of

programming languages, such as Python, where the test can be

applied using the scipy.stats.kstest function

The choice to use the KS test was made because for

samples with a size equal to or greater than 30, it is advisable

to use the KS test, whereas the Shapiro-Wilk test, for example,

is recommended to use with smaller data dimensions, as

referenced in [18].

The formula to calculate the KS is:

D = max|Fn(x) - F(x)|

Where:

• D is the value of the test statistic,

• Fn(x) is the empirical distribution function of the

sample,

ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

M. Klinczak and E. Wildauer,

“A Comparative Study Between the Brazilian Stock Market and Cryptocurrencies”,

Latin-American Journal of Computing (LAJC), vol. 11, no. 2, 2024.

• F(x) is the theoretical distribution function, usually

the CDF (Cumulative Distribution Function) of the

distribution being tested.

The value of D is compared with the table of critical values

to determine if there is a sufficient evidence to reject the null

hypothesis that the two samples come from the same

distribution.

In practice, the KS test allows us to verify if the volatility

of the Ibovespa has any similarity with the volatility of

Bitcoin, Ethereum, or Solana, which enables investors to make

better-informed decisions regarding the allocation of their

assets.

III. S

IMILAR WORKS

Among some of the similar works found, the highlight is

on the comparison of cryptocurrencies, typically Bitcoin, with

some other index or indicator, such as the dollar, stock market

indices like the Dow Jones, as seen in the aforementioned

works by [15] and [10].

In addition to these studies, [14] examined the risk

propagation among the Bitcoin market, crude oil, and six other

traditional markets (US stocks, Chinese currency, US

Treasury bonds, gold, bonds, and US currency) between 2019

and 2020, a period that also included the Covid-19 pandemic.

Among other methods, they used the Kolmogorov-Smirnov

test, and the authors found that during this period, the risk of

all markets increased, suggesting caution to investors during

times of uncertainty.

[2] and [7] compared the correlation between

cryptocurrencies and different currencies such as the dollar,

euro, yen, pound, among others. They concluded that the

correlation between the assets is practically zero and that there

is no dependence between the groups.

The Kolmogorov-Smirnov test has also been used in the

verification of criminal transactions, as seen in the work of

[19], where the Kolmogorov-Smirnov test, Anderson-Darling

test, and Crame-von Mises criterion were used to verify if

transactions on the Bitcoin blockchain network originate from

illegal sources. The BABD-13 database was used to identify

these addresses and serve as a test point. Of the three

applications, the Kolmogorov-Smirnov test had the best result

in detecting illegal addresses, while the Anderson-Darling test

performed better in detecting legal addresses.

These studies are relevant as they allow us to see other

comparisons that have already been made and by what

method, besides enabling a better understanding of

cryptocurrencies and how they relate to the traditional stock

and exchange markets. Moreover, knowing the correlation or

lack thereof between these means may enable investors to

choose investments with lower risk during times of political or

economic instability.

Furthermore, it can be seen that the Kolmogorov-Smirnov

test has been considered relevant by other authors in

2 https://numpy.org/

3 https://pandas.pydata.org/

4 https://scipy.org/

5 https://docs.python.org/3/library/datetime.html

6 https://matplotlib.org/

comparing data that is non-parametric, such as those produced

by the fluctuation of asset and currency values.

IV. M

ETHODOLOGY

The methodology used is exploratory, where data

acquisition and pre-processing were performed, followed by

the bivariate application of the KS test. All development was

done using the Python programming language and the libraries

numpy

, pandas

, scipy

, datetime

, matplotlib

, and

yfinance

. The numpy library handles large data in formats

such as dataframes and arrays, matplotlib is used for

generating graphs, datetime was used to convert the timestamp

to a readable format, pandas is responsible for reading data

from text files, scipy has the implementation of the KS

method, and yfinance was used to obtain data for the Brazilian

index Ibovespa and other assets.

The data preparation was done independently for each

cryptocurrency with which we worked, as their creation dates

are different. They needed to be prepared to have the same

dates as the Ibovespa database.

The Ibovespa data was obtained via the yfinance library

from the Yahoo Finance website, representing the official

quotes of the index, and the choice of this method of obtaining

data was due to the site already having an API that easily

provides the information. This eliminates the need to create a

webcrawler for the official pages of the Brazilian stock

exchange B3, as the API already returns the following data:

Date, Open, High, Low, Close, Volume, and Adj Close. From

the information obtained, only the adjusted closing value (Aj

Close), which represents the closing value of the asset on the

day, was used, and the other values were discarded.

Since the quotes presented by Yahoo Finance are identical

to the official quotes, there are no null or blank values.

Therefore, no value from the Ibovespa needed to be discarded,

grouped, or treated.

A. Bitcoin and Ibovespa

Data collection was carried out in 2 stages. First, historical

Bitcoin data was obtained, followed by the Ibovespa index

data for the same period, as mentioned above. Bitcoin data was

obtained directly from the Kaggle website

(which is a site that

has various databases already compiled in csv format,

therefore, it was not necessary to manually acquire the data

from any cryptocurrency exchange), which already has the

compiled historical database, covering the period from Jan

2012 to May 2021, with minute-by-minute updated data. The

dataset includes Timestamp (Unix time), Open, High, Low,

Close, and Volume, with some values as NaN, indicating a

possible API failure in capturing the data at that moment. In

total, 4,857,377 data points were obtained, with null (NaN)

values disregarded, leaving 3,613,769 data points.

Since the data was obtained from Kaggle, in this case no

additional cleaning was required other than the exclusion of

7 https://pypi.org/project/yfinance/

8 https://www.kaggle.com/datasets/mczielinski/bitcoin-historical-data

ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

null values, which is the main advantage of using the dataset

provided by the site.

The Ibovespa data was obtained via the yfinance library

from the Yahoo Finance website, considering the same period,

totaling 2,263 data points, and only the date and adjusted

closing value (Adj Close) columns were kept, discarding the

others.

Due to a much larger amount of Bitcoin price data, as it

represents minute-by-minute asset acquisition, it was

necessary to aggregate values by date and keep the value of

the median daily quotation to normalize the dataset with the

same pattern as the Ibovespa index, resulting in 3,376 data

points. The difference with the Ibovespa is that Bitcoin

operates every day of the week, 24 hours a day, while the

Brazilian stock market operates only on business days during

a certain period (usually from 10 a.m to 5 p.m), not trading on

weekends, holidays, and overnight.

To solve this problem, the two datasets were merged,

considering only the days when both had quotation values,

resulting in a total of 2,260 data points as final population to

the follow tests. However, when generating the initial graph, a

significant interval gap between the assets was observed

because the Ibovespa data is in Brazilian real, while Bitcoin

price is linked to the dollar.

To solve this problem, the Brazilian real versus dollar

exchange rate data was obtained through the yfinance library

for the same period mentioned, and its median was calculated.

All quotation values were then multiplied by the obtained

median value to approximate the Ibovespa value to that of the

dollar within the proposed period. The preliminary graph with

the values can be viewed in Figure 1, where the green line

corresponds to the Bitcoin value, the orange line to the

adjusted Ibovespa, and the blue line to the Ibovespa in real.

Fig. 1.

Generation of the Bitcoin x Ibovespa x Adjusted Ibovespa quotation

chart. Legend: Green: corresponds to the value of Bitcoin; Orange:

corresponds to the value of the adjusted Ibovespa; Blue: corresponds to the

value of the Ibovespa in real terms.

B. Ethereum and Ibovespa

The Ethereum data was obtained from the Kaggle

platform, which already has it in compiled csv format. Upon

9 https://www.kaggle.com/datasets/prasoonkottarathil/ethereum-historical-

dataset

downloading the database, it comes in 3 files: one with daily

movements, one with minute-by-minute movements, and one

with hourly movements, that covers the period from May 9,

2016, to April 15, 2020. We opted to work with the daily data,

resulting in 1,438 rows and 8 attributes: Date, Symbol, Open,

High, Low, Close, Volume ETH, and Volume USD.

We removed all columns except for Date and Close, which

represent the daily closing value of the asset. The dataset

contains no null values, leaving us with 1,438 records after this

initial preprocessing step.

Since the data was obtained also from Kaggle, in this case

no additional cleaning was required, and the dataset did not

have null values, so no data treatment was necessary.

The steps for obtaining the Ibovespa data are the same as

described above, with only the collection period changed to

start from May 9, 2016, to April 15, 2020. The acquisition also

considered the adjusted Ibovespa base and in Brazilian real.

After unifying the databases, considering common days

across all databases, we were left with a population of 975

data points, as shown in Figure 2. The green line corresponds

to the Ethereum value, the orange line to the adjusted

Ibovespa, and the blue line to the Ibovespa in Brazilian real.

Fig. 2.

Generation of the Ethereum x Ibovespa x Adjusted Ibovespa

quotation chart. Legend: Green: corresponds to the value of Ethereum;

Orange: corresponds to the value of the adjusted Ibovespa; Blue: corresponds

to the value of the Ibovespa in real terms.

C. Solana and Ibovespa

For Solana, a database provided also by Kaggle

was also

utilized, resulting in 1,402 data points spanning from April 17,

2020, to February 17, 2024, compiled on a daily basis. The

dataset contains the following information: Date, Open, High,

Low, Close, Adj Close, and Volume. Only the Adj Close and

Date columns were retained, and as with the Ethereum dataset,

there were no null values and no additional data treatment was

necessary.

For the Ibovespa, the same steps of acquisition mentioned

previously were followed, considering the same period as the

Solana data. After merging the dates present in the databases,

952 data points remained, and the preliminary result is

presented in Figure 3. The green line corresponds to the value

10 https://www.kaggle.com/datasets/ahmadalijamali/cryptourrenciesprices

ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

M. Klinczak and E. Wildauer,

“A Comparative Study Between the Brazilian Stock Market and Cryptocurrencies”,

Latin-American Journal of Computing (LAJC), vol. 11, no. 2, 2024.

of Solana, the orange line to the adjusted Ibovespa, and the

blue line to the Ibovespa in Brazilian real.

Fig. 3.

Generation of the Solana x Ibovespa x Adjusted Ibovespa quotation

chart. Legend: Green: corresponds to the value of Solana; Orange:

corresponds to the value of the adjusted Ibovespa; Blue: corresponds to the

value of the Ibovespa in real terms.

Finally, the KS test was performed for all sets of data,

Bitcoin and Ibovespa, Ethereum and Ibovespa and Solana and

Ibovespa, considering Ibovespa in real terms and for the

adjusted Ibovespa. We use the ktest function from the SciPy

library in the Python language.

This test was chosen because the data does not follow a

normal distribution, as it exhibits a distribution different from

the bell curve. Therefore, solely obtaining means or standard

deviations may not be entirely effective in interpreting the

information. Thus, the Kolmogorov–Smirnov test is used to

compare two samples with each other to verify their equality,

which in our case implies they have similar volatility. We did

not consider using the Shapiro-Wilk test because it is

typically used for smaller datasets.

Finally, the significance test allows for a decision to be

made between two or more hypotheses, as it indicates the

probability of rejecting the null hypothesis when it is true,

considering a p-value of 0.05.

V. R

ESULTS

Just like in the methodology, the results are separated by

the sets of databases worked on: Bitcoin Ethereum and

Ibovespa, all being compared with the Ibovespa index.

The static value corresponds to the percentage value of the

KS test, the static location corresponds to the distance between

the empirical distribution function and the measure in the

observation, and the p-value is the probability of the value

being less than 5%, indicating that the variables have a

probability of being part of the same model, contributing to its

solution.

A. Bitcoin

Thus, Table 2 summarizes the results considering the null

hypothesis that the distributions are equal, Table 4 shows the

results where the Bitcoin distribution is greater, and Table 3

where the null hypothesis states that the Bitcoin distribution is

smaller.

TABLE II. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTIONS ARE EQUAL

Static (%) pvalue

Static

Location

Adjusted Ibovespa 100 0.0 58901.8

Ibovespa in brazilian real 98.23 0.0 37393.49

TABLE III. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTION OF

BITCOIN IS SMALLER THAN THAT

OF THE

IBOVESPA.

Static (%) pvalue

Static

Location

Adjusted Ibovespa 0 1.0 406412.696

Ibovespa in brazilian real 0 1.0 125077.0

TABLE IV. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTION OF

BITCOIN IS GREATER THAN THAT

OF THE

IBOVESPA.

Static (%) pvalue

Static

Location

Adjusted Ibovespa 100 0.0 58901.8

Ibovespa in brazilian real 98.230 0.0 37393.49

Observing Table 3, it is noted that the p-value is equal to

1, meaning it is equal to the level of significance, where the

probability of any element from the sample participating and

impacting the model is low, thus lying outside the confidence

interval, as it neither impacts nor contributes to the model.

On the other hand, the results from Tables 2 and 4 are

identical, demonstrating that Bitcoin may have a distribution

greater than or equal to that of the Ibovespa, both in its

adjusted version and in Brazilian currency (real), indicating

that the study holds a valid significance.

B. Ethereum

Table 5 summarizes the results considering the null

hypothesis that the distributions are equal, Table 7 shows the

results where the Ethereum distribution is greater, and Table 6

shows the results under the null hypothesis that the Ethereum

distribution is smaller.

TABLE V. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTIONS ARE EQUAL

Static (%) pvalue

Static

Location

Adjusted Ibovespa 100 0.0 1292.25

Ibovespa in brazilian real 100 0.0 1292.25

ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

TABLE VI. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTION OF

BITCOIN IS SMALLER THAN THAT

OF THE

IBOVESPA.

Static (%) pvalue

Static

Location

Adjusted Ibovespa 0 1.0 119528.0

Ibovespa in brazilian real 0 1.0 426021.68

TABLE VII. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTION OF

BITCOIN IS GREATER THAN THAT

OF THE

IBOVESPA.

Static (%) pvalue

Static

Location

Adjusted Ibovespa 100 0.0 1292.25

Ibovespa in brazilian real 100 0.0 1292.25

Similarly to the experiment involving Bitcoin and the

Ibovespa index, Table 6 shows a p-value equal to 1,

demonstrating that the probability of its participation and

impact on the model is low. Also similar to the previous

results, Tables 5 and 7 demonstrate that Ethereum has a

distribution greater than or equal to that of the Ibovespa, both

in its Brazilian real form and in the adjusted form, indicating

that the study has a valid degree of significance.

C. Solana and Ibovespa

Table 8 summarizes the results considering the null

hypothesis that the distributions are equal, Table 10 presents

the results where the Solana distribution is greater, and Table

9 shows where the null hypothesis states that the Solana

distribution is smaller.

TABLE VIII. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTIONS ARE EQUAL

Static (%) pvalue

Static

Location

Adjusted Ibovespa 100 0.0 248.46

Ibovespa in brazilian real 100 0.0 248.46

TABLE IX. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTION OF

BITCOIN IS SMALLER THAN THAT

OF THE

IBOVESPA.

Static (%) pvalue

Static

Location

Adjusted Ibovespa 0 1.0 134194.0

Ibovespa in brazilian real 0 1.0 698466.32

TABLE X. SUMMARY OF RESULTS CONSIDERING THE NULL

HYPOTHESIS THAT THE DISTRIBUTION OF

BITCOIN IS GREATER THAN THAT

OF THE

IBOVESPA.

Static (%) pvalue

Static

Location

Adjusted Ibovespa 100 0.0 248.46

Ibovespa in brazilian real 100 0.0 248.46

Similarly to the previous studies involving Bitcoin and

Ibovespa, and Ethereum and Ibovespa, the result shows that

Solana has a greater distribution than or equal to that of the

Ibovespa, both in its Brazilian real form and in the adjusted

form, with a valid significance (Tables 8 and 10). Meanwhile,

in Table 9, the p-value equal to 1 indicates that the contribution

of the data to the model is low or of little importance.

This means that the distributions are weakly correlated,

which from a practical standpoint, means that if the Ibovespa

index is experiencing internal or external pressures and

declining, Bitcoin, Ethereum, or Solana could be an option to

avoid asset loss or be used as a store of value. Since they are

weakly related, this downward volatility would not necessarily

impact cryptocurrencies.

Conversely, if Bitcoin, Ethereum, or Solana were

experiencing downward volatility due to possible regulation

or bans, the Ibovespa index would not necessarily be affected

for the same reasons, potentially being used strategically to

maintain invested capital with lower risk.

Therefore, knowing whether assets of different types have

any correlation can be important for investors to make good

decisions not only for profit but also to protect their capital,

especially in times of great economic or political instability,

such as during wars, uncertainties, or pandemics.

Additionally, Brazil being a developing country may

experience events from external sources with varying degrees

of intensity, especially significant events like Brexit or the

Russia-Ukraine war. This could be considered a positive point

as it puts the country outside the radar of macroeconomic

uncertainties, that makes it a lower-risk investment possibility

in some scenarios, unlike cryptocurrencies, which, is traded

globally 24/7, may experience higher volatility during periods

of uncertainty.

VI. C

ONCLUSIONS

Blockchain technology has become quite popular, and one

of its most well-known applications is Bitcoin, a decentralized

virtual currency that ensures transparency and integrity of

transactions. As a counterpoint to this popularization, its

volatility tends to be high in various periods.

Based on this, the study sought to understand the distance

of its curve with the Brazilian stock market, represented by the

Ibovespa index, which comprises the main Brazilian stocks.

The KS test was then applied under 3 null hypotheses for 3

cryptocurrencies (Bitcoin, Ethereum and Solana): that the

distribution of the cryptocurrency is equal to that of the

Ibovespa, smaller or larger, considering both the index

adjusted in dollars and in Brazilian real.

As final results, the focus of the work is on the distance

that the curves represent through the KS test, that is, the greater

the distance, the greater the dispersion of the data, leading to

the interpretation that they are weakly correlated, or the

adherence of one may not influence the other, as the market

would like (or desire) it to follow (in the trend of value),

ending up with lower (or higher) market values. This is

because the calculated value (p-value) is less than 0.05 or 5%,

demonstrating that the null hypothesis that cryptocurrencies

has a similar distribution to that of the Brazilian market or

larger is true, which can be interpreted as markets still in

development.

The same result occurs for all three analyzed

cryptocurrencies: Bitcoin, Ethereum, and Solana. The test

considering that they would be smaller than the Brazilian

ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

DOI:

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

10.5281/zenodo.12192176

M. Klinczak and E. Wildauer,

“A Comparative Study Between the Brazilian Stock Market and Cryptocurrencies”,

Latin-American Journal of Computing (LAJC), vol. 11, no. 2, 2024.

market showed to be unlikely, and for the tests taking into

account that the Brazilian market would be greater than or

equal to them, similar results were obtained.

As a practical result, the fluctuation of one does not

necessarily imply the fluctuation of the other, which can allow

investors to protect their capital during times of crisis. Given

that Brazil is still a developing country, it usually does not

have a significant participation in external events such as wars

or international political disputes. On the other hand, when the

country experiences instabilities, cryptocurrencies can be a

good source of profit or store of value, again enabling

investors to protect their wealth.

Based on this, the contribution of the study has a social

bias, allowing for greater decision-making and risk

management by providing a better understanding of the

correlation or lack thereof between different assets. And the

choice of the KS test was made because it applies to

continuous distributions (as is the case with stocks and their

values) and its values are more sensitive near the center of the

distribution than to the tails.

As future work, we intend to continue the research by

applying other tests focused on non-parametric distributions

and also focusing on developing markets, but seeking to

extend the analysis to explore additional factors, such as global

economic indicators, money supply, inflation rates, public

perception, confidence in cryptocurrencies, among others,

thereby enriching and broadening the analysis, using this study

as an initial basis.

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ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024

LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024

AUTHORS

PhD student in Information Management at UFPR, Master's degree in

Applied Computing from UTFPR, holds the following specializations in

the ﬁeld of computer science: Specialization in Software Development

in International Markets from UFPR, Postgraduate studies in Internet

Law from FAEL, Postgraduate studies in Ethical Hacking and Cyber

Security from Vincit, Postgraduate studies in Oensive Security and

Cyber Intelligence from Vincit. Bachelor's degree in Internet Systems

Development from FAE. Working since 2007 with web and mobile

development both on the front-end (HTML, CSS, JavaScript, jQuery,

Angular) and on the back-end (PHP, ASP.NET, VB.NET, Solana, Python,

C#, Ionic, React, MySQL, PostgreSQL, SQL Server), and since 2012

owns a company in the ﬁeld of full-stack web and mobile development

services (Mosaic Web). Additionally, has been a Professor in

programming, artiﬁcial intelligence, and data science at Unifatec-PR

since 2019. Holds the following international certiﬁcations: ISO 27005,

Ethical Hacking, LGPD, and ISO/IEC 38507 from Itcerts.

Bachelor in Informatics - Federal University of Paraná, specialist in

Computer Science PUC-PR, improvement in Pedagogy PUC-PR,

master in Production and Quality Engineering UFSC and doctor

in Forestry Engineering, Forest Management - Computational

Production Systems (UFPR, with studies at the Albert Ludwig Freiburg

Universität, Freiburg – Germany). Bureau Manager at Schlumberger

Inc. in the IT area, Coordinator and Director of the Computer Science

area and holds a Bachelor's degree in Information Systems from

Centro Universitário Campos de Andrade in Curitiba. Was professor

at CEPROTEC in Mato Grosso, Sinop-MT. Since 2005 have been

professor at UFPR, member of the CPPD; Deputy Coordinator of

the Postgraduate Program in Information Management - PPGGI; was

AGTI - Technology and Information Governance Advisor at UFPR,

Head of the Information Management Department; participates in the

Strictu sensu Postgraduate Program, line 2, of the Master's Course

in Information Science and Management-PPCGTI-UFPR where he

teaches the IoT and Data Analysis discipline; Statistics and Data

Analysis. Coordinator of the enGlobe, AWARE, UFPR and Technische

Hochschule Ingolstadt - Germany project and Coordinator of the MBA

Management in Engineering specialization course at UFPR.

Marjori Klinczak

Egon Wildauer

M. Klinczak and E. Wildauer,

“A Comparative Study Between the Brazilian Stock Market and Cryptocurrencies”,

Latin-American Journal of Computing (LAJC), vol. 11, no. 2, 2024.