The article is devoted to the study and comparative analysis of the stock quotes dynamics for the world's leading companies in the IT sector and the entertainment industry. Today, these areas are developing the fastest and most powerful, which attracts the attention of investors around the world. This is due to the rapid development of digital communication technologies, the growth of intellectualization and individualization of goods and services, and so on. These spheres have strong development potential, but the question to how their companies' stock quotes respond to the impact of such a natural but crisis phenomenon as the COVID-19 pandemic remains open. Based on the nonlinear paradigm of the financial markets dynamics, the paper considers and conducts a comprehensive fractal analysis of the quotations dynamics for six leading companies (Apple Inc., Tesla Inc., Alphabet Inc., The Walt Disney Company, Sony Corporation, Netflix) in this area before and during the COVID-19 pandemic. As a result of the application of the rescaled range analysis (R/S analysis), the presence of the persistence property and long-term memory in the stock quotes dynamics for all companies and its absence in their time series of profitability was confirmed. The application of the method of sequential R/S analysis made it possible to construct fuzzy sets of memory depths for the considered time series and to deepen the analysis of the dynamics due to the quantitative characteristics calculated on their basis. Taking into account the characteristics of memory depth in the dynamics of quotations made it possible to conduct a comparative analysis of the dynamics, both under the influence of the natural crisis situation and in terms of investing in diferent terms. The peculiarities of the delayed profitability dynamics of quotations for each of the companies are also taken into consideration and compared. The developed recommendations can be used in investment activities in the stock market.
Trading in financial instruments on stock exchanges is increasingly becoming a source of income for various investors. At the same time, investors face the problem of choosing financial instruments in which to invest. For the investor, efective management of their financial
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CEUR Workshop Proceedings (CEUR-WS.org) LGOBE nEvelop-O http://sites.znu.edu.ua/cms/index.php?action=news/view_details&news_id=37228&lang=eng&news_code= resources now – means to get additional benefits in the future. But in order to get these benefits, they need to compare financial instruments and choose the most profitable and least risky among them.
The issue of analyzing the stock markets dynamics in order to develop practical
recommendations for the investor is not new, but it remains relevant and extremely important [
For comparative analysis, traditionally, statistical characteristics of dynamics are used.
Traditionally, statistical methods have been used to confirm the eficient market hypothesis [
An alternative theory of financial markets is the fractal market hypothesis [
The most popular method of studying the fractal properties of dynamics is the Hurst exponent
(R/S analysis) [
Along with the Hurst exponent for the study of financial markets and, in particular, stock
markets, the following indicators are used: Lyapunov exponent (indicator of nonlinear dynamics)
to diagnose the crash of stock markets [
In particular, in the works [
The authors also consider the use of diferent tools of nonlinear dynamics in terms of
different stock markets and their segments. For example, in [
The research and comparison object of this work is the dynamics of shares quotations of leading companies in the IT sector and the entertainment industry. Today, these areas are developing the fastest and most powerful, which attracts the attention of investors around the world. This is due to the rapid development of digital communication technologies, the growth of intellectualization and individualization of goods and services, and so on. These areas have strong development potential, but the question of how stock quotes in this area respond, for example, to the impact of such a natural but crisis phenomenon as the COVID-19 pandemic remains open.
The hypothesis of this work is that the characteristics of long-term memory can also be used for comparative analysis and development of recommendations for investors operating in the stock market. The purpose of this work is to study the characteristics of the memory depth for the stock quotes dynamics of selected companies, their stability under the influence of such a crisis as the global COVID-19 pandemic, conducting a comparative analysis based on them and developing recommendations for investors.
2.1. Materials and methods
Since the behavior of stock prices in the stock markets is mostly not normally distributed or
close to normal distribution [
Let the time series (TS) be considered. The result of applying method _1 is to determine the Hurst exponent ( ) and check its significance based on the application of the mixing test.
The value of the Hurst exponent ∈ [0; 1] determines the presence of certain properties of the dynamics: the value of ∈ (0; 0.5) corresponds to the antipersistent or ergodic TS; the value of = 0.5 (and in its vicinity) indicates a random TS, in which events are random and uncorrelated, the present does not afect the future; the value of ∈ (0.5; 1] indicates that the TS is persistent or trend-resistant, characterized by the presence of long-term memory. The closer the value of to 1, the more correlated the levels of the series.
Recall that the essence of the method of the Rescaled range exponent of Hurst _1 is to
construct the R/S trajectory for the TS and determine the angle of the linear trend, built
on its (R/S trajectory) starting points. At some value of = 0 R/S trajectory changes its
slope quite sharply, i.e. at the point ( 0, 0) the trajectory receives a significant in absolute
value negative gain = (+1) − – there is a break from the trend and there is no return
to the previous trend. It is assumed that at the point 0 the efect of “long-term memory of
the beginning of the series” dissipates. That is, the “breakdown of the trend” demonstrates
the loss of memory about the initial conditions, and also signals (possibly with a lag, ie with
some delay) the exhaustion of the cycle or quasi-cycle contained in the initial segment of this
TS. According to [
However, the method of sequential R/S analysis _2 [
Performing an iterative procedure (method _3) using method _2 and detecting the point
of memory loss at the beginning of the time series for a set of nested segments =
… ⊃ ⊃ −3 (a family of time series difering by the starting point) allows to estimate the
0 ⊃ 1 ⊃
memory depth as a fuzzy set “memory depth of the TS as a whole” [
{( , ( )); ∈ } , ∶ ⟶ [0; 1], assess the uncertainty degree regarding the variety of TS’s behavior variants: – information entropy indicator for the fuzzy set of memory depth ( ) – used to
Note that the scale for estimating the degree of uncertainty is considered to be ordinal by type.
Thus, the use of the selected considered characteristics of the memory depth for time series allows to deepen the comparative analysis of the stock prices dynamics for companies in the IT sector and the entertainment industry. where =
{ , = 1, 2, ... } – natural numbers set – set of basic values for memory depth, ( ) = ( ) – the value of the membership function, which determines the degree of belonging of a natural number (“depth ”) to a fuzzy set ( ) . The function ( ) displays the base value in the interval [0; 1] and displays the degree of possibility (confidence measure) in relation to the membership of the element fuzzy set of memory depth ( ) .
The carrier of the fuzzy set ( ) is the set “supp” ( ) = 0 = { ∈ , = 1, 2, .... ∶ ( ) > 0}.
Therefore, we finally consider the fuzzy set of memory depth of the time series as a whole in the form ( ) = {(, ()), ∈
Important characteristics based on the use of fuzzy memory set (2) are given in [
as a whole – is obtained using the defuzzification procedure: = max ,
∈ 0 ( ) = max (),
∈ 0
=
∑∈ 0[ ⋅ ()]
∑∈ 0 ()
2.2. Stock market overview and input data
Today in the modern stock market there are separate sectors, which on the basis of information
from sites [
The names of the companies for reduction are given according to their stock tickers.
Very high volatility: energy sector – oil (PZE, EC, HOM), gas (GAS, WGR, SPH), coal (BTU, ACI, MEE), alternative fuel (PTOI, GRPEF, BLDP); Industrial sector – industrial electronics (EDIG, SIRC, RGSE), industrial products (BOOM, PLPC, TPIC), machinery (SOHVY, CTEQF, PERT), aviation and space (Boeing, Generaldynamics, Tesla).
High volatility: Basic resources and materials – gold (HGLC, RMRK, NSRPF), metals (ACH, USNZY, GGIFF), chemical products (SKVI, LPAD, NL), forest resources and paper production (AZFL, NKSJF, FBI); Financial services – brokers (GS, LEH, BSC), banks (C, USB, NYB), insurance companies (AIG, XL, JH), management companies (WM, JNS, JNC), stock exchanges (CME, NYX, ICE), mortgage (FNM, FRE, AHM); Media / Entertainment – Worldflix Inc (WRFX), Dolby Laboratories (DLB), Disney (DIS), New-York times (NYT), Netflix (NFLX).
Average volatility: Retail and wholesale – clothing (DEST, BGI, ANF), food (WDRP, CHEF, GPDB), medicines (THCBF, HEWA), household goods (UPPR, RH); Medicine, pharmaceuticals, health care – biotechnology (VKTXW, DMTX, GNLKQ), pharmaceuticals (GMBL, MNZO), honey equipment (ARYC, SMLR, PLSE); Technology sector – Apple (APPL), Nvidia (NVDA), China Intelligence Information Systems (IICN), Genesis Electronics Group (GEGI), Microsoft (MSFT), Google (GOOG); Leisure / Restaurants / Tourism – casino (ERI, NNSR, SGMS), hotel and restaurant business (WTBDY, BCCI, UPZC), travel agencies (ACGX, AIOM, BDGN); Automotive sector – General motors (GM), Tesla Inc (TSLA), Harley Davidson (HDL).
Below average volatility: Telecommunication sector – wire communication (LICT, NULM, OTEL), wireless communication (TALK, NTL, MFOYY).
In 2020, the media and entertainment sector, especially HBO, Disney+ and Netflix, the pharmaceutical and medical sector, and the technology sector, thanks to Tesla, became the most popular in the world among investors.
Among investors, the most relevant financial instrument are shares, which are a security that certifies the participation of its owner in the formation of the authorized capital of the company and gives the right to receive a share of its profits in the form of dividends and accumulated capital.
Stock investing strategies are based on the purpose: − receive a fixed income immediately. To do this, shares with the maximum dividends should be bought. In most cases, these are preferred shares; − buy shares on the electronic exchange platform and wait until their value increases to sell profitably. In this case, you need to choose stocks with maximum growth potential. Experienced financiers prefer such an investment strategy, as after a steady rise in shares, the proceeds from the sale will significantly exceed the size of any dividends.
However, investing in stocks has both advantages and disadvantages. The advantages include reliability, protection against fraud, small amounts at the start of the investment, acceptable liquidity (quite high) and reliability. The disadvantages of stocks can be described as the complexity of investing, because any investment requires an understanding of the process and nuances.
Another disadvantage is the inaccessibility of investing for most Ukrainian investors, despite the fact that although almost everyone can open a brokerage account technically, not everyone will be able to put a serious amount on it. The requirements of financial monitoring and the low level of tax culture lead to shadowing of revenues. Because of this, many Ukrainians simply cannot invest in this way.
And the last disadvantage, but very significant – is the risk of losing the value of the asset. Securities can lose quite sharply in price. If, except in case of force majeure, this is not typical for real estate and individual business, then for stocks it is a reality. Unsuccessful financial statements and securities lose in value. Unsuccessful actions of the government and the price of the financial instrument falls. At the same time, the value of securities may not be restored.
Therefore, to choose a financial instrument, both an experienced investor and a beginner need to conduct a thorough analysis and choose the best instruments with minimal risk to themselves.
Today, the IT industry in quarantine is developing the fastest, modernizing and finding ways to move production to remote work. In second place in terms of development is the field of cinema. Many cinema companies are creating online broadcasting services for the library of iflms and TV programs to compete between companies and attract more consumers.
Financial instruments were selected for comparative analysis – shares of the six most famous companies in the world in the IT sphere and entertainment industry.
Apple Inc. — American technology company with an ofice in Cupertino (California), which
designs and develops consumer electronics, software and online services [
Tesla Inc. – American car company – startup from Silicon Valley. Focused on the design,
manufacture and sale of electric vehicles and their components. The main production facility is
the Tesla plant [
Alphabet Inc. — an international conglomerate of companies created on October 2, 2015 by
American programmers and entrepreneurs Larry Page and Sergey Brin, which includes Google
and other companies they owned directly or through Google [
The Walt Disney Company — one of the largest corporations in the entertainment industry
in the world. Founded on October 16, 1923 by brothers Walter and Roy Disney as a small
animation studio, as of June 2015 it is one of the largest Hollywood studios, the owner of 11
theme parks and two water parks, as well as several television and radio networks, including
American Television and Radio ABC [
Netflix Inc. — an American media service provider and production company. As of April
2020, Netflix has 182 million subscribers worldwide, of which 69 million are in the United States.
Netflix is available in all countries and regions except mainland China (due to local restrictions),
Iran, Syria, North Korea and the Autonomous Republic of Crimea (due to US sanctions). The
company also has ofices in Brazil, the Netherlands, India, Japan and South Korea. Netflix is a
member of the American Film Association [
Sony Corporation is one of the world’s largest media companies. Sony manufactures consumer
and professional electronics and other high-tech products. In addition, Sony is one of the world’s
largest media companies, with the record label Sony BMG (jointly with Bertelsmann), Columbia
Pictures and TriStar Pictures, as well as a complete archive of MGM films (jointly with Comcast)
[
Stock prices dynamics for the period from September 2017 to September 2020 (daily values) for selected companies can be seen in the figure 1.
The input data for the study are daily, weekly and monthly prices for the period from
09/11/2017 to 09/08/2020 obtained from the site Investing.com [
For the selected time series (TS), let’s define the following notation: = ⟨ ⟩; ∈ ( 1, 6), (7) where ∈ {, , } , index denotes daily, – weekly, – monthly prices;
= 1 – corresponds to the time series of Apple Inc., = 2 – time series of Tesla Inc., = 3 – time series of Alphabet Inc., = 4 – time series of The Walt Disney Company, = 5 – time series of Netflix Inc., = 6 – time series of Sony Corporation. 2.3. Results For a general understanding of the series dynamics based on the input data, historical volatility is calculated for each selected investment instrument (table 1).
Let’s move on to the comparative analysis of the stock markets using the methodology of fractal analysis and calculation of memory depth characteristics. Note that February and March 2020 were the worst months for global stock markets since 2008. Stock indexes lost tens of percent, and experts said that the 11-year growth cycle since the last financial crisis has come to an end.
The cause of the fall – an outbreak of coronavirus, which grew into a pandemic. Against
the background of the COVID-19 outbreak, investors have reconsidered their views on the
future of the global economy [
In connection with the consequences of the pandemic, the dynamics of stock prices for six corporations before and after the pandemic were analyzed. According to figure 1, we can see a fairly stable situation of all corporations until 2020, fluctuations in company share prices are quite small, almost imperceptible, but from February to March 2020, this situation is changing.
Consider the obtained values of the Hurst exponent (table 2).
They indicate that all time series throughout the study period from September 2017 to
The method of sequential R/S analysis [
Based on the fuzzy memory depth using formulas (3) - (6), the following characteristics of
the time series dynamics were calculated: the greatest value of the memory depth ; the
gravity center for the fuzzy set of memory depth ; the most common memory depth and
information entropy ( ) [
When studying the dynamics of stock prices before the pandemic, it was found that for TS 1 the most often memory is stored for 5 and 6 days, where the gravity center to the fuzzy set February 2020 are persistent, i.e. have a long-term memory. The value of the Hurst exponent for all time series is in the range ∈ [0.89; 0.95] . For mixed values, the Hurst exponent is in the range ∈ [0.56; 0.66] . The results of fractal analysis TS during a pandemic show that the dynamics of all financial instruments for the entire study period from February 2020 to September 2020 is persistent, i.e. have long-term memory. The value of the Hurst exponent for all time series is in the range ∈ [0.90; 0.92] . For mixed values, the Hurst exponent is in the range ∈ [0.61; 0.71] . 1 2 3 during the pandemic of memory depth is 21.8, and the most common memory depth is 7, for TS 2 – during 4 and 5 days, where = 8 and
= 21.7, for TS 3 – during 5, 8 days, where the center of gravity is 18.7, and the memory depth, which is most common from the fuzzy set of memory depths – 6, days, where for TS 4 – during 6 and 7 days, where the center of gravity is 17.4, and the memory depth, which is most common from the fuzzy set of memory depth – 5, for TS 5 – during 6 and 8 = 5 and = 19.7, and for TS 6 – during 5 and 9 days, where the center of gravity is 17.8 and the depth of memory is often 8, respectively (the number days is given in ascending order of the value of the membership function , ≥ 0.60 ).
Let’s analyze the results of a consistent R/S analysis for the dynamics of stock prices during the pandemic. Long-term memory changed for all tested TS: for TS 1 the memory is stored for 7 and 11 days, for TS 2 – 7 and 9 days, for TS 3 – 5 and 8 days, for TS 4 – 4, 5 and 10 days, for TS 5 – 8 and 9 days, and for TS 6 – 5 and 7 days (the number of days is given in ascending order of the value of the membership function , ≥ 0.60 ). According to the results, during the pandemic period, long-term memory in some TS is shifted.
The following conclusions can be drawn from the analysis of the fuzzy set of memory depth. The most stable and trend-resistant series were TS 2, 3 and 6. For these time series, the indicator is at a relatively high level and does not decrease during the pandemic, which indicates the trend stability of the time series. Shannon’s entropy decreases (for TS 2, 3), which shows a decrease in uncertainty, or remains unchanged (for TS 6). It should be noted that for TS 2 the entropy was at the highest level, however, during the pandemic this indicator improved. That is, the crisis in the economy did not afect the increasing uncertainty of the time series.
decreased, which showed instability of these series to external risks.
For TS 1 negative is a significant decrease in from 7 to 3. TS 4 was marked by an increase in the uncertainty (entropy), and for TS 5, despite the decrease in entropy, and
It should be noted that the Hurst exponent of all series is at a high level, which indicates the persistence of the series. analysis of stock profitability.
In addition to the fractal analysis of corporate stock prices, we conduct a corresponding In this regard, the TSs of stock profitability are built and studied: = ⟨ ⟩ (8) with lag = 1, 7, 10, 14, 21, 28, 30, 37, 42 . ( = 1 ) indicate the randomness of TSs (table 6).
(−) where = 1 – corresponds to the time series of Apple Inc., = 2 – time series of Tesla Inc., = 3 – time series of Alphabet Inc., = 4 – time series of The Walt Disney Company, = 5 – time series of Netflix Inc., = 6 – time series of Sony Corporation; = − (−) ∗100% ‒ price profitability on day relative to price on day ( − ), i.e. profitability
The calculation results of the Hurst exponent for time series of profitability with the lag 1 The results of the application of The Hurst’s rescaled range method for profitability time series before the pandemic and during the pandemic
TS Pd1 Pd2 Pd3
As a result of the study of the time series of the delayed profitability, it was found that the nature of the dynamics of profitability varies from stochastic to persistent depending on the magnitude of the time lag and acquires the characteristics inherent in the “parent” TS of price. But the lag for each time series is diferent:
TS 1 (Apple), 6 (Sony) acquire persistence at a lag(s) value of 14 days, and the Hurst exponent is already 0.70;
TS 3 (Alphabet), 5 (Netflix) acquire persistence at a lag(s) value of 10 days, and the Hurst exponent is already 0.74;
TS 4 (Disney) acquires persistence at a lag(s) value of 7 days, and the Hurst exponent is already equal to 0.71;
TS 2 (Tesla) acquires persistence at a lag(s) value of 21 days, and the Hearst index is already 0.70.
A graphical representation of the values of the Hurst exponent for profitability TS with diferent lag is shown in figure 2.
Therefore, the time series 4 (Disney) acquires persistence the fastest. We observe that with increasing lag, the Hurst exponent increases and becomes suitable for study by fractal analysis. This allows the investor to unify the analysis tools and forecast profitability in accordance with the characteristics of the price dynamics of a particular investment instrument.
Lack of investment strategy can cause loss of funds and complete frustration in the choice of a particular stock market by the investor. To reduce the level of risk, it is necessary to choose how long the wherewithal will be invested before making the investment. According to the term of investment, there are three strategies: short-term, medium-term and long-term strategy.
Short-term investment can last from a few days to 3 months. The medium term lasts from 3 months to 3 years. Long-term – from 3 years.
The results of the research allow us to ofer the following (certain) recommendations for choosing an investment strategy for each selected security.
The first factor for choosing an appropriate strategy for investing in stocks is usually the price and volatility of the security and the sector as a whole. The media and entertainment sectors, automotive and technology have average volatility, ie price change, the rate of change is average. However, the selected financial instruments are characterized by a fairly high historical volatility (table 1). It follows that for all selected financial instruments, we can recommend a short-term investment strategy (table 7) with the possibility of investing for a small period.
Netflix and Disney remain the best option for a short-term strategy, because due to the pandemic, which will cover the world for another one or two years, the stock prices of these companies will be constantly volatile. The price will fluctuate depending on the growth of demand for remote viewing of movies, series and shows, or the return of demand again for watching movies in regular cinemas. As a result, there is a constant risk of losing money if you invest them for more than 3 months.
Consider the second investment strategy – medium-term. To do this, we turn to the analysis of the results of complex fractal analysis. All series are persistent both before the pandemic and now, ie persistent (tables 2, 3). However, the profitability of instruments is not persistent, and the time series of delayed profitability with diferent time lag was used to study the level of trend stability (figure 2). Due to which it was determined that Tesla Inc., Apple Inc. and Sony gained the fastest profitability, ie you can invest in these shares for more than a week or two. Because in 7–14 days, the yield becomes persistent and it can be predicted for more than three months. These shares will generate passive income and can be reinvested again. In addition, these corporations are quite ambitious and have grand plans for the future, such as space exploration and shuttle construction, the creation of an electric car, etc., so the prices of their securities will only increase.
Alphabet Inc. has the most stable results, this corporation is often chosen for long-term investment, the results of volatility are the lowest, because the price does not fluctuate strongly enough, the dynamics of the time series is persistent, deferred profitability becomes persistent with a lag of 10 days. The results of the memory depth study show the stability of the corporation even under the influence of natural external factors such as the COVID-19. Stable memory depth characteristics during the pandemic were also demonstrated by shares of Tesla Inc. and Sony (table 7).
Note that these recommendations are formed only on the basis of this study and they may change depending on changes in the dynamics of financial instruments under the influence of various external and internal factors.