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Risk That Can Be Eliminated Through Diversification Is Called

Open up access peer-reviewed chapter

Measuring the Systematic Chance of Sectors within the US Marketplace Via Master Components Analysis: Before and during the COVID-19 Pandemic

Submitted: September sixth, 2021 Reviewed: December 2d, 2021 Published: January 7th, 2022

DOI: 10.5772/intechopen.101860

From the Edited Book

Psychosocial, Educational, and Economic Impacts of COVID-nineteen

Dr. Jose C. Sánchez-García, Dr. Brizeida Hernandez-Sanchez, Dr. António Carrizo Moreira and Associate Prof. Alcides Monteiro

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Abstruse

This research measures the systematic risk of 10 sectors in the American Stock Market, discerning the COVID-19 pandemic flow. The novelty of this study is the use of the Master Component Analysis (PCA) technique to measure the systematic risk of each sector, selecting five stocks per sector with the greatest marketplace capitalization. The results show that the sectors that accept the greatest increase in exposure to systematic risk during the pandemic are restaurants, clothing, and insurance, whereas the sectors that show the greatest decrease in terms of exposure to systematic risk are automakers and tobacco. Due to the results of this study, it seems advisable for practitioners to select stocks that vest to either the automakers or tobacco sector to go protection from health crises, such as COVID-19.

Keywords

  • sectors
  • Principal Component Analysis
  • systematic risk
  • American stock market
  • COVID-19

1. Introduction

Co-ordinate to Sullivan and Sheffrin [i], diversification is the process of allocating capital in a way that reduces the exposure to any detail asset or hazard. Fama and Miller [ii] state that the Capital letter Nugget Pricing Model (CAPM) introduces the concepts of diversifiable and non-diversifiable risk. Synonyms for diversifiable risk are unsystematic risk and security-specific risk. Synonyms for non-diversifiable risk are systematic take chances, beta adventure, and market place adventure. Thus, the CAPM argues that investors should just be compensated for not-diversifiable take chances.

According to Pasini [3], the master Component Assay (PCA) is a method of multivariate analysis. The idea behind the PCA is to reduce the dimensionality of a dataset in which there are a large number of interrelated variables, to maximize the variance of a linear combination of the variables. It is a method practical to data with no groupings among the observations and no partitioning of the variables into subsets y and x . Particularly, the chief components are obtained by applying this method. The first ane is the linear combination with maximal variance, the second one is the linear combination with maximal variance in the orthogonal management to the first primary component and so for the others. Moreover, they are ordered sequentially with the first one explaining much of the variation as it tin can.

With the assist of the PCA, we measure how each sector is affected by market place risk, measured past the beginning component. This article proceeds equally follows. The next section presents relevant literature on PCA and the stock market, and the third section describes our methods and data. The fourth section presents the analyses of the findings, and lastly, we present our conclusions in the fifth section.

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2. Literature review

two.1 Systematic risk

Lakonishok and Shapiro [4] conclude that neither the traditional measure of risk (beta) nor the alternative risk measures (variance or residual standard departure) can explain the cantankerous-sectional variation in returns; only size seems to thing. Gencay et al. [5] propose a new approach to estimating systematic risk (the beta of an asset) and observe that the relationship betwixt the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Campbell et al. [6] country that the systematic risks of individual stocks with similar accounting characteristics are primarily driven by the systematic risks of their fundamentals. Xing and Yan [7] signal that improving bookkeeping information quality causes the systematic risk to subtract, thus having important implications for disclosure decisions, portfolio management, and asset pricing.

ii.2 PCA and the stock market place

Liu and Wand [8] report the Chinese stock market place and find that the performance of the BP model integrating PCA is closer to that of the proposed model in a relatively large sample. Hargreaves and Mani [9], using PCA through a perceptual map, provide a clear motion picture of the winning stocks that should be selected for trading. Wang et al. [10] accomplish a skillful level of fettle, using two-directional two-dimensional PCA and Radial Footing Functional Neural Networks (RBFNN) in the Shangai stock marketplace. Zahedi and Rounaghi [11], studying the Tehran stock exchange, through the usage of artificial neural network models and PCA method, note that prices have been accurately predicted and modeled in the course of a new pattern consisting of all variables. Noby and Lee [12] analyze global financial indices in the years 1998–2012 and betoken that the dynamics of private indices inside the group increase in similarity with fourth dimension, and the dynamics of indices are more similar during crises. Gao et al. [13] experiment the prediction of the closing price of the stock market place with two-dimensional PCA and deep belief networks (DBNs).

Waqar et al. [14] clarify three stock exchanges and show how PCA can assist to amend the predictive functioning of machine learning methods while reducing the redundancy amid the information. Zhing and Enke [xv] forecast the daily direction of the Due south&P 500 Index ETF (SPY) render and evidence that DNNs using two PCA-represented datasets give slightly college classification accuracy than the entire untransformed dataset. Nahil and Lyhyaoui [xvi] show that the structure of the investment decision system can be simplified through the application of kernel PCA. Berradi and Lazaar [17], using both PCA and recurrent neural network model, reduce the number of features from viii to half dozen, giving a good prediction of full Maroc stock price. Cao and Wang [xviii] compare the performance of both PCA and backpropagation (BP) neural network algorithms and discover that the latter has the highest prediction accuracy.

More recently, Wen et al. [19] demonstrate how both PCA and LTSM tin can accurately predict the stock cost fluctuation tendency of Pingon Banking company. According to Liang et al. [xx], using volatility information of grains and softs through PCA and FA, find significant predictive ability in forecasting the RV of the South&P 500. Xu et al. [21], through the utilize of PCA, investigate the Chinese A-shares market over the 2013–2019 period and discover that no matter investor sentiment, stock prices react significantly to rumors as well as when the rumor goes public. Yaojie et al. [22], using PCA and other methods, show the significant ability of the combined international volatility to predict U.s.a. stock volatility. The literature review shows how PCA has been useful in dimensionality reduction, predicting prices, and other features of the stock market, in particular, this paper applies this mathematical technique in an innovative fashion, namely measuring the systematic run a risk in various sectors of the U.s.a. stock market.

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iii. Methods & data

According to Ross et al. [23], systematic hazard is the i that influences a big number of assets, thus having market place-wide furnishings. On the other hand, unsystematic risk is the 1 that affects a single nugget or a group of avails. Since the former cannot be eliminated through diversification is called non-diversifiable risk, whereas the latter is called diversifiable risk because it tin can be eliminated through portfolio diversification.

three.1 Principal Component Analysis

According to [24], PCA is a technique that may exist useful where explanatory variables are closely related. In specific, if there are m explanatory variables in the regression model, PCA will transform them into k uncorrelated new variables. To explain, suppose that the original explanatory variables are denoted 10 1, 10 two, …, xk, and denote the primary components by p i, p 2, …, pk. These chief components are independent linear combinations of the original data

p 1 = α 11 x one + α 12 ten 2 + … + α ane k x k p 2 = α 21 x ane + α 22 x 2 + … + α two k 10 grand … … … … … … … … … … … … … … p 3 = α thou ane 10 one + α grand two ten 2 + … + α k g ten thou

E1

Where αij are coefficients to be calculated, representing the coefficient on the j thursday explanatory variable in the principal component. These coefficients are also known every bit factor loadings. The principal components are derived in such a manner that they are in descending order of importance. In particular, for this study, we take the showtime component as a representative of systematic adventure, that is, the adventure that affects the whole sector and cannot be diversified in a stock portfolio. For this analysis we write a script in Python, specially we use sklearn library to compute the principal components.

We gather all data from yahoo finance, where we include 10 sectors of the US stock market, choosing the biggest 5 companies per stock by market capitalization (Table 1), taking daily log returns of stock prices, and dividing the periods of study into two—the pre-COVID-19 era—January x to May x, 2021.

Ticker Company
Insurance
UNH UnitedHealth Grouping
ANTM Anthem Inc
MMC Marsh & McLennon Companies
CI Cigna Corp
PGR The Progressive Corp
Article of clothing
Burl Burlington Stores Inc
COLM Columbia Sportswear
SFIX Sew Fix Inc
Boot Kicking Barn Holdings
ANF Abercombie & Fitch Co.
Software
AAPL Apple
MSFT Microsoft
GOOGL Alphabet
ADBE Adobe
CRM Salesforce.com, Inc
Tobacco
PM Philip Morris
MO Altria Grouping
BTI British American Tobacco
XXII 22nd Century Group
UVV Universal Corp
Restaurants
MCD Mc Donald's
CMG Chipotle Mexican Grill
YUM Yum! Brands Inc
QSR Restaurants Brands International
DRI Darden Restaurants Inc
Healthcare
UNH UnitedHealth Group
CVS CVS Health Group
HCA HCA Healthcare Inc
MCK Merck
ABC Amerisource Bergen Corp
Banks
JPM JP Morgan Chase
BAC Bank of America
WFC Wells Fargo
MS Morgan Stanley
C Citigroup
Hotels
MAR Marriot
HLT Hilton
LVS Las Vegas Sands Corp
MGM MGM Resorts International
WYNN Wynn Resorts Limited
Airlines
LUV Southwest
DAL Delta Airlines
UAL United Airlines
AAL American Airlines
CEA China Eastern Airlines
Automakers
TSLA Tesla
TM Toyota
F Ford
GM Full general Motors
HMC Honda Motor Company

Table one.

List of sectors/companies.

Source: Yahoo Finance.

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4. Findings

Table ii displays the explained variance per master component by sector, in specific nosotros consider the first main component to be representative of the systematic hazard, whereas the other two are representative of non-systematic risk, that is, the diversifiable take chances. The iii principal components embody the majority of the variance, having a range from 86.3% (restaurants), to 95.5% (airlines) during the pre-COVID period, in dissimilarity, during the COVID flow, the range goes from 88.1% (clothing) to 97.one% (banks). Figure 1 shows the overall results for the explained variance by the start primary component of all sectors analyzed. Earlier the pandemic, the three sectors with the highest systematic risk are—measured by the first master component—banks, free energy, and airlines; and the sectors with the everyman systematic gamble are restaurants, healthcare, and automakers. Nevertheless, during the COVID-19, the three sectors that augmented the exposure to systematic risk are the restaurants' sector with an increase of 39.3%, clothing with 22.2%, and insurance with 14.five%. On the other manus, the sectors that presented a reduction of systematic risk during COVID-19 are automakers with thirteen.ii% and tobacco with 10.3%.

Sector Pre-COVID COVID
First component Second component Third component Total First component Second component Third component Full
Insurance 69.1 15.8 vii.3 92.2 79.iii 9.0 5.iv 93.7
Wear 45.four 22.9 nineteen.2 87.5 55.2 25.1 7.8 88.i
Software 71.five eleven.9 7.7 91.1 79.i 9.7 five.i 93.ix
Tobacco 77.ix 13.0 four.6 95.five lxx.1 21.vii 3.5 95.3
Restaurants 56.3 17.0 thirteen.0 86.three 78.one 9.5 5.5 93.one
Healthcare 62.8 17.0 9.0 88.8 66.i nineteen.0 7.5 92.6
Banks 87.seven 5.0 3.vi 96.3 xc.viii 3.four two.9 97.one
Hotels 77.three 10.iii half dozen.8 94.four 84.6 6.7 5.1 96.iv
Airlines 85.0 half-dozen.one 4.5 95.six 83.i vii.3 5.3 95.vii
Automakers 67.8 21.8 5.8 95.four 58.6 29.iv 6.2 94.ii

Tabular array 2.

Explained variation per primary component in percentage by sector.

Source: Python.

Figure 1.

Explained variance by first component pre-COVID and during COVID past sectors. Source: Own elaboration.

The interpretation of the results is that co-ordinate to our proposed metric of systematic adventure, the sectors that are afflicted the most due to crises such pandemics are the restaurants, the habiliment, and the insurance sector; in contrast, the sectors that evidence reliability during the pandemic are the automakers and tobacco. Due to these results, it seems advisable for practitioners to rely more on stocks that are both in the automakers and tobacco sectors, due to lesser exposure to systematic risk.

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5. Conclusions

The innovation of this research is twofold—first, we utilise PCA to mensurate systematic risk, and 2nd, nosotros discern systematic risk before and during COVID-19. In particular, the sectors that increase the well-nigh in terms of exposure to systematic take a chance are—the restaurants, clothing, and insurance sectors; in contrast, the sectors that show a decrease in systematic hazard during the pandemic are—automakers and tobacco sectors, showing resilience during the pandemic. The results betoken that for portfolio managers it is better to pick stocks that belong to sectors, such as automakers and tobacco sectors in times of health crises such as pandemics, enhancing the benefits of diversification, and creating a shield against the increment of systematic risk due to these kinds of shocks. Consequently, further enquiry could utilise the methodology proposed in this newspaper to measure systematic hazard to improve protect against crises such as COVID-19, thus having practical implications effectually the globe (Video, https://youtu.be/o5SIhEHrRW8).

References

  1. 1. O'Sullivan A, Sheffrin S. Economics: Principles in Action. Upper Sadddle River, New Bailiwick of jersey: Prentice Hall; 2003. ISBN: 013063459X 9780130634597 0130634506 9780130634504
  2. 2. Fama E, Miller 1000. The Theory of Finance. New York: Holt Rinehart & Winston; 1972. DOI: 10.1080/00137917308902739
  3. 3. Pasini Yard. Principal component analysis for stock Portfolio management. International Periodical of Pure and Applied Mathematics. 2017;115(1):153-167. DOI: 10.12732/ijpam.v115i1.12
  4. 4. Lakonishok J, Shapiro A. Systematic risk, total risk and size as determinants of stock market returns. Periodical of Banking & Finance. 1986;10(1):115-132. DOI: 10.1016/0378-4266(86)90023-three
  5. 5. Gencay R, Selcuk F, Whitcher B. Multiscale systematic risk. Journal of International Money and Finance. 2005;24(1):55-70. DOI: 10.1016/j.jimonfin.2004.x.003

Written Past

Jaime González Maiz Jiménez and Adán Reyes Santiago

Submitted: September 6th, 2021 Reviewed: December 2nd, 2021 Published: January 7th, 2022

© 2022 The Author(s). Licensee IntechOpen. This affiliate is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Source: https://www.intechopen.com/chapters/79946