Virtual reality and a firm’s idiosyncratic risk:e-commerce case1

Anna Loukianova, PhD (in Mathematics)Saint-Petersburg State University

Ekaterina SmirnovaInstitute for Regional Economic Studies RAS

1This research was conducted with the use of library and information resources of the FederalState Budgetary Educational Institution of Higher Education «Saint-Petersburg State University»

A. Loukianova, E. Smirnova Virtual reality and a firm’s idiosyncratic risk: e-commerce case 1 / 40

1 Background

2 The Data

3 Model

4 Results

5 Discussion

6 Software applied & References

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Background

Background

Photo by Lucrezia Carnelos on UnsplashA. Loukianova, E. Smirnova Virtual reality and a firm’s idiosyncratic risk: e-commerce case 3 / 40

Background

Virtual business…

Figure 1: width=2cm

”Even today, not all retailershave embraced data fullyto the point where they thinkof themselves as datacompanies, and it might be whymany companies are suffering”.

(S.M. Datar, C.N. Bowler (as citedin (D. Gerdeman, 2018)a)a https://digital.hbs.edu/data-and-

analysis/on-target-rethinking-the-retail-web#site/

Photo by Zane Lee on Unsplash

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Background

E-commerce market challenges

Study Topic Model/ method(Akter, Wamba,2016)

big data analyticsuse in e-commerce literature review

(Singh et al.,2017)

consumer reviews’helpfulness’ assessmentfor the other consumers

machine learning-basedmodels with the use oftextual features

(Wang et al.,2016) last-mile delivery a network min-cost flow

model(Steinker et al.,2017)

the impact of weatheron fashion e-commerceretailer’s operations

correlation and regressionanalyses

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Background

E-commerce sales growth foresight

“Volume growth in our US e-commerce channel in Q4 2019 waslower than our initial forecast.”

“… we now have a fully operational e-commerce fulfillment centerfor Rugs in the US and are expecting solid growth in 2020-21”

— Thomson Reuters Eikon. (2020). [Balta Industries n.v. (2020, March6).Balta FY 2019 Results [Press release]]. Retrieved March 6, 2020 fromhttps://eikon.thomsonreuters.com/index.html

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Background

What is the study’s aim?

An algorithm development for a company’s sales changesnowcast adjustment for the company’s idiosyncratic risk

Is approached through the objectives:

define the idiosyncratic riskchoose an approach to the idiosyncratic risk modellingtrain the approach on the real data

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Background

What is the idiosyncratic risk

The risk of the company’s cash flows being affectedby the industry factors

The idiosyncratic risk has the following attributes:

the concept has emerged from the studies on the boarder of themarket risk and the firm-specific risk managementthe idiosyncratic risk is traditionally assessed with the use ofaccounting data

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The Data

The data source

Data used in the study is from Amadeus Bureau van Dijk database.

The companies from the industries “Computer programming, consultancyand related activities” and “Computer programming activities” wereselected according to NACE Rev. 2 classification

(Source: Amadeus, Bureau van Dijk).

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The Data

Companies’ country of headquarters

Belgium

Sweden

Romania

United Kingdom

Russian Federation

Hungary

Netherlands

Germany

Czech Republic

0 5 10 15 20Percentage

Cou

ntry

Countries of Companies in the Sample

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The Data

Defining the optimal number of clusters

According to the silhouette method, the optimal number of clusters insidethe sample equals 2 clusters.

0.00

0.25

0.50

0.75

1 2 3 4 5 6 7 8 9 10Number of clusters k

Ave

rage

silh

ouet

te w

idth

Silhouette method

Optimal number of clusters

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The Data

Cluster analysisThe two clusters in the sample evidence that software development marketis low competitive:

the ‘leaders’ have higher market share and tend to obtain higher bookvalue: cluster 1‘all the others’ have similar book value, but tend to have minormarket share: cluster 2

0.0

2.5

5.0

7.5

10.0

0 2 4 6 8Sales growth in 2017

Tota

l Ass

ets

in 2

017

cluster

1

2

Cluster plot

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The Data

The sales growth values’ distribution

Sales growth-1st cluster Sales growth-2nd clusterKolmogorov-Smirnov logistic logisticCramer-von Mises logistic logisticAnderson-Darling logistic gammaAIC logistic logisticBIC logistic logistic

The distribution analysis summarising provided the following conslusion:

sales growth in bowth clusters follow primarily logistic distributionsoftware development clusters are not homogeneous

This conclusion may indicate, that the real situation is rather morecomplicated than only a two-cluster model.

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The Data

Imitation modelling

The data was simulated using the logistic distribution for both clusterswith the parameters:

Sales growth, cluster 1 Sales growth, cluster 2location 0.60 0.46scale 0.07 0.00

There were simulated 998 data sets of both clusters’ artificial sales growthvalues. Each artificial dataset contained 10 thousand observations for eachcluster.

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Model

ModelPhoto by Jared Murray on Unsplash

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Model

The econometric models appliedThe baseline model

The “naive” nowcast, whichimplies that the averageimaginary company’s salesgrowth would be distributedas in the past (base) periodwith the same parameters.

The idiosyncratic risk-based model

The simulation from pair copula model (Aas,Czado, Frigessi, & Bakken, 2009). Copulamodel developed by A. Sklar (as cited in(Genest, Ghoudi, & Rivest, 1995)) has thefollowing definition:

(𝑢1, 𝑢2, …, 𝑢𝑝) =𝑃𝑟(𝐹1(𝑋1) ≤ 𝑢1, …, 𝐹𝑝(𝑋𝑝) ≤ 𝑢𝑝)),

where (𝑋1, …, 𝑋𝑝) – a random vector withcontinuous marginals𝐹𝑖(𝑥𝑖) = 𝑃𝑟(𝑋𝑖 ≤ 𝑥𝑖); C – its associatedcopula or dependence function, defined forall (𝑢1, …, 𝑢𝑝) ∈ [0, 1]𝑝.

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Model

Idiosyncratic risk’s indicator

Kendall’s tau (Kendall, 1938) was applied as the idiosyncratic risk’sindicator:

𝜏 = 2𝑆𝑛(𝑛 − 1),

where 𝑆-the sum of the ranks;𝑛 - the number of observations.

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Model

Copula model selection algorithm

Akaike Information Criterion (H. Akaike, as cited in (Nagler et al.2019)) was used as the base for copula model selection:

𝐴𝐼𝐶 ∶= −2𝑁

∑𝑖=1

ln [𝑐(𝑢𝑖,1, 𝑢𝑖,2|𝜃)] + 2𝑘,

where 𝑢1, 𝑢2− the two cluster companies’ sales growth;𝑖 - an observation index;𝑁 - the number of observations;𝜃 - the copula’s parameter (parameters);𝑘- the quantity of the copula’s parameters.

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Model

Copula model selection

Rotated BB6 90 degrees

Rotated BB1 270 degrees

Frank

10 25 40Percentage

Mod

el

Simulation Modelling for a Model Selection

Copula model selection results indicate Frank copula as the mostpreferrable by the algorithm on the base of AIC criterion.

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Model

Sales growth simulationThe sales growth simulated from Frank copula for two notional companies,representing two clusters. Frank copula was proposed by the AIC-basedalgorithm in most cases.

0.2

0.4

0.60.8

0.2

0.4

0.6

0.8

0

1

2

3

4

5

6

Company 1

Company 2

Pr

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Model

The Models’ BacktestingThree copula models proposed by AIC-based algorithm were backtestedwith the use of 2017-2018 sales growth data.

0.00

0.25

0.50

0.75

1.00

factadj naive BB1(270) BB6(90) Frank WeightedModel

Sal

es c

hang

es a

djus

ted

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Model

The Tukey test

−0.6 −0.4 −0.2 0.0 0.2 0.4

factadj−Weighted

factadj−Frank

Weighted−Frank

factadj−BB6(90)

Weighted−BB6(90)

Frank−BB6(90)

factadj−BB1(270)

Weighted−BB1(270)

Frank−BB1(270)

BB6(90)−BB1(270)

factadj−naive

Weighted−naive

Frank−naive

BB6(90)−naive

BB1(270)−naive

95% family−wise confidence level

Differences in mean levels of variable

The Tukey testindicated statisticallysignificant differencesfor the most of themodels with theadjusted fact values ofthe sales growth andwith each other. Theonly exception isJoe-Gumbel copularotated by 90 degrees,which difference withthe adjusted factvalue is statisticallyinsignificant.

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Results

Results

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Results

The sales growth’s idiosyncratic factors

copula model parameter 1 parameter 2 Kendall’s tauFrank -12.58 - - - -0.72Rotated BB1 270 degrees -4.64 -1.36 -0.78Rotated BB6 90 degrees -4.22 -1.64 -0.77

Kendall’s tau indicates strong degree of the rank negative associationbetween the two clusters’ sales growth simulated. As Kendall’s tau in thestudy is used as the idiosyncratic risk indicator, the conclusion could bemade, that on the e-commerce software development market thecompanies experience the ‘positive’ influence of the idiosyncratic risk.

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Results

A software companies’ sales growth nowcastingalgorithm

Sales changes adjustment

Sales changes distribution analysis

Sales changes simulation

Copula model selection

Sales changes simulation from the copula model

The algorithm of the salesgrowth nowcast proposeddiffers from the naive forecastmodel in two last steps.

The idiosyncratic riskadjusted algorithm producedmore accurate result duringthe process of backtesting.

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Results

E-commerce business model’s connecting points

Advertising Logistics

Packaging

The analysis indicated the followinge-commerce business critical points:

marketing and advertisingpackaginglogistics and supply chainmanagement

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Discussion

Discussion

Current research proposes the idiosyncratic risk concept’s amplification:

the idiosyncratic risk’s indicator measurement with Kendall’s tauto add the idiosyncratic risk’s attribute “positive interconnection withan industry competitiveness level”

To summarise, the idiosyncratic risk could be itself a proxy for anindustry’s level of competition.

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Software applied & References

Software applied:

The following R packages were used in the study:

ggpubr factoextra bookdown knitrreshape forcats webshot kableExtra

RColorBrewer stringr png statsVineCopula purrr rsvg graphics

CDVine readr svglite grDevicesfitdistrplus tidyr magrittr utils

npsurv tibble DiagrammeRsvg datasetslsei tidyverse DiagrammeR methods

survival zoo magick baseMASS ggplot2 dplyr ggpubr

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Software applied & References

References I

Aas, Kjersti, Claudia Czado, Arnoldo Frigessi, and Henrik Bakken. 2009.“Pair-copula constructions of multiple dependence.” Insurance:Mathematics and Economics 44 (2): 182–98.https://doi.org/10.1016/j.insmatheco.2007.02.001.

Akter, Shahriar, and Samuel Fosso Wamba. 2016. “Big data analytics inE-commerce: a systematic review and agenda for future research.”Electronic Markets 26 (2): 173–94.https://doi.org/10.1007/s12525-016-0219-0.

Bache, Stefan Milton, and Hadley Wickham. 2014. Magrittr: AForward-Pipe Operator for R.https://CRAN.R-project.org/package=magrittr.

Balta Industries n.v. 2020. “Balta FY 2019 Results.” Thomson ReutersEikon. https://eikon.thomsonreuters.com/index.html.

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Software applied & References

References II

Brechmann, Eike Christian, and Ulf Schepsmeier. 2013. “ModelingDependence with c- and d-Vine Copulas: The R Package CDVine.”Journal of Statistical Software 52 (3): 1–27.http://www.jstatsoft.org/v52/i03/.

Chang, Winston. 2019. Webshot: Take Screenshots of Web Pages.https://CRAN.R-project.org/package=webshot.

Delignette-Muller, Marie Laure, and Christophe Dutang. 2015.“fitdistrplus: An R Package for Fitting Distributions.” Journal ofStatistical Software 64 (4): 1–34. http://www.jstatsoft.org/v64/i04/.

Delignette-Muller, Marie-Laure, Christophe Dutang, and AurelieSiberchicot. 2019. Fitdistrplus: Help to Fit of a ParametricDistribution to Non-Censored or Censored Data.https://CRAN.R-project.org/package=fitdistrplus.

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Software applied & References

References IIIGenest, C, K Ghoudi, and L.-P. Rivest. 1995. “A semiparametric

estimation procedure of dependence parameters in multivariate familiesof distributions.” Biometrica 82 (3): 543–52.

Gerdeman, D. 2018. “On Target: rethinking the retail website | HarvardBusiness School Digital Initiative.” https://digital.hbs.edu/data-and-analysis/on-target-rethinking-the-retail-website/%7B/#%7Dsite/.

Henry, Lionel, and Hadley Wickham. 2019. Purrr: FunctionalProgramming Tools. https://CRAN.R-project.org/package=purrr.

Iannone, Richard. 2016. DiagrammeRsvg: Export Diagrammer GraphvizGraphs as Svg.https://CRAN.R-project.org/package=DiagrammeRsvg.

———. 2020. DiagrammeR: Graph/Network Visualization.https://CRAN.R-project.org/package=DiagrammeR.

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Software applied & References

References IV

Kassambara, Alboukadel. 2020. Ggpubr: ’Ggplot2’ Based PublicationReady Plots. https://CRAN.R-project.org/package=ggpubr.

Kassambara, Alboukadel, and Fabian Mundt. 2019. Factoextra: Extractand Visualize the Results of Multivariate Data Analyses.https://CRAN.R-project.org/package=factoextra.

Kendall, M. G. 1938. “A NEW MEASURE OF RANK CORRELATION.”Biometrika 30 (1-2): 81–93.https://doi.org/10.1093/biomet/30.1-2.81.

Muller, Kirill, and Hadley Wickham. 2019. Tibble: Simple Data Frames.https://CRAN.R-project.org/package=tibble.

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Software applied & References

References VNagler, Thomas, Ulf Schepsmeier, Jakob Stoeber, Eike Christian

Brechmann, Benedikt Graeler, and Tobias Erhardt. 2019. VineCopula:Statistical Inference of Vine Copulas.https://CRAN.R-project.org/package=VineCopula.

Neuwirth, Erich. 2014. RColorBrewer: ColorBrewer Palettes.https://CRAN.R-project.org/package=RColorBrewer.

Ooms, Jeroen. 2018. Rsvg: Render Svg Images into Pdf, Png, Postscript,or Bitmap Arrays. https://CRAN.R-project.org/package=rsvg.

———. 2020. Magick: Advanced Graphics and Image-Processing in R.https://CRAN.R-project.org/package=magick.

R Core Team. 2020. R: A Language and Environment for StatisticalComputing. Vienna, Austria: R Foundation for Statistical Computing.https://www.R-project.org/.

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Software applied & References

References VI

Ripley, Brian. 2019. MASS: Support Functions and Datasets for Venablesand Ripley’s Mass. https://CRAN.R-project.org/package=MASS.

Schepsmeier, Ulf, and Eike Christian Brechmann. 2015. CDVine:Statistical Inference of c- and d-Vine Copulas.https://CRAN.R-project.org/package=CDVine.

Singh, Jyoti Prakash, Seda Irani, Nripendra P. Rana, Yogesh K. Dwivedi,Sunil Saumya, and Pradeep Kumar Roy. 2017. “Predicting the‘helpfulness’ of online consumer reviews.” Journal of Business Research70 (January): 346–55. https://doi.org/10.1016/j.jbusres.2016.08.008.

Steinker, Sebastian, Kai Hoberg, and Ulrich W. Thonemann. 2017. “TheValue of Weather Information for E-Commerce Operations.”Production and Operations Management 26 (10): 1854–74.https://doi.org/10.1111/poms.12721.

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Software applied & References

References VII

Terry M. Therneau, and Patricia M. Grambsch. 2000. Modeling SurvivalData: Extending the Cox Model. New York: Springer.

Therneau, Terry M. 2020. Survival: Survival Analysis.https://CRAN.R-project.org/package=survival.

Urbanek, Simon. 2013. Png: Read and Write Png Images.https://CRAN.R-project.org/package=png.

Venables, W. N., and B. D. Ripley. 2002. Modern Applied Statistics withS. Fourth. New York: Springer.http://www.stats.ox.ac.uk/pub/MASS4.

Wang, Yong. 2017. Npsurv: Nonparametric Survival Analysis.https://CRAN.R-project.org/package=npsurv.

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Software applied & References

References VIIIWang, Yong, Charles L. Lawson, and Richard J. Hanson. 2017. Lsei:

Solving Least Squares or Quadratic Programming Problems UnderEquality/Inequality Constraints.https://CRAN.R-project.org/package=lsei.

Wang, Yuan, Dongxiang Zhang, Qing Liu, Fumin Shen, and Loo Hay Lee.2016. “Towards enhancing the last-mile delivery: An effectivecrowd-tasking model with scalable solutions.” Transportation ResearchPart E: Logistics and Transportation Review 93 (September): 279–93.https://doi.org/10.1016/j.tre.2016.06.002.

Wickham, Hadley. 2007. “Reshaping Data with the Reshape Package.”Journal of Statistical Software 21 (12).http://www.jstatsoft.org/v21/i12/paper.

———. 2016. Ggplot2: Elegant Graphics for Data Analysis.Springer-Verlag New York. https://ggplot2.tidyverse.org.

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Software applied & References

References IX

———. 2018. Reshape: Flexibly Reshape Data.https://CRAN.R-project.org/package=reshape.

———. 2019a. Stringr: Simple, Consistent Wrappers for Common StringOperations. https://CRAN.R-project.org/package=stringr.

———. 2019b. Tidyverse: Easily Install and Load the ’Tidyverse’.https://CRAN.R-project.org/package=tidyverse.

———. 2020. Forcats: Tools for Working with Categorical Variables(Factors). https://CRAN.R-project.org/package=forcats.

Wickham, Hadley, Mara Averick, Jennifer Bryan, Winston Chang, LucyD’Agostino McGowan, Romain François, Garrett Grolemund, et al.2019. “Welcome to the tidyverse.” Journal of Open Source Software 4(43): 1686. https://doi.org/10.21105/joss.01686.

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Software applied & References

References X

Wickham, Hadley, Winston Chang, Lionel Henry, Thomas Lin Pedersen,Kohske Takahashi, Claus Wilke, Kara Woo, Hiroaki Yutani, and DeweyDunnington. 2020. Ggplot2: Create Elegant Data Visualisations Usingthe Grammar of Graphics.https://CRAN.R-project.org/package=ggplot2.

Wickham, Hadley, Romain François, Lionel Henry, and Kirill Müller. 2020.Dplyr: A Grammar of Data Manipulation.https://CRAN.R-project.org/package=dplyr.

Wickham, Hadley, and Lionel Henry. 2020. Tidyr: Tidy Messy Data.https://CRAN.R-project.org/package=tidyr.

Wickham, Hadley, Lionel Henry, Thomas Lin Pedersen, T Jake Luciani,Matthieu Decorde, and Vaudor Lise. 2020. Svglite: An ’Svg’ GraphicsDevice. https://CRAN.R-project.org/package=svglite.

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Software applied & References

References XIWickham, Hadley, Jim Hester, and Romain Francois. 2018. Readr: Read

Rectangular Text Data. https://CRAN.R-project.org/package=readr.Xie, Yihui. 2014. “Knitr: A Comprehensive Tool for Reproducible Research

in R.” In Implementing Reproducible Computational Research, editedby Victoria Stodden, Friedrich Leisch, and Roger D. Peng. Chapman;Hall/CRC. http://www.crcpress.com/product/isbn/9781466561595.

———. 2015. Dynamic Documents with R and Knitr. 2nd ed. BocaRaton, Florida: Chapman; Hall/CRC. https://yihui.org/knitr/.

———. 2016. Bookdown: Authoring Books and Technical Documentswith R Markdown. Boca Raton, Florida: Chapman; Hall/CRC.https://github.com/rstudio/bookdown.

———. 2020a. Bookdown: Authoring Books and Technical Documentswith R Markdown. https://CRAN.R-project.org/package=bookdown.

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Software applied & References

References XII

———. 2020b. Knitr: A General-Purpose Package for Dynamic ReportGeneration in R. https://CRAN.R-project.org/package=knitr.

Zeileis, Achim, and Gabor Grothendieck. 2005. “Zoo: S3 Infrastructure forRegular and Irregular Time Series.” Journal of Statistical Software 14(6): 1–27. https://doi.org/10.18637/jss.v014.i06.

Zeileis, Achim, Gabor Grothendieck, and Jeffrey A. Ryan. 2020. Zoo: S3Infrastructure for Regular and Irregular Time Series (Z’s OrderedObservations). https://CRAN.R-project.org/package=zoo.

Zhu, Hao. 2019. KableExtra: Construct Complex Table with ’Kable’ andPipe Syntax. https://CRAN.R-project.org/package=kableExtra.

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