Unveiling the directional network behind the financial statements data using volatility constraint correlation
aa r X i v : . [ q -f i n . GN ] A ug Unveiling the directional network behind thefinancial statements data using volatility constraintcorrelation
Tomoshiro OchiaiFaculty of Social Information Studies, Otsuma Women’s University,12 Sanban-cho,Chiyoda-ku,Tokyo 102-8357, Japan,e-mail: [email protected] C. NacherDepartment of Information Science, Faculty of Science, Toho University,Miyama 2-2-1, Funabashi, Chiba 274-8510, Japan,e-mail: [email protected] 19, 2020
Abstract
Financial data, such as financial statements, stores valuable andcritical information to potentially assist stakeholders and investors op-timize their capital so that it maximizes overall economic growth. Sincethere are many variables in financial statements, it is important to de-termine the causal relationships, that is, the directional influence be-tween them in a structural way, as well as to understand the relatedaccounting mechanisms. However, the analysis of variable-to-variablerelationships in financial information by using the standard correla-tion functions is not sufficient to unveil directionality. Here, we use thevolatility constrained correlation (VC correlation) method that enablesus to predict the directional relationship between the two variables. Tobe precise, we apply the VC correlation method to five major finan-cial information variables (revenue, net income, operating income, owncapital and market capitalization) of 2321 firms in 28 years from 1990to 2018 listed on Tokyo Stock Exchange in order to identify whichvariables are influential and which are susceptible variables. Our find-ings show that operating income is the most influential variable andmarket capital and revenue are the most susceptible variables amongthe five major accounting variables. Surprisingly, the results are dif-ferent from the existing intuitive understanding suggested by widelyused investment strategy indicators known as PER and PBR, whichreport that net income and own capital are the most influential vari-able on market capital. Taken together, the presented analysis mayassist managers, stakeholders and investors to improve performance of nancial management as well as optimize financial strategies for firmsin future operations. The advent of information technology has made it possible to storeand classify large amount of financial data in real-time in an unprece-dented scale. The analysis of large volume of data by using latestdata science techniques may unveil new mechanisms and associationsbetween financial entities and variables that may lead to significantimprovements of investment strategies[1, 2, 3, 4, 5].Financial statements are important for decision making such asinvestment and M&A (Mergers and Acquisitions) by shareholders, in-vestors, managers. They help to improve optimal allocation of capitaland promote whole economies. Data analyses for financial statementshave been done in various contexts such as fraud detections and firm’searnings prediction [6, 7, 8, 9, 10, 11, 12, 13, 14].Here we collect five main financial accounting data, namely revenue,operating income, net income, own capital and market capitalization,corresponding to more than two thousands firms listed on the TokyoStock Exchange (TSE), which is a standardized equities market inJapan.Although standard data analyses may reveal positive correlationtendencies among most of these accounts values, the causality betweenthem has not been sufficiently investigated and clarified from a datascience view point, because the causality or directionality of influencebetween them is difficult to determine by using standard methods suchas standard correlation coefficients.In [15, 16, 17], we introduced volatility constrained correlation (VCcorrelation) method, which enables us to determine the directionalityof influence, a key feature that could not be determined by only apply-ing standard correlation analysis techniques. In [15], we determinedthe directionality of influence between Japanese Nikkei 225 stock in-dex and other financial markets. In [16], we applied VC correlation todaytime and overnight return and confirm the amplification of nega-tive correlation between them and consistency with causality of time.Moreover, we applied VC correlation to biological data, where generegulation interactions are identified by VC correlation with high ac-curacy [17].Here, we determine the direction of influence among the five majoraccounting variables by using data-driven Volatility Correlation (VC)technique from the accounting data of 2321 firms from 1990 to 2018listed on Tokyo Stock Exchange. The observed directionality networkof accounting variables enables us to observe for the first time the di-rection of influence between accounting variables, which can be usedto suggest investment strategies as well as in financial operations man-agement. Data
We use the five major annual accounting data (revenue, operating in-come, net income, own capital, market capitalization) of 2321 firmsin 28 years from 1990 to 2018 listed on Tokyo Stock Exchange. Here,we exclude accounting data of banks, securities, non-life insurance, andlife insurance companies, whose accounting data structure are differentfrom general business companies.
Let r c ( t ), i c ( t ), p c ( t ), o c ( t ), m c ( t ) be revenue, net income, operatingincome, own capital and market capitalization of company c in year t ,respectively.We define the rate of change of the five accounting data (revenue,income, operating income, own capital and market capitalization) asfollows. The rate of change of revenue, own capital and market capitalare respectively defined by R cr ( t ) = r c ( t + 1) − r c ( t ) r c ( t ) , (1) R co ( t ) = o c ( t + 1) − o c ( t ) o c ( t ) , (2) R cm ( t ) = m c ( t + 1) − m c ( t ) m c ( t ) . (3)In a similar way, the rate of change of net income and operatingincome are respectively defined by R ci ( t ) = i c ( t + 1) − i c ( t ) r c ( t ) , (4) R cp ( t ) = p c ( t + 1) − p c ( t ) r c ( t ) . (5)Here, for the definition of R ci ( t ) and R cp ( t ), we use revenue r c ( t ) asthe denominator instead of i c ( t ) and p c ( t ) in order to properly nor-malize the rate of change. The reason is as follows. If we use netincome i c ( t ) or operating income p c ( t ) as the denominator, they couldbe negative value or exceedingly small value. In such a case, the rate ofchange of income and operating income could take an extreme value,which is difficult to handle. Let R cs ( t ) be the change rate of accounting variable s in year t forcompany c defined in the previous section. Here s can be r , i , p , o , m (resp. revenue, net income, operating income, own capital, and marketcapitalization). he average and standard deviation of R cs ( t ) for a given period[ t i , t f ] are given by E ( R cs ) = 1( t f − t i ) X t i ≤ t 05, we can determine the directionality to be from the firstitem s to the second item s ′ (resp. from s ′ to s ). If p-value is morethan 0 . 05, we can not say anything about directionality. We show thedirectionality in the most right column in Table 2.For example, at the first line in Table 2, we can see the result ofthe pair of net income(i) and market capitalization(m) (i.e. the firstvariable is net income(i) and the second variable is market capital-ization(m).) Because E ∆ F [ i, m ] of the pair [ i, m ] is positive (0 . i, m ] is from the net income(i) to themarket capital(m) with very high statistical significance (p-value is2 . × − ). We show the directionality as a right arrow ( → ) in therightmost column at the first line in Table 2.As a complementary information, Fig, 2(a) shows the distributionof the correlation coefficients between net income and market capi-talization C c [ i, m ]. Fig, 2(b) shows the distribution of the differenceof VC correlations F c [ i, m ]. On the other hand, Fig. 3(a) shows thedistribution of the correlation coefficient between revenue and mar-ket capitalization C c [ r, m ]. Fig. 3(b) shows the distribution of thedifference of VC correlation F c [ r, m ].We can see that the distribution of the difference of VC correlation F c [ i, m ] in Fig. 2(b) is not symmetric, comparing with Fig. 3(b). Thisfinding suggests a directionality from net income to market capitaliza-tion. It is worth mentioning that Fig. 2(b), the asymetry looks smallbut the number of samples are great, which implies enough statisti-cal significance for directionality with very small p-value (p-value is2 . × − ) as we can see at the first line in Table 2.Although Table 1 and Fig. 1 show that all the correlations be-tween the accounting variables are positively related, some pairs ofthe accounting variables have directionality of influence with statisti-cal significance shown in Table 2. From the directionality shown inTable 2, we show the directionality network in Fig. 4. The six pairsof the average of the difference of VC correlation E ∆ F has statistical ignificance and we show them as six oriented links (six pairs of theaccounting variables) in Fig. 4. Comparing Fig. 4 with Fig 1, weclearly see the directionality between the accounting variables.In our analysis, the accounting variables belong to several financialaccounting categories. Revenue, operating income, and net income aremajor accounting variables belonging to income statement in financialstatements. From an accounting point of view, revenue is the firstitem to calculate, secondly operating income is calculated, and net in-come is the last variable to compute. Own capital is an accountingvariable belonging to balance sheets, which is equal to total asset sub-tracting liabilities. Market capitalization is the total market value ofpublicly traded shares, which is equal to the stock price multiplied bythe number of shares. By bearing in mind these important concepts,our data-driven analysis has derived the following main findings.Firstly, in Fig. 4, we can see that operating income is a sourcenode, while market capitalization and revenue are sinking nodes. Inother words, operating income is the most influential accounting vari-able, while the market capitalization and the revenue are the mostsusceptible variables. Market capitalization is determined by balanceof supply and demand of market participants and shareholder’s strat-egy which are mainly affected by the result of operational managementof firms. Therefore, it is reasonable that market capitalization is themost susceptible variable.Second, and more importantly, in Fig. 4, we can see that netincome and own capital are influential to market capital. This can beunderstood as follows. Market participants often evaluate share priceby P/E ratio (price to earnings ratio) and P/B ratio (price to bookRatio) computed from net income and own capital. Therefore, netincome and own capital are thought to be the most influential item tomarket capital (because most investors often use P/E ratio and P/Bratio as indicators). However, Fig. 4 reveals that operating income ismore influential to all accounting variables than net income and owncapital, which are only middle of influence flow. This novel findingsuggests that the usage of operating income rather than net incomeand own capital, which have been traditionally used as P/E ratio andP/B ratio indicators for investment, could lead to notably improveinvestment strategies.Thirdly, in Fig. 4, we can see that operating income is the mostinfluential item, and it affects net income, which finally affects revenue.Revenue is the most susceptible item, which is against the calculationorder of statement of operation. Operatively net income is calculatedfrom operating income, which is calculated from revenue. So, the orderof influence as the context of income statements calculation are sup-posed to be from revenue to net income via operating income. How-ever, from our analysis, the influence order is different, which impliesthat operating income rather than revenue should be focused on for amanagement strategy, which is our third main finding. Discussion In this work, the VC correlation approach was able to unveil the di-rectionality between the five major accounting variables, which aredifficult to obtain by standard correlation methods. The data-drivencomputations led to new insights on major accounting variables whichcan be translated into novel recommendations for investment strate-gies. We summarize our findings as follows:Firstly, from the directionality network, we observed that operatingincome is the origin of influence to the other four accounting variables(net income, own capital, market capitalization, revenue). Market cap-italization and revenue are the most susceptible accounting variables.Second and more importantly, although market participants often fo-cus on net income and own capitalization to evaluate share price forinvestment strategy, operating income may be better accounting vari-able to focus on. Thirdly, influence order of revenue, operating incomeand net income is different from the order of accounting calculation ofincome statement.Taken together we believe that these results may lead to improveperformance of financial management as well as apply optimal financialstrategies for firms in future operations. In future work, we may expandthe number of accounting variables to obtain a large-scale map of thedirectional interactions that governs world-wide financial flows. T.O. was partially supported by JSPS Grants-in-Aid for Scientific Re-search (Grant Number 15K01200) [ s, s ′ ] E C σ C N c [net-income(i), market-capital(m)] 0.308 0.219 1421[own-capital(o), market-capital(m)] 0.337 0.232 1434[revenue(r), market-capital(m)] 0.169 0.218 1211[operating-income(p), market-capital(m)] 0.317 0.206 1429[net-income(i), own-capital(o)] 0.427 0.216 1532[net-income(i), operating-income(p)] 0.660 0.268 1532[net-income(i), revenue(r)] 0.273 0.293 1279[operating-income(p), own-capital(o)] 0.302 0.221 1439[operating-income(p), revenue(r)] 0.505 0.278 1516[own-capital(o), revenue(r)] 0.293 0.257 1388Table 1: The average of the correlation coefficients E C [ s, s ′ ], the standarddeviation of the correlation coefficients σ C [ s, s ′ ] and the number of firms N c for each pair of the accounting variables [ s, s ′ ] are shown.8 s, s ′ ] E ∆ F σ ∆ F p value directionality[net-income(i), market-capital(m)] 0.0176 0.0841 2 . × − → [own-capital(o), market-capital(m)] 0.0141 0.0786 8 . × − → [revenue(r), market-capital(m)] 0.00157 0.0562 0 . . → [net-income(i), own-capital(o)] 0.0170 0.0969 5 . × − → [net-income(i), operating-income(p)] -0.00491 0.0610 0 . ← [net-income(i),revenue(r)] 0.00371 0.0760 0 . . . . → Table 2: The average E ∆ F [ s, s ′ ] and standard deviations σ ∆ F [ s, s ′ ] of thedifference of VC correlation, p-value and directionality of each pair of theaccounting variables [ s, s ′ ] are shown. Threshold of p-value for determiningdirectionality is 0.05. In the most right column, → (resp. ← ) means thatthe directionality is from s to s ′ (resp. from s ′ to s ). References [1] R.N.Mantenga, H.E.Stanley, An Introduction to Econophysics,Cambridge University Press, Cambridge,UK, 2000.[2] T. Preis, D. Y. Kenett, H. E. Stanley, D. Helbing, E. Ben-Jacob,Quantifying the Behavior of Stock Correlations under MarketStress, Nature Scientific Reports 2 (2012) 752.[3] X. Yan, L. Zheng, Fundamental analysis and the cross-section ofstock returns: A data-mining approach, The Review of FinancialStudies 30(4) (2017) 13821423.[4] A. M. Ozbayoglu, M. U. Gudelek, O. B. Sezer, Ahmet Mu-rat Ozbayoglu, Mehmet Ugur Gudelek, Omer Berat Sezer, Deeplearning for financial applications : A survey, Applied Soft Com-puting, Volume 93 (2020) 106384.[5] W. Bao, J. Yue, Y. 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(cid:286)(cid:448)(cid:286)(cid:374)(cid:437)(cid:286)(cid:75)(cid:449)(cid:374)(cid:3)(cid:272)(cid:258)(cid:393)(cid:349)(cid:410)(cid:258)(cid:367)(cid:75)(cid:393)(cid:286)(cid:396)(cid:258)(cid:410)(cid:349)(cid:374)(cid:336)(cid:3)(cid:349)(cid:374)(cid:272)(cid:381)(cid:373)(cid:286) (cid:69)(cid:286)(cid:410)(cid:3)(cid:349)(cid:374)(cid:272)(cid:381)(cid:373)(cid:286)(cid:68)(cid:258)(cid:396)(cid:364)(cid:286)(cid:410)(cid:3)(cid:18)(cid:258)(cid:393)(cid:349)(cid:410)(cid:258)(cid:367) Figure 1: Correlation network. Thickness is linearly determined by the ex-pectation value of correlation coefficient E C [ s, s ′ ] between accounting vari-able s and s ′ . 11 (cid:1004)(cid:856)(cid:1006)(cid:1004)(cid:856)(cid:1008)(cid:1004)(cid:856)(cid:1010)(cid:1004)(cid:856)(cid:1012)(cid:1005)(cid:1005)(cid:856)(cid:1006)(cid:1005)(cid:856)(cid:1008)(cid:1005)(cid:856)(cid:1010)(cid:1005)(cid:856)(cid:1012)(cid:1006) (cid:882)(cid:1005) (cid:882)(cid:1004)(cid:856)(cid:1013) (cid:882)(cid:1004)(cid:856)(cid:1012) (cid:882)(cid:1004)(cid:856)(cid:1011) (cid:882)(cid:1004)(cid:856)(cid:1010) (cid:882)(cid:1004)(cid:856)(cid:1009) (cid:882)(cid:1004)(cid:856)(cid:1008) (cid:882)(cid:1004)(cid:856)(cid:1007) (cid:882)(cid:1004)(cid:856)(cid:1006) (cid:882)(cid:1004)(cid:856)(cid:1005) (cid:1004) (cid:1004)(cid:856)(cid:1005) (cid:1004)(cid:856)(cid:1006) (cid:1004)(cid:856)(cid:1007) (cid:1004)(cid:856)(cid:1008) (cid:1004)(cid:856)(cid:1009) (cid:1004)(cid:856)(cid:1010) (cid:1004)(cid:856)(cid:1011) (cid:1004)(cid:856)(cid:1012) (cid:1004)(cid:856)(cid:1013) (cid:1005) (cid:87) (cid:396) (cid:381) (cid:271) (cid:258) (cid:271) (cid:349)(cid:367)(cid:349) (cid:410) (cid:455) (cid:3) (cid:282) (cid:286) (cid:374) (cid:400) (cid:349) (cid:410) (cid:455) (cid:18) (cid:272) (cid:896)(cid:349)(cid:853)(cid:373)(cid:897) (a) (cid:1004)(cid:1005)(cid:1006)(cid:1007)(cid:1008)(cid:1009)(cid:1010)(cid:1011)(cid:1012)(cid:1013)(cid:1005)(cid:1004) (cid:882)(cid:1005) (cid:882)(cid:1004)(cid:856)(cid:1013) (cid:882)(cid:1004)(cid:856)(cid:1012) (cid:882)(cid:1004)(cid:856)(cid:1011) (cid:882)(cid:1004)(cid:856)(cid:1010) (cid:882)(cid:1004)(cid:856)(cid:1009) (cid:882)(cid:1004)(cid:856)(cid:1008) (cid:882)(cid:1004)(cid:856)(cid:1007) (cid:882)(cid:1004)(cid:856)(cid:1006) (cid:882)(cid:1004)(cid:856)(cid:1005) (cid:1004) (cid:1004)(cid:856)(cid:1005) (cid:1004)(cid:856)(cid:1006) (cid:1004)(cid:856)(cid:1007) (cid:1004)(cid:856)(cid:1008) (cid:1004)(cid:856)(cid:1009) (cid:1004)(cid:856)(cid:1010) (cid:1004)(cid:856)(cid:1011) (cid:1004)(cid:856)(cid:1012) (cid:1004)(cid:856)(cid:1013) (cid:1005) (cid:87) (cid:396) (cid:381) (cid:271) (cid:258) (cid:271) (cid:349)(cid:367)(cid:349) (cid:410) (cid:455) (cid:3) (cid:282) (cid:286) (cid:374) (cid:400) (cid:349) (cid:410) (cid:455) (cid:564)(cid:38) (cid:18) (cid:896)(cid:349)(cid:853)(cid:373)(cid:897) (b)Figure 2: (a)Probability density of the correlation coefficients between netincome and market capital C c [ i, m ]. (b)Probability density of the differenceof VC correlations between net income and market capitalization ∆ F c [ i, m ].In (b), we can see an asymmetry with respect to zero, which implies thedirectionality from net income to market capitalization with enough statis-tical significance (p-value is 2 . × − ). See the first line in Table 2. Inboth (a) and (b), the probability density is computed by normalizing thedistribution. 12 (cid:1004)(cid:856)(cid:1006)(cid:1004)(cid:856)(cid:1008)(cid:1004)(cid:856)(cid:1010)(cid:1004)(cid:856)(cid:1012)(cid:1005)(cid:1005)(cid:856)(cid:1006)(cid:1005)(cid:856)(cid:1008)(cid:1005)(cid:856)(cid:1010)(cid:1005)(cid:856)(cid:1012)(cid:1006) (cid:882)(cid:1005) (cid:882)(cid:1004)(cid:856)(cid:1013) (cid:882)(cid:1004)(cid:856)(cid:1012) (cid:882)(cid:1004)(cid:856)(cid:1011) (cid:882)(cid:1004)(cid:856)(cid:1010) (cid:882)(cid:1004)(cid:856)(cid:1009) (cid:882)(cid:1004)(cid:856)(cid:1008) (cid:882)(cid:1004)(cid:856)(cid:1007) (cid:882)(cid:1004)(cid:856)(cid:1006) (cid:882)(cid:1004)(cid:856)(cid:1005) (cid:1004) (cid:1004)(cid:856)(cid:1005) (cid:1004)(cid:856)(cid:1006) (cid:1004)(cid:856)(cid:1007) (cid:1004)(cid:856)(cid:1008) (cid:1004)(cid:856)(cid:1009) (cid:1004)(cid:856)(cid:1010) (cid:1004)(cid:856)(cid:1011) (cid:1004)(cid:856)(cid:1012) (cid:1004)(cid:856)(cid:1013) (cid:1005) (cid:87) (cid:396) (cid:381) (cid:271) (cid:258) (cid:271) (cid:349)(cid:367)(cid:349) (cid:410) (cid:455) (cid:3) (cid:282) (cid:286) (cid:374) (cid:400) (cid:349) (cid:410) (cid:455) (cid:18) (cid:272) (cid:896)(cid:396)(cid:853)(cid:373)(cid:897) (a) (cid:1004)(cid:1005)(cid:1006)(cid:1007)(cid:1008)(cid:1009)(cid:1010)(cid:1011)(cid:1012)(cid:1013)(cid:1005)(cid:1004) (cid:882)(cid:1005) (cid:882)(cid:1004)(cid:856)(cid:1013) (cid:882)(cid:1004)(cid:856)(cid:1012) (cid:882)(cid:1004)(cid:856)(cid:1011) (cid:882)(cid:1004)(cid:856)(cid:1010) (cid:882)(cid:1004)(cid:856)(cid:1009) (cid:882)(cid:1004)(cid:856)(cid:1008) (cid:882)(cid:1004)(cid:856)(cid:1007) (cid:882)(cid:1004)(cid:856)(cid:1006) (cid:882)(cid:1004)(cid:856)(cid:1005) (cid:1004) (cid:1004)(cid:856)(cid:1005) (cid:1004)(cid:856)(cid:1006) (cid:1004)(cid:856)(cid:1007) (cid:1004)(cid:856)(cid:1008) (cid:1004)(cid:856)(cid:1009) (cid:1004)(cid:856)(cid:1010) (cid:1004)(cid:856)(cid:1011) (cid:1004)(cid:856)(cid:1012) (cid:1004)(cid:856)(cid:1013) (cid:1005) (cid:87) (cid:396) (cid:381) (cid:271) (cid:258) (cid:271) (cid:349)(cid:367)(cid:349) (cid:410) (cid:455) (cid:3) (cid:282) (cid:286) (cid:374) (cid:400) (cid:349) (cid:410) (cid:455) (cid:564)(cid:38) (cid:18) (cid:896)(cid:396)(cid:853)(cid:373)(cid:897) (b)Figure 3: (a)Probability density of the correlation coefficients between rev-enue and market capital C c [ r, m ]. (b)Probability density of the differenceof VC correlations between revenue and market capitalization ∆ F c [ r, m ].In (b), we can not see asymmetry with respect to zero, which implies thatthere is no directionality between revenue and market capitalization. Seethe third line in Table 2. In both (a) and (b), the probability density iscomputed by normalizing the distribution.13 (cid:286)(cid:448)(cid:286)(cid:374)(cid:437)(cid:286)(cid:75)(cid:449)(cid:374)(cid:3)(cid:272)(cid:258)(cid:393)(cid:349)(cid:410)(cid:258)(cid:367)(cid:75)(cid:393)(cid:286)(cid:396)(cid:258)(cid:410)(cid:349)(cid:374)(cid:336)(cid:3)(cid:349)(cid:374)(cid:272)(cid:381)(cid:373)(cid:286) (cid:69)(cid:286)(cid:410)(cid:3)(cid:349)(cid:374)(cid:272)(cid:381)(cid:373)(cid:286)(cid:68)(cid:258)(cid:396)(cid:364)(cid:286)(cid:410)(cid:3)(cid:18)(cid:258)(cid:393)(cid:349)(cid:410)(cid:258)(cid:367)(cid:286)(cid:448)(cid:286)(cid:374)(cid:437)(cid:286)(cid:75)(cid:449)(cid:374)(cid:3)(cid:272)(cid:258)(cid:393)(cid:349)(cid:410)(cid:258)(cid:367)(cid:75)(cid:393)(cid:286)(cid:396)(cid:258)(cid:410)(cid:349)(cid:374)(cid:336)(cid:3)(cid:349)(cid:374)(cid:272)(cid:381)(cid:373)(cid:286) (cid:69)(cid:286)(cid:410)(cid:3)(cid:349)(cid:374)(cid:272)(cid:381)(cid:373)(cid:286)(cid:68)(cid:258)(cid:396)(cid:364)(cid:286)(cid:410)(cid:3)(cid:18)(cid:258)(cid:393)(cid:349)(cid:410)(cid:258)(cid:367)