Mathematical modelling and the empirical validation of organisational financial performance – conceptual insights Into the inferential focus of the analytical perspectives in the finance

This study traces the evolution of analytical methods in building Finance Theory with a view to strike an ‘optimal’ balance between the analytical rigour and the real-world inferential insights.

International Journal of Management (IJM) Volume 11, Issue 3, March 2020, pp 399–407, Article ID: IJM_11_03_042 Available online at http://www.iaeme.com/ijm/issues.asp?JType=IJM&VType=11&IType=3 Journal Impact Factor (2020): 10.1471 (Calculated by GISI) www.jifactor.com ISSN Print: 0976-6502 and ISSN Online: 0976-6510 © IAEME Publication Scopus Indexed MATHEMATICAL MODELLING AND THE EMPIRICAL VALIDATION OF ORGANISATIONAL FINANCIAL PERFORMANCE – CONCEPTUAL INSIGHTS INTO THE INFERENTIAL FOCUS OF THE ANALYTICAL PERSPECTIVES IN THE FINANCE DISCIPLINE Dr P Raghunadha Reddy Professor and Head, Department of Management Studies, Sri Venkateswara University, Tirupati, India V.G Siva Sankara Reddy Research Scholar, Department of Management Studies, Sri Venkateswara University, Tirupati, India ABSTRACT Purpose of the Study: This study traces the evolution of analytical methods in building Finance Theory with a view to strike an ‘optimal’ balance between the analytical rigour and the realworld inferential insights Methodology: The theoretical developments in the latter half of the 20th century, in the field of Finance, have focused, extensively, on the Analytical basis of sound theory building and its Empirical validation using the Statistical tools The pioneering work of Miller and Modigliani that analytically established the relationship between the firm’s financial leverage (Debt component) and the Value of the firm, under varying assumptions marked the beginning of analytical approaches to building Finance Theory The corporate bankruptcy model developed by Altman was also studied The subsequent empirical studies have also been examined to assess the practical validity and relevance of their findings http://www.iaeme.com/IJM/index.asp 399 editor@iaeme.com Dr P Raghunadha Reddy and V.G Siva Sankara Reddy Main Findings: a) While the analytical modelling, by virtue of its elegance of logic and causation, has been widely acclaimed as the most efficient tool of theory building, it is beset with certain inherent limitations More specifically, the field of Social sciences, which includes several functional areas of management, is intrinsically determined by behavioral factors and therefore, the stand-alone mathematical modelling (that overlooks the ‘unpredictability’ of behavioral parameters) is fraught with the danger of erroneous conclusions b) The Behavioral parameters are, in turn, determined by the psycho-sociological, ethnic, geographic and other factors; this makes the ‘analytical’ handling of the behavioral parameters more cumbersome and therefore inefficient c) The ‘percolation’ of Statistical analysis into conceptually deterministic models has blurred the researcher’s distinction between the Stochastic and Deterministic (tautological) models thereby, resulting in ‘proving’ the obvious d) Finally, the article concludes with the observation that the utility of mathematical modelling can be enhanced by articulating the broad contours of causal relationships among the various parameter so as to gain tangible insights into the real-life decision situations and also by suitably modifying the rigidities of the model to suit the ‘nuances’ of the specific situation In other words, the researcher should stress more on the ‘spirit’ of the model as opposed to its elegantly framed ‘structure’ of equations Applications of this Study: This study is expected to make the Finance researchers to focus on the inferential insights into the ‘quantitative’ parameters emerging from the analytical models so as to enhance the utility of Analytical methods employed in Finance Key words: Mathematical modelling, behavioral factors, Inferential Focus, Stochastic versus Deterministic models, Theory building Cite this Article: Dr P Raghunadha Reddy and V.G Siva Sankara Reddy, Mathematical Modelling and the Empirical Validation of Organisational Financial Performance – Conceptual Insights into the Inferential Focus of the Analytical Perspectives in the Finance Discipline, International Journal of Management (IJM), 11 (3), 2020, pp 399–407 http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=11&IType=3 INTRODUCTION TO ANALYTICAL PERSPECTIVES IN FINANCE The Finance discipline has its foundations in the Economic Sciences and therefore, the most of the analytical approaches in Finance have been adopted from Economics In the earlier days, when reasoning in Economics was based on the Subjective Knowledge (as opposed to Objective) that was accumulated through past experiences and observations, the greatest of economic thinkers applied the non-mathematical logic in their deductive approaches to Knowledge building We may trace the beginnings of calculus-based reasoning approaches in Economics to Alfred Marshall, who believed that analytical methods lead to precision of definition that leads to the ‘accuracy’ of the deductions and conclusions that emanate from it The Nobel Laureate Paul Samuelson may be credited with popularizing the analytic formalism in the basic courses in Economics The Finance discipline has been essentially based on the numerical inputs and therefore the use of Quantitative methods in Finance are obvious However, as Accounting (in the earlier days) was considered the prime objective of the Finance function, the earlier theories in Finance were mostly confined to elementary analysis of the numerical figures generated by the http://www.iaeme.com/IJM/index.asp 400 editor@iaeme.com Mathematical Modelling and the Empirical Validation of Organisational Financial Performance – Conceptual Insights into the Inferential Focus of the Analytical Perspectives in the Finance Discipline Accounting System As a result, until the mid-twentieth century, the Finance discipline was considered to be a ‘number crunching’ job that was not ‘intellectually’ demanding However, the pioneering work of Modigliani and Miller in 1958, which was popularly known as the MMHypothesis, initiated the development of the Analytical approaches in the field of Finance Today, we are witnessing a phenomenal growth in Financial Modelling that is threatening to replace the human wisdom by the Algorithmic wisdom in several areas of Finance Therefore, this is the time for the researchers in Finance to ‘reflect’ on the likely ‘erroneous’ conclusions flowing out of the ‘excessive’ mathematical modelling in Finance that may lead to several dysfunctional consequences DuPont Chart and the evolution of Financial Performance Modelling The DuPont chart illustrates the components that contribute to the Return on Capital Employed that forms the basis of a simple equation that links the Total Asset Turnover ratio and the Profitability ratio to the Return on Total Assets The basic equation is given below ROA = (Total Asset Turnover ratio)*(Profit Margin) or (Net Income/Total Assets) = (Sales/Total Assets)*(Net Income/Sales) This leads to the basic deduction that the ROA can be increased by either increasing the Total Asset Turnover or by increasing the Profit margin (or both) In other words, the DuPont chart based analysis provided the Finance manager with the basic tools for achieving the ROA objective The researchers in the Finance field (since the end of 1960s) attempted to bring in a greater analytical focus into the theoretical foundations of Finance This approach is clearly evidenced in the landmark paper published by Edward Altman titled, “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy” in the Journal of Finance (1968) In his introductory remarks, the author stated as follows “Can we bridge the gap, rather than sever the link, between traditional Ratio “analysis” and the more rigorous statistical techniques which have become more popular among academicians in the recent years?” This work by Altman has made the Z-score metric developed by him very popular amongst Finance professionals to evaluate the credit strength of the concerned organizations While it is not the main purpose of this article to make a critical appraisal of the Z-score, the Altman’s work has been referred to trace the analytic evolution in Finance Research The researchers in their enthusiasm to add ‘rigor’ to their research work have ended up being ‘dominated’ by the predictions of the man-made ‘mathematical/statistical’ models; this has made the decisionmakers increasingly ‘algorithmic’ driven during the present times The point is that the researchers should attempt to promote a ‘symbiotic’ relation-ship between the ‘model-driven’ logic and the ‘practical’ wisdom of the decision-makers Such an approach is needed to factorin the ‘behavioral’ parameters which are subject to ‘erratic’ fluctuations; this phenomena ‘appears’ to be adequately captured by the introduction of a ‘statistical’ random variable governed by a ‘mathematically’ defined probability distribution For instance, the Nobel laureates who popularized the extensive use of the Black-Scholes option pricing model towards the end of the 20th century, based their rigorous analysis assuming the ‘log normal property’ of Stock prices (that is ‘too’ idealistic, if not unrealistic) The researchers in Finance should note that ‘behavioral’ variables not fit a standard stochastic process that is valid across different time horizons (unlike the random variables encountered in the physical sciences; for instance the Brownian motion Most of the present day research on financial performance is focused on Multivariate linear Regression models that are designed to explain ROA or ROE in terms of the various other financial ratios such as Debt-ratio and Total Asset Turnover http://www.iaeme.com/IJM/index.asp 401 editor@iaeme.com Dr P Raghunadha Reddy and V.G Siva Sankara Reddy The researcher’s focus on the mathematical/statistical ‘nuances’ of the model is diverting the attention of the readers from the ‘validity’ aspects of the underlying parameters that the Accounting System provides The point is that the ‘validity’ of the parameters are intrinsically dependent on the ‘objectivity’ and ‘standardization’ of the Accounting outputs and surely, we are not anywhere near the goal of ‘international convergence of accounting principles’ that is vital for cross-border comparison of financial performance Further, the Accounting policies are varying across business sectors due to the peculiarities of the environment surrounding the specific sector Therefore, the rigorous model building approach to Theory-building in Finance may satisfy the ‘intellectual’ self-actualization needs of the researcher but may not be ‘practically’ beneficial REGRESSION MODELS AND THE BOUNDARY CONDITIONS The primary limitation of fitting the Regression model is that it is based on an ‘implied’ assumption that the data fit is described by an ‘elegantly’ defined mathematical function (be it Linear, Polynomial, Logarithmic, trigonometric or Differential) In reality, a given set of data may be fitted into a ‘standard’ mathematical function using the ‘Least Squares’ argument But, the truth is that such regressions are valid only within a specified range of values of the independent variables; these are commonly known as the Boundary conditions (a term used in Physical Sciences) With respect to the linear regression models frequently used in financial performance analysis, it should be noted that the partial derivatives are ‘constant’ terms; this is not a ‘realistic’ assumption For instance, if Y = f(x1, x2 xN) is a linear regression function, then the ‘Beta’ coefficients βj, for j=1 to N, are all constants Mathematically speaking βj is the partial derivative of Y with respect to xj or we may write (∂Y/∂xj) = βj; but, in a real-life situation, not all the partial derivatives are constant This is the one serious limitation of using the elegantly defined mathematical functions for Theory building in the Social Sciences STOCHASTIC VERSUS DETERMINISTIC MODELS Conceptually, the researchers in Finance should clearly appreciate the basic distinction between the Stochastic and Deterministic models The mathematical relationship that is defined by parameters that take ‘specific’ values (as opposed to ‘random’ values) is known as a Deterministic model In contrast, when the parametric inputs defining the mathematical relationship are ‘random’ variables, we refer to them as stochastic models A Stochastic model is based on the underlying probability distribution that is generally governed by the two important parameters called the ‘mean’ and ‘standard deviation’ In other words, a simple deterministic Revenue model may be represented by “R=p*Q” where ‘R’ is the sales revenue and ‘p’ is the price and ‘Q’ is the sales quantity However, the same equation becomes a stochastic model when ‘Q’ is considered as a ‘random’ variable and such models call for statistical validation However, some researchers attempt to validate a deterministic model using the statistical tests of significance which are ‘superfluous’ Thus, such validations end up proving the ‘obvious’ Such redundancies occur when the researcher attempts to prove the significance of the ‘slope’ of a deterministic linear model For instance, consider a deterministic Total cost model, “C=f0+v*Q” where ‘C’ is the Total cost, ‘f0’ is the fixed cost and ‘v’ is the unit variable cost and ‘Q’ is the output quantity We need not use elaborate Statistical model building tools to develop this relationship and prove the statistical significance of the ‘slope’ of the cost function which is obviously (tautologically) equal to ‘v’ (a ‘determinable’ parameter, as opposed to ‘random’ parameter) http://www.iaeme.com/IJM/index.asp 402 editor@iaeme.com Mathematical Modelling and the Empirical Validation of Organisational Financial Performance – Conceptual Insights into the Inferential Focus of the Analytical Perspectives in the Finance Discipline GLOBAL STOCK-MARKET INDICES AS A FACTOR IN EVALUATING FINANCIAL PERFORMANCE Some researchers have used the ratio, (market price of the share/book value) as an independent variable in the Regression model determining the ROE (Return on Equity) which has certain ‘inherent’ flaws The Stock market price of the shares is a highly volatile variable whose ‘stability’ is limited to a very short time interval This is basically due the market sentiment/expectations of the investors (including speculators) which makes the Regression model a ‘Time’ dependent function that has only a ‘momentary’ utility Today’s Stock markets have grown much beyond their original mandate of providing a market for ‘liquidity and price discovery’ to encourage the retail investor participation in the capitalist economy However, the ‘excessive’ speculation prevalent in the international markets has made ‘Stock Market Price’ a fairly ‘unreliable’ measure of the firm’s economic value (due to the Stock market volatility) The researchers may reflect on this aspect of ‘erratic’ randomness which leads to ‘time-variant’ probability distributions As a result, the models built on the assumption of a ‘precisely’ defined ‘time-invariant’ probability distribution is fraught with the danger of ‘erroneous’ inferences THE SPECTRUM OF GLOBAL RESEARCH FINDINGS BASED ON MATHEMATICAL/STATISTICAL MODELLING: Hansen and Mowen (2005) - “Firm performance measurement is vital for effective management” Fleming and Heany (2005) - “Asset dis-utilization may increase Agency costs” Katja (2009) - “performance measures are used to evaluate the success of Economic units” Okwo (2012) – “Fixed Assets to profitability showed a positive correlation but not statistically significant.” This is because, fixed assets are only one of the factors affecting profitability Further, the other external factors contributing to profitability are generally excluded from the Regression model that may get incorporated in the ‘intercept’ which is the constant parameter β0 However, the study by Xu and Xu (2013) titled, “A study on optimal allocation of asset structure and business performance”, has found that the relationship between Fixed assets and Profitability is significant From this, the reader has to realize that there is nothing ‘universal’ about the statistically validated theoretical results based on empirical studies In order to understand the variance between two research findings attempting to build the same conceptual foundations, the astute reader should delve into the ‘specifics’ of the researcher’s empirical settings For instance, the significance of the fixed assets in the manufacturing setting may more than that in the Service sector The other studies that have agreed with the findings of Xu and Xu are, Jose et al (2010), Wu et al (2010) and Seema et al (2011) THE EMPIRICAL RESULTS ON LEVERAGE TO ROE RELATIONSHIP: Acquino (2010) studied the Capital structure of listed and unlisted Filipino firms and concluded that High Debt rate is positively associated with the firm’s growth and profitability Similar conclusions were drawn by Joshua (2005) http://www.iaeme.com/IJM/index.asp 403 editor@iaeme.com Dr P Raghunadha Reddy and V.G Siva Sankara Reddy On the other hand, Aivazania et al (2005) examined the impact of leverage on investment decisions and found it to be negative This may be because the ‘riskiness’ of a highly levered firm is rather high and so the prospective investor may rate such investments low (notwithstanding its prospects of posting higher ROE) Ahna et al (2006) found that the negative relation-ship between the Debt ratio and Investment decisions is more significant in the non-critical sector than in the critical sector H the Statistical significance of ‘Tautologies’ - its ‘Redundancy’: A ‘tautology’ is basically a logical equivalent of an established truth For instance, if we use two regression equations for two different dependent variables Y1 and Y2 which are expressed as a linear combination of several independent variables x1, x2, xN We know that Y2=λ*Y1 where λ is a positive constant Thus Y2 is derived from Y1 by multiplying with a constant λ Further, if we find that the regression coefficient with respect to x1 (β1) is significant in the case of Y1, it need not be again separately mentioned for Y2 as these two are linked by a positive constant multiple λ There are many instances when the significance tests are repeated to arrive at the same truth INFERENTIAL FOCUS – A PRACTICAL ILLUSTRATION The following Regression model developed by a researcher, Mou Hu of the University if Thai Chamber of Commerce, titled, “Factors affecting Financial Performance of firms listed on Shanghai Stock Exchange” which studied the impact of factors like Liquidity, Asset Utilization, Leverage and Firm Size on the Financial performance has considered two Dependent Variables, ROA (Return on Assets) and ROE (Return on Equity) It was found that the ROA and ROE are significantly impacted by Debt ratio (leverage) with a negative slope and Total Asset Turnover (Asset Utilization) with a positive slope The Regression equations are given below: ROA= 26.94+2.115(CR) + 2.294(TAT)-35.452(DR)-2.926(FSD) ROE=23.12+1.162(CR) + 2.493(TAT)-19.325(DR)-2.91(FSD) Where CR is the current ratio, TAT is the Total Asset Ratio, DR is the Debt ratio and FSD is the Firm size discriminant From a practical perspective, the research work could have examined the factors contributing to the difference between the beta-coefficients in respect of DR (-35.452 in the 1st equation and -19.325 in the 2nd equation) Using the basic definition of ROA and ROE, we obtain the following mathematical relationships ROA=EBIT/A, where A is the value of total assets financed by ‘D’ and ‘E’ where ‘D’ is the debt component and ‘E’ is the equity component We may also use the function “E=(1λ)*A” and “D=λ*A” , where ‘λ’ is the Debt ratio or the debt component of the asset-base We may state that ROE= (EBIT- INT on debt- TAX)/E where ‘E’ is the equity Let‘t’ be the tax rate and ‘rD’ be the interest rate on Debt Therefore, the above equation gets rewritten as follows ROE=t*[EBIT – (rD)*(λ*A)]/(1-λ)/A Upon, simplifying this equation, we arrive at the following end result ROE= [t/(1-λ)]*{ROA- λ*(rD)} Any researcher using the basic mathematical reasoning would ‘decipher’ that ROE is ‘Not’ a linear function of ‘λ’ which represents the ‘Debt ratio’ Clearly, this invalidates the ‘Linear’ Regression modelling assumption Such ‘unrealistic’ assumptions can be avoided if only, the researchers adopt an inferential focus into the financial modelling and its validation http://www.iaeme.com/IJM/index.asp 404 editor@iaeme.com Mathematical Modelling and the Empirical Validation of Organisational Financial Performance – Conceptual Insights into the Inferential Focus of the Analytical Perspectives in the Finance Discipline MODEL VALIDATION – THE INDIAN SETTING The above model has been fitted to a leading Indian conglomerate using the year financial results as the base-data for model fitting and the following mathematical relationship has been established ROE = 24.705 + 0.885*(TAT) – 32.21*(DR) In this model, the linear approximation of a non-linear slope (ROE to Debt ratio) is fairly valid considering the fact that the range of variation in the debt ratio is confined to the interval 0.425 to 0.440 The above equation has been obtained using the data collected from the Published financial statements of an Indian conglomerate listed on the Bombay Stock Exchange The details of the workings are presented in Appendix – 10 DISCUSSION AND CONCLUSIONS: From the above, it may be noted that the regressions coefficients are not constant across the industry spectrum; nor are they comparable across divergent world financial markets As a result, the researcher would get better insights into the financial performance metrics by analytically deducing ‘situation specific’ based on certain reasonable assumptions For instance, by assuming that λ=λ0 (a constant debt ratio), we may rewrite the relationship between ROE and ROA as given below “ROE = k*(ROA) – (k*λ0)*(rD) where k={t/(1-λ)} and (rD) is the interest rate on Debt From the above equation we find that the ‘situation specific’ slope of the ROE with respect to Debt ratio(λ) or ∂ROE/∂λ is equal to slope of ROA with respect to debt ratio multiplied by ‘k’ or k*∂ROA/∂λ Thus, the relationship between the absolute values of the two slopes are dependent on the factor ‘k’ referred above This forms the basis for the inferential conclusions that a researcher can draw from the Regression modelling of the financial parameters The Analytical Models developed in Finance should not just be confined to the testing of the significance of the Regression coefficients constituting the model Moreover, the absolute values of these parameters not help the researcher in strengthening his conceptual insights For this purpose, the researchers have to undertake a critical study of the relevant interconnected factors to ‘deduce’ the ‘complex-maze’ of cause-effect linkages which would add new insights into the conceptual foundations governing the subject Thus, the researchers in Finance would serve the professional community better by providing practical insights into the ‘numbers’ generated by the Regression models through an adequate reflection upon the physical reality lying beneath the ‘labyrinth’ of numbers and its ‘modelled’ equations REFERENCES [1] [2] [3] [4] [5] Amalendu, B (2010) Financial Performance of Indian Pharmaceutical Industry: A Case Study Asian Journal of Management Research, ISSN 2229 – 3795 Amarjit, G et al (2010) The relationship between working capital management and profitability: Evidence from the United States Business and Economics Journal, Vol 2010: BEJ-10 Aquino, R (2010) Capital structure of Philippine listed and unlisted firms: 19972008 University of the Philippines, College of Business Administration, Discussion paper 1005 “Impact of Oil Prices On Revenue Growth and Profitability of Saudi Listed 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Reddy, Mathematical Modelling and the Empirical Validation of Organisational Financial Performance – Conceptual Insights into the Inferential Focus of the Analytical Perspectives in the Finance. .. editor@iaeme.com Mathematical Modelling and the Empirical Validation of Organisational Financial Performance – Conceptual Insights into the Inferential Focus of the Analytical Perspectives in the Finance. .. Validation of Organisational Financial Performance – Conceptual Insights into the Inferential Focus of the Analytical Perspectives in the Finance Discipline MODEL VALIDATION – THE INDIAN SETTING The