MSU LIBRARIES “ RETURNING MATERIALS: P1ace in book drop to remove this checkout from your record. Elfl§§_wi11 be charged if book is returned after the date stamped be10w. A THEORETICAL AND EMPIRICAL EXAMINATION OF THE DETERMINANTS OF SYSTEMATIC RISK BY Carolyn M. Callahan A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Accounting 1985 ABSTRACT A THEORETICAL AND EMPIRICAL EXAMINATION OF THE DETERMINANTS OF SYSTEMATIC RISK BY Carolyn M. Callahan The general purpose of this research is to increase the knowledge of the process that link accounting and financial data to the risk components generating equity returns in the capital market. Identifying the determinants of systematic risk have incor- porated two basic research approaches, empirical examination and analytical modeling based on theory. Empirical examinations investigate correlations between accounting measures and systematic risk using univariate or multivariate statistical techniques. The analytical approach utilizes mathematical modeling based on theory to examine the mathematical linkage between security market esti- mates of risk and accounting variables. This research incorporated both empirical examination and analytical modeling. That is, this study examined, for a sample of firms, the relationship between accounting data (reflecting the productive-investment and financing decisions of the firm) and market risk measures. More specifically, this study analytically linked the theoretical models which incorporate business risk to Carolyn M. Callahan the fundamental Ramada—Rubinstein model. Then, the analytically derived risk model was subjected to empirical examination. Finally, a comparative analysis was used to determine the adequacy of utilizing the accounting beta as a surrogate for business risk in theoretically based risk models. The empirical results of this research evidenced, in general, a significant association between the market-based beta and the operationalized theoretical specifications of the accounting determinants of systematic risk. In addition, the results of the comparative analysis indicated substantial similarity between models incorporating the theoretically-determined elements and those utilizing the accounting beta. ACKNOWLEDGMENTS I would like to first thank the members of my dissertation committee. Professors Fred Jacobs (Chairman), Larry Johnson and Rosanne Mohr provided support, guidance and encouragement throughout this research project. Much appreciation is extended to the administrative staff of Ernst and Whinney for the doctoral dissertation grant which they pro- vided. This financial assistance facilitated a more timely completion of my research. As usual, there are those in our lives whose love and support deserve a very special acknowledgment. Special thanks are accorded to my daughter Tamara for her unconditional love and continuous support. In a similar manner, I want to thank my father, other members of my family and close friends who were supportive and under- standing while I was involved with this research effort. Finally, and most importantly, I want to give God the full glory. ii TABLE OF CONTENTS Page LIST OF TABLES. o o o o o o o o o o o o o o o o o o o o o o o o v Chapter 1 INTRODUCT ION O O O O O O O O O O O O O O I O O O 9 . 1 2 REVIEW OF THE RELATED RESEARCH . . . . . . . . . . . 13 2.1 Empirical Beta Association Studies. . . . . . 13 2.2 Theoretical Examinations of the Financial Leverage Component of Systematic Risk . . . . . . . . . . . . . 18 2.3 Theoretical Examinations of the Operating Risk Component of Systematic Risk . . . . . . . . . . . . . 20 2.4 Theoretical Examinations of Systematic Risk Supported by Empirical Analysis. . . . . . . . . . . . 23 2 O 5 smary O I O O O O O O I O O O O O O O O O O 26 3 THEORY UNDERLYING THE MODEL DEVELOPMENT AND mPIRICAL TESTS O O O O O O O O O O O O O O O O 29 3.1 Theory Underlying Analytical Systematic Risk Research . . . . . . . . . . 30 3.2 Systematic Risk Model Development . . . . . . 33 3.3 Alternative Systematic Risk Model Development. . . . . . . . . . . . . . 40 3.4 Summary . . . . . . . . . . . . . . . . . . . 42 4 METHODOLOGY 0 O I O O O O O O O O O O O O O O O O O O 4 4 4.1 Sample Selection Procedures . . . . . . . . . 46 4.2 Estimation of the Components Of Model 1 O O I O O I C O O O O O O O O O O 47 iii Chapter Appendix A B C References. 4.2.1 Estimation of the Firm's Market-Based Beta . 4.2.2 Estimation of the Contribution Margin Variable . . 4.2.3 Estimation of the Output Covariability Measure . 4.2.4 Estimation of the Financial Risk Component. . . 4.3 Estimation of the Components of Model 2 4.3.1 Estimation of the Accounting Beta. 4.4 Functional Forms of the Models. 4.5 Purpose of the Empirical Investi- gations O O O O O O O O O O 4.6 Summary . . . . . . . . . . RESULTS 0 O O O O O O O O O O O O O 5.1 Results of the Preliminary Data Manipulation . . . . . . . 5.2 Statistical Analysis and Testing of the Systematic Risk Models. 5.3 Summary . . . . . . . . . . CONCLUSIONS. . . . . . . . . . Mathematical Integration of Theoretical Risk Models . . . . . . . . . . . NYSE Sample Firms. . . . . . . . . Electric Utility Firms . . . . . . iv Page 47 50 52 57 61 61 67 68 7O 78 79 93 106 109 114 121 122 123 Table 2.1 4.1 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 LIST OF TABLES Empirical Beta Association Studies . . . . . Definitions of Market-Based and Accounting Risk Measures. . . . . . . . . . Summary Statistics--Market Model Regressions Summary Statistics--Contribution Margin Regr8881ons O O O O O I O O O O O O O O O 0 Summary Statistics——Output Volatility Measure Based on Sales Regressions. . . . . Summary Statistics--Output Volatility Measure Based on Kilowatt Hours . . . . . . Summary Statistics for the Business Risk Component. . . . . . . . . . . . . Summary Statistics for the Debt—to- Equity Ratios I O O O O O O O O O O O O O 0 Summary Statistics for the Accounting Beta Regression . . . . . . . . . . . . . Ordinary Least Squares Regression Results (Additive Models) . . . . . . . . . . . . Ordinary Least Squares Regression Results (Multiplicative Models) . . . . . . . . . . Ordinary Least Squares Regression Results (Additive Fit - Model 2). . . . . . . . . . Page 15 74 82 84 86 88 89 90 92 98 101 104 CHAPTER I INTRODUCTION It is a widely accepted premise that the purpose of accounting information is to facilitate the decision-making process of the users of the financial statements. This focus on the decision-usefulness of accounting data is evident in the review of two significant statements on accounting theory, Accounting Principles Board (APB) Statement No. 4, "Basic Concepts and Accounting Principles Underlying Financial State- ments of Business Enterprises," and Financial Accounting Standards Board (FASB) Statement of Financial Accounting Concepts No. 1, "Objec- tives of Financial Reporting by Business Enterprises." In addition to these two pronouncements, a report issued by the Wheat Commission, a study group established in 1971 by the American Institute of Certified Public Accountants (AICPA), further emphasizes the importance of the decision-usefulness attribute of accounting information. An examina- tion of the content of these three documents will substantiate that there is authoritative support for this objective of financial reporting. That is, authoritative bodies support the contention that the primary purpose of financial reporting is to provide information that is useful to financial statement users in making rational economic decisions. The APB's Statement No. 4 (1970) is descriptive in nature, and deals with the broad, qualitative objectives of financial statements. 2 In this statement, the focus on the desirability of providing for the informational needs of the users of the financial statements is clearly evident: Accounting is a service activity. Its function is to pro- vide quantitative information, primarily financial in nature, about economic entities that is intended to be useful in making economic decisions -- in making reasoned choices among alternative courses of action. Whereas APB Statement No. 4 is primarily descriptive in nature, the Report of the Study Group on the Objectives of Financial Statements (1973) presents a set of objectives primarily normative in their scope. Among the objectives presented and defended by the Study Group is the following: The fundamental function of financial accounting has been unchanged from its inception. Its purpose is to provide users of financial statements with information that will help them make decisions.2 A more recent pronouncement that emphasizes the decision-useful- ness criterion of accounting information is Statement of Financial Accounting Concepts (SFAC) No. 1, "Objectives of Financial Reporting by Business Enterprises" (1978). In this conceptual statement, the FASB expressed the following view: Financial reporting should provide information that is useful to present and potential investors and creditors and other users in making rational investment, credit and similar decisions. The information should be comprehen- sible to those who have a reasonable understanding of busi- ness and economic activities and are willing to study the information with reasonable diligence.3 One of the user groups specifically mentioned in the preceding quotation is the security investor. The security investor is interested in information that facilitates the portfolio selection process. Investors have the opportunity to invest in portfolios of securities, 3 thereby diversifying some of the risks associated with the holding of a single security. Successful diversification, however, requires an assessment of the risk of each security and the contribution of each security to overall portfolio risk. As such, information that aids in the determination of these risk components should benefit the security investor. Specifically, knowledge on the individual investor level of the risk generating process should improve the prediction of ex ante risk (and hence portfolio selection). Again, on the authoritative level, the FASB has recognized the need for providing financial statement users with information that aids in the assessment of risk. In November of 1981, the FASB issued an exposure draft for a proposed Statement of Financial Accounting Concepts. In the proposed SFAC No. 5, "Reporting Income, Cash Flows, and Financial Position of Business Enterprises," the FASB expressed the following view on providing information for risk determination: The risk involved in investment in the enterprise may depend on the deployment of resources by the enterprise and on the relationships among particular types of assets and liabilities. Information needed for the assessment of some aspects of risk is provided by different parts of financial reporting; for example, information about components of income may help the assessment of the relationship between revenues and expenses and, hence, provide a basis for assessing the effect of changes in demand on income. Information about the relationship between cash flows from operations and debt service requirements may provide a basis for assessing the risk involved in the capital structure of the enterprise. The emphasis by the FASB and various other groups on the desirability of risk assessment information has led to academic research that attempts to link accounting and financial data to the risk components of the return generating process. The impetus for 4 this type of research is expressed well by Beaver, Kettler and Scholes [1970] in their seminal article on risk assessment: We cannot hope to construct an accounting system or eval- uate the current system in terms of decision making criterion without a knowledge of the interaction between the accounting data and the market price variables. The relationship between accounting data and market-determined systematic risk is the general concern of the present study. There are two basic research approaches, empirical examination and analytical modeling based on theory, which could be used to examine this relation- ship. An empirical examination would investigate correlations between accounting measures and systematic risk using univariate or multivari— ate statistical techniques. An analytical approach would utilize mathematical modeling based on theory to examine the analytical linkage between security market estimates of risk and accounting vaiables. The present research incorporates both empirical examination and analytical modeling. That is, this study examines, for a sample of firms, the relationship between accounting data (reflecting the productive-investment and financing decisions of the firm) and syste- matic risk as measured by "beta." ("Beta" is defined as the covari- ability of the returns on the individual security with the returns on a market index.) More specifically, this study analytically links the theoretical models which incorporate business risk to the funda- mental Hamada-Rubinstein model. Then, the_analytically-derived systematic risk model, which simultaneously captures both the business and financial risk elements of beta, is subjected to an empirical examination. Finally, a comparative analysis is used to determine the adequacy of the accounting beta6 as a surrogate for business risk in theoretically-based risk models. A finding of association between measures derived from accounting data and market-based measures of systematic risk would support the joint hypothesis that accounting data do reflect informa- tion about the risk of capital assets and that such information is im— pounded in the market price of securities.7 In short, this study em- bodies a joint test of the descriptive validity of a theoretical model of systematic risk and of the information content of the publicly available accounting measures used to operationalize that model. The results of this study should be of interest to various groups or constituencies in the financial reporting environment. These groups include investors, financial information intermediaries,8 management, and financial reporting regulators. The interest of the investment community in security risk assessment is founded in modern financial theory. Mean-variance port- folio theory indicates that an optimal investment strategy involves the selection of "efficient" portfolios based on individual risk preferences.9 Within this decision framework, the objects of choice are the expected return and the variance of the portfolio return. Furthermore, within the context of various capital asset pricing models, the portfolio choice problem reduces, theoretically, to choosing the risk level or beta of the portfolio. Therefore, in order for investors to select portfolios that accurately reflect their tastes for expected risk and expected return, they must be able to obtain estimates of beta. Beta estimation and prediction is enhanced by risk assessment models. That is, models which relate accounting measures of the firm's financial and operating characteristics (e.g., output level, 6 capital structure, capital intensity, etc.) to market risk should increase investor understanding of the determinants of systematic risk. The present study presents and empirically tests a risk assessment model. Specifically, the model describes risk in terms of microeco— nomic variables of the firm. A finding of empirical support for the model should provide investors with a theoretically-derived basis for assessing the risk effects of certain firm activities, such as changes in product lines, changes in input mix, and changes in product output and price levels. The interest of the investor group in beta assessment is shared by a second group identified above, the financial information inter- mediaries. This group is closely aligned with the investor group. Therefore, financial information intermediaries are also concerned with risk assessment. A major function of this group is to design models that provide estimates of the risk levels of the various equity instru- ments traded in financial markets. Financial analysts utilize accoun- ting and other information sets in estimating security risk. Similarly, bond rating agencies, another type of financial information intermediary, attempt to rank bonds on the basis of default probability or riskiness. The present study incorporates model construction and empirical testing procedures that may be useful to these financial information inter- mediaries. Specifically, an understanding of the relationship between accounting risk measures and equity instrument risk should enhance the risk assessment function of these agent groups. A third group, the managers of firms, should also be concerned with risk assessment. That is, managers could benefit from knowing the effects of their financing and operating decisions on the perceived 7 risk level of the firm. A major contention of corporate financial theory is that the goal of management is to maximize shareholder wealth. In theory, managers interested in maximizing shareholder wealth should seek to maximize the value of the firm's common stock through efficient operations. To accomplish this goal, management must make certain policy decisions (e.g., line of business, scale of oper- ations, product mix, financing mix, etc.) which affect the firm's earnings stream. The market's evaluation of the firm's expected earn- ings stream over time and the riskiness of this stream is then reflected in the value of the firm's equity shares. Hence, models which relate accounting measures of the firm's financial and operating structure to systematic risk can assist management in evaluating the influence of corporate policy decisions on the firm's risk level. Such a model is examined in the present study. As has been stated, the model analyzed herein indicates the relationship between managerial decision variables and market factors in the determination of systematic risk. The potential benefit of this model can be demonstrated more clearly by reviewing the three major decisions (production, investment, and financing) made by corporate managers. First, the production decision involves a two-step procedure for corporate managers. The manager must project the level of sales by product line based on expected demand as well as estimate the price level associated with the projected output quantity. The models presented in this study indicate how factors such as stochastic prices and output levels can influence the firm's beta. Thus, the model could be potentially useful to managers in evaluating the impact of alternative pricing policies and demand fluctuations on the systematic risk of the firm. In addition to the production decision, corporate managers must make the capital investment decision (which projects to invest in) as well as the financing decision (the source of funds to be used to finance projects undertaken). These decisions are linked through the risk-adjusted discount rate appropriate for evaluating the new project.10 That is, each project must be evaluated at a discount rate which reflects the systematic risk of its operating cash flows as well as the "optimal" financial leverage of the firm as a whole. In accord with modern capital budgeting theory, the appropriate discount rate is determined by the project's systematic risk or beta. The risk assessment model presented in this study could be used to estimate the systematic risk of a project. Specifically, the model incorporates the effect of cost structures and debt financing on beta. In fact, the model shows that the covariance risk of a project can be parti- tioned into other volatility elements. Such information could aid managers in estimating the appropriate capitalization rate for alter- native investment projects. In addition to investors, financial information intermediaries and corporate managers, accounting regulators or policymakers were identified as a fourth group which may be interested in the results of this study. The primary regulators in the financial reporting environment are the FASB and the Securities and Exchange Commission (SEC). Both regulators share a concern over the effects of financial reporting requirements on investors. It is argued that inequities may befall investors because of informational deficiencies (i.e., failure to disclose). In addition, policymakers appear to share a 9 concern over the effects of fuller disclosure on resource allocation and capital formation (FASB [1976] and SEC [1977]). Although the model in the present study does not investigate the contention that alternative reporting disclosures influence investor decisions, the present model does provide a theoretical framework for evaluating the efficacy of certain required disclosures. That is, a model such as the one presented herein may aid policymakers in their attempt to pro- vide financial information that is useful to the investor decision making process. In a related vein, risk assessment models can be used to examine one aspect of the economic consequences of a proposed regu- lation and of the disclosure once a regulation has been implemented.11 There is considerable controversy over which economic consequences to the various constituencies should be considered by financial reporting policymakers. To address such issues, policymakers need models that recognize the role of information in the investor's and other user's decision settings. This study presents and empirically examines one such model. The remainder of this study is organized as follows: Chapter 2 is a review of the existing literature that is related to the present research. This review includes a discussion of studies which have empirically linked accounting, financial, and economic variables to a systematic risk measure. Also discussed in Chapter 2 are analytical studies which have used the theory of the firm to determine the com- ponents associated with systematic risk. Chapter 3 presents the theory underlying the present study. Specifically, the presentation in Chapter 3 includes a discussion of the theory underlying the market model beta and an analytical development of a theoretically derived 10 systematic risk model that simultaneously captures both business and financial risk factors. Chapter 4 is a description of the methodology used to empirically test the models developed in Chapter 3. The empir- ical tests and a discussion of the results of those tests are presented in Chapter 5. Finally, Chapter 6 includes a discussion of the impli- cations and scope of the study, as well as suggestions for future research. 11 Chapter 1 Footnotes 1Accounting Principles Board, Statement No. 4, "Basic Con- cepts and Accounting Principles Underlying Statements of Business Enterprises" (New York: AICPA), 1970), para. 9. 2American Institute of Certified Public Accountants, Objec- tives of Financial Statements, Report of the Study Group on the jgbjectives of Financial Statements (New York: AICPA, 1973), 13. 3Financial Accounting Standards Board, Statement of Financial Accounting Concepts No. 1, "Objectives of Financial Reporting by Busi- ness Enterprises" (Stamford, Connecticut: FASB, 1978), para. 34. 4Financial Accounting Standards Board, Exposure Draft - State- ment of Financial Accounting Concepts No. 5, "Reporting Income, Cash Flows, and Financial Position of Business Enterprises" (Stamford: FASB, 1981), para. 23, 24. 5William Beaver, Paul Kettler, and Myron Scholes, "The Associ- ation Between Market Determined and Accounting Determined Risk Mea- sures," The Accountinngeview (October 1970), 654. 6The accounting beta measures the covariability of a firm's accounting income with the average accounting income across the market. This measure may be represented mathematically as: = cov (xj. X“) 83 02(x ) M where X. = the accounting income of firm j XM = the average accounting income across the market 02(XM) the variance of the average accounting income across the market 7Semi-strong market efficiency is a key principle underlying research on the association between accounting information and market based variables. In semi-strong efficient markets, prices "fully reflect" all publicly available information. Therefore, the returns implicit in the price reflect the risk involved, so that expected return is consistent with risk borne. For a complete synthesis of the theory and empirical work on efficient capital markets, see Fama [1970] and Dyckman, Downes and Magee [1975]. 8The term financial information intermediaries indicates those groups involved in the analysis, processing, and interpretation of financial information (e.g., financial analyst, bond rating agencies, brokerage firms, etc.). 12 9An efficient portfolio is a well diversified portfolio. For a well diversified portfolio, the unsystematic risk is approximately zero. Diversification is accomplished by increasing the number of securities, such that no one security or industry represents a dispro— portionate share of the portfolio. In short, an efficient portfolio yields the minimum variance for a given rate of return. For a more complete discussion, see Sharpe [1970]. 10The cost of capital, the capital structure of the firm, and the investment decision are all inextricably linked. For a discussion of the existing theory and underlying assumptions of market conditions, see Haley and Schall [1972]. 11There are many examples of security price research used to examine the effects of financial reporting regulations. Dhaliwal [1978] is an example of a research study that has examined shifts in systematic risk (or beta) as an economic effect that may accompany the adoption of an accounting regulation. CHAPTER 2 REVIEW OF RELATED RESEARCH The focus of this chapter is a review of the existing litera- ture concerned with the determination of systematic risk. This review is divided into five sections. The first section includes a table which details the empirical work linking accounting, financial, and economic variables to a systematic risk measure. The second section focuses on analytical studies which have been concerned with a theoret- ical examination of the financial risk component of beta. Section three is similar to section two; it focuses on analytical studies which have been concerned with a theoretical examination of the oper- ating risk component of systematic risk. Section four reviews research studies which have provided empirical support for theoretical models of systematic risk. Such studies are most closely related to the present study. The final section, section five, is a summary of the chapter. 2.1 Empirical Beta Association Studies The empirical analyses of systematic risk have examined the correlations between beta and various accounting, financial, and eco- nomic variables. A common methodological approach used in these studies has been the linear multiple regression model. Reflective of this approach, a systematic risk measure is expressed as a function of numerous variables derived from various financial data bases. 13 14 Using this approach, Beaver, Kettler and Scholes [1970] conducted one of the earliest studies in the risk assessment area. These researchers sought support for the joint hypothesis that accounting data do reflect information about the risk of capital assets and that such information is impounded in the market price of the securities. The statistical test consisted of correlating seven accounting measures with market model betas. The seven accounting variables used were: divided pay- out, asset growth, leverage, liquidity, asset size, earnings vari- ability, and an accounting beta (earnings covariability).1 There were two major findings of this pioneering work. First, a significant con- temporaneous association was detected between several of the accounting risk measures and the market-determined beta. Secondly, a beta pre- diction model incorporating the accounting risk measures as intrumental variables was superior to a naive model. Utilizing the basic methodological approach of Beaver, Kettler and Scholes (cross sectional linear regression and correlation analysis), various other researchers have examined the relationship between accoun- ting risk measures and systematic risk. Some empirical studies have examined the association between market-based betas and various mea- sures derived from accounting variables. Other empirical analyses have investigated the association between beta and various ad hoc proxies for other possible determinants of systematic risk. Most com- monly seen in the literature is a multiple regression model of beta as a function of various accounting variables combined with ad hoc proxies. Table 2.1 contains a listing of the empirical beta associ- ation studies. 15 TABLE 2.1 Empirical Beta Association Studies Authors Measures which were related to market- based betas Ball and Brown [1969] Beaver, Kettler, and Scholes [1970] Beaver and Manegold [1975] Ben Zion and Shalit [1975] Bildersee [1975] Boness, Chen & Jatusipitak [1974] Bowman [1980a] Breen and Lerner [1973] Collins and O'Connor [1978] Derstine and Huefner [1974] Specifications of the accounting beta based on three different income mea- sures Seven accounting-based variables: dividend payout, asset growth, lever- age, liquidity, asset size, earnings variability and an accounting beta Three specifications of the accounting beta examined at the portfolio level Two accounting—based ratios for lever- age and firm size, variable for divi— dend payout record Various corporate decision variables, six accounting-based ratios, industry classes Market value measures of the debt-to- equity ratio. Divided sample into three classes based on their amount of change in leverage (greater than 16%, between 8 and 16%, and less than 8%) Two specifications of the accounting beta, a debt-to-equity ratio and a lease-to-equity ratio, industry classes Seven variables from accounting and market data Seven accounting-based ratios used by _Beaver,.gt.§l. [1970]; (sample classi- fied as full cost vs. successful efforts, and producer vs. integrated petroleum firms) Four accounting-based ratios found significant by Beaver, 35 El- [1970]; (sample classified by inventory valu- ation method: LIFO vs. FIFO) 16 TABLE 2.1--Continued Authors Measures which were related to market- based betas Eskew [1975] Eskew [1979] Fabozzi and Francis [1979] Gonedes [1973] Gordon and Halpern [1974] Griffin [1976] Hamada [1972] Hill and Stone [1980] Johnson and Deckro [1981] Lev [1974] Lev and Kunitzky [1974] Seven accounting-based ratios used by Beaver 33 a1. [1970]; (sample classi- fied as successful efforts vs. full cost petroleum firms) Nine accounting-based ratios including the seven ratios used by Beaver_gt.al. [1970] (examined the forecasts of mar- ket risk produced by models based on accounting data) Three measures based on accounting and market data (model also included a binary qualitative variable to capture the effect of twenty-three industry categories) Two accounting betas based on net in- come and net income per dollar of assets A specification of an accounting beta based on growth in firms' earnings ,per share Several risk measures derived from quar- terly earnings and quarterly dividends Three measures of the debt-to-equity ratio Various accounting measures of risk (developed an accounting equity beta and related it to an accounting oper- ating beta and accounting measure of financial leverage) A cash flow measure computed using various economic indicators Average per unit variable cost (sample classified by industry: steel, elec- tric utilities, oil producers) Nine risk measures derived from accoun- ting and dividend record data 17 TABLE 2.l--Continued Authors Measures which were related to market- based betas Logue and Merville [1972] Melicher [1974] Melicher and Rush [1974] Moyer and Chatfield [1983] Pettit and Westerfield [1972] Robinchek and Cohn [1974] Rosenberg and McKibben [1973] Thompson [1976] Woodward and Baesel [1975] (incorporated smoothing indicators in the risk model Nine variables derived from financial and market data Twenty-eight variables were reduced to seven financial dimensions using factor analytic procedures (sample restricted to the electric utility industry) Eleven selected financial variables based on Melicher [1974] were reduced to seven financial dimensions using factor analytic procedures to explain contemporaneous changes in systematic risk Seven variables derived from accoun- ting, market and economic data sum- marized as market power variables Three measures of a firm's cash-flow beta, various accounting-based ratios Two economic indicators (real personal income and the change in the Consumer Price Index) Thirty—two variables derived from both accounting and stock market data (model included binary variable for NYSE membership) Forty-three variables derived from accounting, market and economic data (explanatory variables examined in their mean, variance and covariance forms) A price elasticity measure based on successive changes in the gross product of the macroeconomy 18 In general, the empirical evidence presented by the studies listed in Table 2.1 suggests an association between systematic risk and five factors derived from accounting, financial, and economic data: earnings covariability (accounting betas), earnings volatility, lever— age, growth, and possibly, dividend payout. However, despite the substantial number of studies cited, the empirical results are some- what inconsistent and the factors identified (except for the accoun- ting beta and leverage factors) are not linked to the theoretical determinants of systematic risk. This same observation was made by Lev [1974]: Here, as in many other areas of financial analysis research, the empirical investigation was basically a fishing expedition: a large number of financial vari- ables were correlated in various statistical forms with systematic risk measures, yielding in some cases sig- nificant correlations.2 ‘ Thus, much of the past empirical work has failed to identify the basic firm characteristics that should theoretically determine the risk of common stocks. The link between the characteristics of the firm and the beta of its securities has been explored at a theoretical level in several important papers. These papers will be briefly discussed in this chapter with a more complete mathematical development relegated to chapter three. 2.2 Theoretical Examinations of the Financial Leverage Component of Systematic Risk Hamada [1969, 1972] was the first to analytically examine the relationship between a firm's capital structure (debt-to-equity ratio) and systematic risk. First, Hamada [1969] used the Capital Asset Pricing Model (CAPM) of Sharpe [1964], Lintner [1965a; 1965b], and l9 Mossin [1966] to demonstrate that the cost of equity capital in a levered firm is a linear function of the debt-to-equity ratio.3 Relying on the propositions of Modigliani and Miller [1958, 1963] (MM), Hamada [1972] showed that the beta of a levered firm consists of two elements: (1) a financial leverage component (the debt-to-equity ratio), and (2) an operating risk component (the unlevered beta of the firm). It should be noted that this important result is fundamental to all subsequent analytical papers which have mathematically decomposed the beta measure. Research studies extending the financial leverage element of Hamada's analysis have focused on the effects of two market imperfec- tions: (1) taxes (personal and corporate) and (2) risky corporate debt. With regard to the first type of market imperfection, Hamada [1969] examined the impact of corporate taxes on the equilibrium expected rate of return to the levered firm. In the CAPM framework, Hamada demonstrated that, in the presence of corporate taxes, leverage has the effect of increasing the firm's beta by an after-tax factor (one minus the tax rate) per marginal unit of the debt-to—equity ratio. In comparison with the without-tax case, wherein the debt-to- equity ratio increases beta on a marginal unit-by-unit basis, the inclusion of corporate taxes implies a reduction of the firm's market- based beta. That is, as the tax advantage of debt lessens the cash outflow effects of the firm's fixed interest charges, the volatility of the residual (equity) return will be reduced. The impact of personal taxes on Hamada's corporate tax analysis has been investigated by several researchers (Farrar and Selwyn [1969], Stiglitz [1973], Miller [1977], Arditti,_g£ El. [1977], and Yagill 20 [1982]). In brief, the existence of personal taxes may reduce the corporate tax advantage associated with leverage. The specific effect of personal taxes on valuation and hence, on systematic risk, depends upon the personal income tax rate applicable to common stock income, the personal tax rate applicable to income from the company's debt, and differential tax rates on ordinary income and capital gains. In a final extension of Hamada's financial leverage component, Conine [1980] investigated the effect of risky debt4 on beta. Relying on the analytical results of Rubinstein [1973] and Bierman and Oldfield [1979], Conine analytically showed that the systematic risk of a levered firm is decreased by the introduction of risky debt into the firm's capital structure. This result is consistent with the fact that the volatility in the firm's earnings stream is now shared by both debt and equity claimants. 2.3 Theoretical Examinations of the Operating Risk Component of Systematic Risk Other researchers have chosen to focus on the theoretical relationship between beta and various aspects of operating risk. Research papers which have explored the role of operating risk as a determinant of systematic risk may be classified into two major groups based on the mode of inquiry: (1) an income statement approach which assumes accounting rates of return may be equated with market rates of return, and (2) a cash flow approach which integrates the equilibrium analysis of the product and factor markets with risk assessment. Several researchers used the income statement approach to analytically decompose the operating component of systematic risk: Rubinstein [1973], Magee [1975], Long and Racette [1974], Lev [1974], 21 Percival [1974], Brenner and Smidt [1978], Gahlon [1981, 1982], and Conine [1982]. Rubinstein [1973] demonstrated that there was a posi— tive relationship between systematic risk and operating risk. He then further explored the determinants of the unlevered beta (operating risk) of a multiactivity firm in terms of familiar accounting vari- ables such as fixed cost, variable cost per unit, and sales price per unit of output. In a related manner, Lev [1974], Long and Racette [1974], Percival [1974], and Gahlon [1981; 1982] analytically demon- strated that there was a positive relationship between a firm's oper- ating leverage (the ratio of fixed to variable operating costs) and beta.5 That is, other things being equal, the higher the firm's oper- ating leverage, the higher the systematic risk of the firm. Other income statement models analytically linking beta and operating risk were developed by Magee [1975], Brenner and Smidt [1978], and Bowman [1979]. These authors made no attempt, however, to decompose the earnings stream. Instead, they concentrated on the co- variability of the final earnings figure with either a market return measure or an aggregate market earnings measure. For example, with the restrictive assumption of a market consisting of pure equity firms only, Bowman [1979] established a theoretical relationship between systematic risk and a covariability measure of the firm's earnings with all other earnings in the market (the accounting beta). Finally, in the most recent study utilizing an income state- ment approach, Conine [1982] developed a theoretical relationship between systematic risk and the microeconomic determinants of business risk. Conine, in a manner similar to Rubinstein [1973], demonstrated analytically that if price, variable cost, and output demand are 22 multivariate normal random variables, then the firm's unlevered beta is a function of the covariability of the firm's output level with the market return, the covariability of the firm's contribution mar- gin with the market return, and the expected values of the firm's out- put level and contribution margin. Conine, as many other researchers, did not, however, provide empirical support for his systematic risk model. While the research incorporating an income statement approach to beta decomposition is insightful in delineating the accounting ele- ments of systematic risk, other analytical researchers have utilized a cash flow approach which integrates risk assessment with an economic analysis of the product and factor markets. Analytical work of this nature has been accomplished by Greenberg, Marshall and Yawitz [1978], Subrahamanyam and Thomadakis [1980], and Conine [1983]. Greenberg, ‘gt al., presented several analytical models of systematic risk that combined the microeconomic theory of the firm with the capital asset valuation theory of the financial markets. Specifically, the authors incorporated a firm's production and demand functions (characterizing a specific market structure) into the analytical cash flow decomposi- tion of beta. While the scope of Greenberg, gt_§1,, was quite broad, Subrahamanyam and Thomadakis [1980] developed a more specific model of beta that included an index of monopoly power, a demand elasticity factor, and a labor-capital ratio. In.a very similar manner, Conine [1983] analytically linked systematic risk to constant price elasticity of demand, the certainty equivalents of random output and variable cost measures, and the covariance of these measures with the cash flow of the market portfolio. 23 Although the models that link behavior in the product and financial markets illustrate the interdependence of the microeconomic decisions of the firm and the market's valuation of its capital assets, these models have not been empirically verified. In fact, this is a criticism of much of the analytical work in the risk assessment area. Several researchers (e.g., Hamada [1972], Lev [1974], and Bowman [19803, 1980b] have attempted, however, to empirically examine certain aspects of their theoretical work. Studies of this nature are most closely related to the present research, and, as such, a more detailed discus- sion of these studies follows. 2.4 Theoretical Examinations of Systematic Risk Supported by Empirical Analysis The lack of empirical support for theoretical models of syste- matic risk is undoubtedly because the data necessary to operationalize the models pose some difficult estimation issues. Nonetheless, some researchers have tried to solve the methodological and measurement issues in an effort to examine the empirical validity of their models. Hamada [1972] provided empirical support for his theoretically-derived relationship between financial leverage and systematic risk by devising an indirect test which isolated the financial leverage effect on beta. He grouped a sample of 304 firms into nine homogeneous industry groups and computed unlevered betas for each firm. The following four market models were tested using the data of the 304 firms for the years 1948 to 1967: Rait - a “i + aBi R"mt + aeit Rbit ' b"1 + 1381 Rmt + bait 24 ll Q 8 E In (1+Ra + i In (1+Rmt) + it) ac 1 ac ac it 1" (1+Rbit) = bcai + chi 1“ (“R1“) + bceit where R1t is the return on company i in time t, o and 81 are regres- i sion coefficients for each firm, Rmt is the market rate of return including dividends, e is the residual error term with the standard it econometric properties, and subscripts a and b, respectively, denote unlevered and levered return factors. Hamada then demonstrated that the dispersion of the firms' betas in a specific risk class was reduced by the unlevering process. This result led Hamada to conclude that "leverage has explained as much as, roughly, 21 to 24 per cent of the value of the mean beta."6 Another study, Lev [1974], has investigated the analytical relationship between systematic risk and operating leverage. Lev's analytical work suggested that the systematic risk of common stocks should be positively associated with the degree of operating leverage or negatively associated with the level of variable costs. Lev's empirical sample consisted of firms with similar sales pattern in homogeneous industries. First, Lev used a time series regression to separate the variable cost component from fixed costs: TC = a. + v . + U J JQJt it it where TC is total cost of firm j in period t, a and v are regres- Jt j J sion coefficients, th is a physical output measure, and U a jt is residual error term with the standard econometric properties. Next, 25 Lev ran a cross-sectional regression relating beta to the variable cost component obtained from the time series regression. Lev's cross- sectional regression (fitted for each homogeneous industry) was of the form: where Bj is the market model beta of firm j, a2 and b2 are regression coefficients, and €2j is a residual error term with the standard prop- erties. Lev's empirical results, although statistically "weak" for some of the industries, were supportive of the hypothesized relation- ships. That is, average variable costs were negatively associated with systematic risk measures for all three industries examined. While Lev provided empirical support for the operating risk component of beta and Hamada concentrated on providing empirical sup- port for the leverage component, Bowman [1980a, 1980b] accomplished empirical work relative to both theoretical components of risk. In the Bowman studies, a significant association was detected between an estimated beta and the leverage component as measured by the debt-to- equity ratio. These empirical results are, of course, consistent with the theoretical work of Hamada [1969; 1972]. In addition, Bowman [1980a] found a direct association between operating risk (measured by the accounting beta) and systematic risk. In summary, several researchers have examined the empirical validity of derived models of systematic risk. As indicated in this section, the empirical results were consistent with the hypothesized relationships presented in the theoretical risk models. Similar to the studies discussed in this section, the present research combines 26 analytical modeling of systematic risk with empirical verification. The present research is an extension of the Rubinstein [1973] analytical work. As such, the present research will integrate the business risk analysis of Rubinstein [1973] and Conine [1982] with the earlier financial risk analysis of Hamada [1969; 1972]. In addition, the present study will empirically test the resulting theoretically- derived model of systematic risk, thus addressing the major criticism of the empirical work in the systematic risk assessment research area. In fact, the published literature to date does not reveal an empirical test of a theoretical systematic risk model which incorporates both financial and business risk. Although Bowman [1980a] did empirically test a general model of systematic risk, his business risk component did not incorporate the analytical work of either Rubinstein [1973] or Conine [1982] with regard to the theoretical determinants of business risk. Instead, as indicated earlier, Bowman included the accounting beta as a surrogate for business risk. Yet, in the presence of lever- age, the accounting beta captures both business and financial risk. Bowman states that "a variable which has no contamination from finan- cial risk is preferred but unavailable."7 It is suggested that the present research addresses this issue by estimating an analytically- derived business risk component. Furthermore, the comparative analysis portion of the research will examine the adequacy of using the accoun- ting beta as a surrogate for business risk in systematic risk models. 2.5 Summary The purpose of this chapter was to provide a review of the existing studies which are related to the present research. The 27 empirical beta-association studies listed in section 2.1 were grouped according to the nature of the variables associated with the risk mea- sures. Analytical studies which have examined the theoretical deter- minants of beta were discussed in sections 2.2 and 2.3. Such studies are fundamental to the model development in the next chapter. Research studies which have empirically examined the theoretical models of systematic risk were reviewed in section 2.4. These studies are similar in nature to the present research. Specifically, the major focus of the present study is an empirical examination of a theoretical syste- matic risk model. 28 Chapter 2 Footnotes 1See footnote 6 of Chapter 1 for a definition of the accoun- ting beta measure. 2Baruch, Lev, Financial Statement Analysis: A New Approach (New Jersey: Prentice, Hall, Inc., 1974), p. 208. 3The Hamada [1969] analysis in the CAPM framework is consistent with MM [1958; 1963] Propositions l and 2 derived in a partial equili- brium setting (homogeneous risk classes). In addition, the Hamada analysis (consistent with MM) assumes a separability of the production and financing decisions of the firm. 4The Hamada [1969, 1972] results assumed that the firm's debt is riskless (the return is certain). A consideration of bankruptcy costs, agency relationships, etc., implies that the firm's debt return is uncertain and, therefore, risky. 5Differences among the models derived by these authors depend on the underlying assumptions. For example, Long and Racette [l974]’ assumed output and unit variable costs were constant but price of out- put was a random variable. Lev [1974] allowed output quantity to be a random variable but held price constant while considering only firms in homogeneous industries with similar sales patterns. Gahlon [1981; 1982] assumed contribution margin and fixed costs were known with certainty but output quantity was a random variable. 6Robert Hamada, "The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stocks," Journal of Finance, May 1972, p. 442. 7Robert G. Bowman, "The Debt Equivalence of Leases: An Empirical Investigation," The Accounting Review, LV (April 1980), p. 239. CHAPTER 3 THEORY UNDERLYING THE MODEL DEVELOPMENT AND EMPIRICAL TESTS As was stated in the introductory chapter, this research addresses both theoretical and empirical aspects of the risk deter- mination literature. That is, the primary focus of this study is to examine, for two samples of firms, the relationship between accounting data (reflecting the operating and financing decisions of the firm) and systematic risk (as measured on a market index). The purpose of this chapter is to discuss the theory under- lying the present research, as well as to present the mathematical development of two general models of systematic risk. Section 3.1 con- sists of a review of the theory relevant to the analytical modeling of systematic risk. The mathematical development of a risk model which simultaneously captures both business and financial risk factors is presented in section 3.2. This model indicates a hypothesized rela- tionship between beta and several theoretical variables that can be estimated from accounting data. An alternate model which incorporates an accounting beta as the business risk measure is developed in sec- tion 3.3. Both risk models are operationalized in the empirical examinations of Chapter 4.. A summary of the chapter is presented in section 3.4. 29 30 3.1 Theory Underlying Analytical Systematic Risk Research Analytical models of systematic risk attempt to explain the manner in which corporate policy affects the firm's beta. Corporate managers must make two major firm policy decisions in an effort to maximize shareholder wealth. First, the operating decision must be determined (e.g., line of business, output level, selling price and investment base). Secondly, a determination of the source of funds to be used to finance the capital asset base must be made. Both corpo- rate policy decisions (operating and financing) directly influence the perceived risk level of the firm in the eyes of the shareholders. Researchers have used a mathematical modeling approach to explore the linkage between corporate policy decisions and the firm's systematic risk. The mathematical development of risk assessment models has, in general, relied upon an acceptance of the theoretical constructs which indicate that the operating decision of the firm may be made without reference to the financing decision.1 In short, mathe- matical models of risk include a separate component for operating risk and for financing risk. The theoretical support for this formulation of risk was set forth in a partial equilibrium framework by Modigliani and Miller (MM) [1958] and in a CAPM context-by Hamada [1969].2 MM examined the interrelationship of security valuation, financial leverage, and the firm's cost of capital. The theoretical propositions developed by MM which are important to risk assessment research are based on three key assumptions: (1) Capital markets are perfect. Information is cost- less and readily available to all investors, there are no transaction costs or taxes, and all securi- ties are infinitely divisible. Investors are 31 assumed to be rational price-takers. (2) The average expected future operating earnings of a firm are represented by a subjective random variable. It is assumed that the expected values of the probability distributions of all investors are the same. (3) Firms can be categorized into "equivalent risk" classes. All firms within a class have the same degree of operating risk. Based on these assumptions, the propositions set forth by MM were: Proposition I: The market value of the firm, in equilibrium, and its cost of capital are independent of the degree of financial leverage employed by the firm. Proposition II: The cost of equity capital of the firm is equal to the capital- ization rate for a pure equity stream in its business risk class, plus a premium that is related to the financial risk and which increases linearly with the debt-to-equity ratio. It should be noted that proposition II follows directly from proposition I. Proposition I indicates that the market value of the firm is determined by capitalizing the firm's expected operating earnings stream at a discount rate appropriate for its business risk class. Although proposition II states that the cost of equity capital increases linearly with the debt-to-equity ratio, the total firm value (debt plus equity) is not affected. Thus, holding all other factors constant, the firm's overall cost of capital and the firm's market value are unchanged by capital structure variations. 32 While both propositions set forth by MM are fundamental to an understanding of the linkage between security valuation, the firm's capital structure, and the cost of capital, proposition II is most directly related to the theoretical risk assessment research. This latter proposition indicates which risk factors determine the expected return to the equity securities of a levered firm. That is, proposi— tion II states that the cost of equity capital is a function of an operating risk measure (the capitalization rate of a pure equity stream within the firm's risk class), a financing risk measure (the firm's debt-to-equity ratio), and a risk premium (the spread between the pure- equity stream capitalization rate and the riskless rate of return for a certain earnings stream). It follows that all relevant properties of an equity security in a partial equilibrium setting (homogeneous risk classes) can be uniquely characterized by specifying: (1) the firm's business risk class, and (2) the firm's financial risk measure (the debt-to-equity ratio). The MM propositions were based on an examination of firms within the same business risk class. Hamada [1969, 1972] demonstrated that the theoretical results posed by MM were valid in a general equil- ibrium setting (firms across all risk classes). Specifically, Hamada used the Capital Asset Pricing Model (CAPM) developed by Sharpe [1964], Lintner [1965], and Mossin [1966] to delineate the determinants of the expected return to the equity securities of a levered firm. Such a return, according to the Hamada results, was uniquely determined by the firm's debt-to-equity ratio and an unlevered systematic risk measure (beta). Next, Hamada related the beta of a levered firm to the beta of an unlevered firm. This analysis showed that the beta of a levered 33 firm consists of two risk components, a financial leverage component and an operating risk component. This important result has been funda- mental to subsequent research assessments of the determinants of the systematic risk, a fact that will become apparent in the analytical development of the next section. In summary, the Modigliani and Miller [1958] propositions are a key result underlying the theoretical risk assessment research. These propositions are directly linked to the risk composition model developed by Hamada [1969; 1972], a model which indicates that the systematic risk of a levered firm may be described by the firm's debt- to-equity ratio and an unlevered beta. 3.2 Systematic Risk Model Development The primary purpose of the present study is to empirically test a theoretically derived systematic risk model. The model development that follows is based on a mathematical integration of the theoretical systematic risk models of Hamada [1969; 1972] and Rubinstein [1973]. Appendix A contains complete details of the model integration. To facilitate the discussion of the model development, the following notation will be employed: t1! ll an expectations operator Q l a variance operator, with o = standard deviation cov = a covariance operator, with D = correlation coefficient RL = the rate of return on a levered firm L (random variable) the rate of return on an unlevered firm U, an all— equity firm with the same asset base as firm L (random variable) e” D = total market value of firm L debt 34 (I) ll total market value of firm L common stock < ll total market value of the firm = risk-free rate of return rate of return on the market portfolio of risky assets (random variable) 37’»? x. = the dollar value of earnings before interest J and taxes, or net operating income (random variable) F = total fixed operating costs of the firm VC = variable cost per unit (random variable) Q = output level of the firm (random variable) P = price per unit of output (random variable) The following model development assumes that firms can borrow and lend at the risk-free rate. In addition, the model abstracts from the effects of T, the corporate tax rate. Although the concepts of risky debt and corporate taxes could logically be incorporated within this study, the present research is viewed as an initial empirical test of a theoretical model of systematic risk. The incorporation of risky debt and corporate taxes represent future extensions of the current research. Given certain assumptions,3 the CAPM developed by Sharpe [1964], Lintner [1965], and Mossin [1966] specifies the following equilibrium pricing relationships for the equity securities of the levered firm L and of its unlevered counterpart firm U: E (RL) = RF + 8L [E(RM) - RF], and (3.1) E (RU) = RF + Bu (mm) - RF] (3.2) 35 ‘where BL cov (RL’RM)’ the systematic risk (or beta) of the equity securities of 02(RM) the levered firm L II) II cov (RU,RM), the systematic risk (or beta) 2 of the equity securities of 0 (RM) the unlevered firm U These relationships imply that the only variable which determines dif— ferential expected returns among the equity securities of firms L and U is the risk coefficient beta. The models further assert that there is a linear relationship between beta and expected return, such that the greater the risk, the higher the expected return. The CAPM is a one-period equilibrium pricing model. It provides a definition for the risk of a security but makes few assumptions about the stochastic proc- ess generating returns over time. Hamada [1969] utilized the CAPM relationships of Eq. (1) and (2) to derive Modigliani and Miller [1958] (MM) proposition II. In the notation of this paper, Hamada's derivation provided the following result: DL E (RL) = E (RU) + [E (RU) — RF] g; (3.3) The implication of Eq. (3) (and MM proposition II) is that the expected return to equity shareholders increases linearly with the debt-to-equity ratio. A definition of BL which is consistent with the above expres- sion can be easily derived. By substituting Eq. (2) for the E(RU) of (3) and simplifying, we obtain DL E(RL)=RF+[E(RM)-RF18U 1+?— L (3.4) 36 Finally, after considering equations Eq. (1) and (4), we can conclude: D B = 8 1 +-—— . (3.5) Equation (5) indicates that the systematic risk of a levered firm is a function of the debt-to-equity ratio and of an unlevered beta, 8 . The type of risk denoted by BU is commonly termed "business U risk" or "operating risk." Rubinstein [1973] built upon Hamada's work by interpreting the operating beta, 8 in terms of microeconomic variables specific to the U, firm. Thus, Rubinstein defined the return to the unlevered firm U as: XU/ F = operating income (3.6) = V , where x = (P - VC) Q - RU U U U U U of firm U. In addition, the Rubinstein analysis assumed that demand (Q) was stochastic while per unit contribution margin (P-VC)U was a constant. Utilizing these definitions and assumptions, Rubinstein derived the following relationship for the operating risk of a multi-activity firm (see Appendix A for the complete derivation and underlying assumptions): A Q o (RU. RM) 0 (RU) = 3 [a3 (P - vc>a o (Qa. RM) 0 aa$u ] (3.7) where A = number of activities (product lines) of the multiactivity firm U a = proportion of the firm's total assets that are devoted to activity a In this formulation: Ga indicates the relative investment of the firm in each activity, (P - VC)a represents the contribution margin of each 37 activity, 9 (Qa’ RM) reflects the influence of economy-wide events on Q a indicates the uncertainty oaVU of output per dollar of asset investment in activity a. As indicated the output of each activity, and <3( in Chapter 2, the published literature does not reveal a comprehensive empirical test of the Rubinstein model. For simplicity, it is next assumed that A and Ga = 1.0 (a one product-line firm). With these assumptions, expression (7) collapses to: QU o (RU. RM) 0 (RU) = (P - vc>U o (QU, RM)0'-V; (3.8) While Appendix A contains a complete derivation consistent with the Rubinstein approach, the algebraic manipulations summarized below lead to a fairly succinct expression for BU. The first step in the manipu- lation utilizes the definition of o and the fact that V is a constant U to obtain: COV (RU. FM) 0 (RU) = my COV (QU, RM) 0(QU) , (3 9) O (Ru) 0(RM) Vu o (QU) 0 (RM) . an expression which reduces to: COV (RU, RM) = (P _ VC) U COV (QU’ iS4) (3.10) 0 (RM) vU 0 (RM) 1 Multiplying both sides of Eq. (3.10) by 0(RM) yields: COV (RU, RM) = (P _ VC) U COV ((211, RM) 2 V 2 0 (RM) U 0 (RM) , or equivalently (3.11) 38 u 8 (3.12) where 8Q = a volume-of-output beta measure. Equation (12) is a reduction of Rubinstein's model of operating risk. It states that operating risk (BU) of a single product firm is a func— tion of a demand volatility measure (8Q) and of the product line's con- tribution margin, (P - VC)U. It is again noted, however, that Eq. (12) assumes that demand (Q) is stochastic, while price (P) and variable cost (VC) are held constant. Conine [1982] has relaxed the constancy assumption with regard to P and VC and, accordingly, has provided a more complete definition of the determinants of business risk. As noted by Conine, his model incorporates all of the following business risk components: a. the degree of operating leverage (i.e., the degree of fixed costs relative to variable costs), b. risk in demand for the firm's output c. risk in the price level received per unit of the firm's output, and d. risk in the variable costs associated with the production and marketing of the firm's output. In his analysis, Conine [1982] demonstrated that if variable cost per unit, price per unit, and output level are all mutually- dependent random variables with a multivariate normal distribution, then the unlevered beta of the firm becomes: SD = cov [(P - VC)U QU. RM] ,l_ 2 VU (3.13) 0 (RM) 39 After applying the operational rule for the covariance of the product of two random variables, Conine concluded that: __1__ _ BU - VU E (P vc>U 8Q + E (QU) 8(P _ VC)U] (3.14) where 8(P _ VC)U = a contribution margin beta measure. Equation (14) shows that if price, variable cost, and demand are all random variables, then business risk becomes a function of two vola- tility measures: BQ’ covariability of the firm's output level with the market return, and , covariability of the firm's con- B(p - vc>U tribution margin with the market return. It is also interesting to note that in a single product—line firm environment with P and VC held constant, Conine's analytical development collapses to Eq. (12), a reduction of the Rubinstein formulation of business risk of Eq. 7. Although Conine's model, by allowing for stochastic price, variable cost, and demand, provides a more complete model, the unit contribution margin covariability measure (8 ) cannot be readily P-VC estimated from publicly available accounting data. As such, the cur- rent study will focus on the operational aspects of Rubinstein's formulation of business risk as stated in Equation (12). Equation (12) does not include, however, a component for financial risk. To add this component to the model, we must return to Hamada's formulation of the systematic risk of the levered firm in Eq. (5). Combining Eq. (5) with Eq. (12) yields: D P-VC L T 8Q 1+? (3.15) L" 40 Operationalizing this expression involves considerable estimation. As such, this study represents an initial attempt to estimate a theoretically derived systematic risk model. Clearly, as more accoun- ting data becomes publicly available, an extension of this study could include an estimation of Conine's business risk formulation as ex- pressed in Equation (14). Hereafter Eq. (15) will be referred to as Model 1. It is noted that Model 1 represents an analytical reduction of the basic Rubinstein model to Eq. (12), and an integration with Hamada's work [Eq. (5)]. The first component of Model 1 represents the business risk of the levered firm while the second component represents financial risk. As such, Model 1 may be viewed as a complete systematic risk model with both of the major components of systematic risk included in its formu- lation. Specifically, Model 1 indicates that the market risk of a leveraged firm with stochastic demand is equal to the market risk of an all-equity firm plus an amount proportionate to the leverage factor as measured by the debt-to-equity ratio. 3.3 Alternative Systematic Risk Model The comparative analysis of the second phase of this research requires the development of a second model of systematic risk. Several accounting researchers have suggested that the accounting beta is a proper surrogate for the business risk component of the systematic risk models. In fact, Bowman [1979] has shown that risk can be analytically linked to the accounting beta. That is, after assuming the existence of pure equity firms only, Bowman derived the following direct rela- tionship between systematic risk and the accounting beta: 41 2 where cov (XU’XM) ' 2 A 0 (KM) VM = total value of the (all-equity) market VU = value of the individual firm U. Thus, under a restrictive all-equity assumption, the accounting beta is directly proportional to the business risk of the firm. However, it should be noted that as risky debt is added to the firm's capital structure, the accounting beta includes both financial and business risk elements.6 For comparative purposes, this research will substitute the accounting beta for the business risk component of Model 1. This subscription leads to Eq. (17), hereafter referred to as Model 2: V D BL -—=BA l +-S—' (3.17) c: If" Model 2 will be used to determine empirically the adequacy of using the accounting beta as a surrogate for business risk in the theo- retical beta decomposition models. If the surrogation proves to be adequate, it could facilitate empirical work in the risk assessment area by reducing the number of variables to be estimated in measuring the business risk component of systematic risk. The empirical tests of this study are directly related to the models formulated in expressions (15) and (17). These expressions 42 are based on the theoretical work of Hamada [1969; 1972] and Rubinstein [1973]. As such, Models 1 and 2 provide the desired linkage of the firm's beta with the corporate characteristics reflected in the production-financing-investment activities of the firm and are the basis for the empirical examination to be described in the next chapter. 3.4 Summary This chapter has presented a discussion of the theoretical constructs linking acc0unting data (reflecting the operating and financing decisions of the firm) to a market based beta (a syste- matic risk measure). In section 3.1, the theoretical relationship between the MM propositions (partial equilibrium analysis) and the Hamada risk formulations (general equilibrium analysis) was discussed. Sections 3.2 and 3.3 presented an analytical development of two general risk models utilizing the theoretical framework of Hamada- Rubinstein. Both models indicate a relationship between beta and several variables that can be derived from accounting data. The oper- ational aspects and empirical testing of the models will be discussed in the next chapter. 43 Chapter 3 Footnotes 1In contrast, Hite [1977] focused on the valuation impact of the interaction of the production decision of the firm with the financing decision. That is, Hite demonstrated that since capital, labor, and output all vary with the degree of leverage, the total leverage effect on value can more than offset the tax shelter from interest deductibility due to a simultaneous shift in the business risk complexion of the firm. 2The MM propositions have theoretical support in the context of other asset pricing models. For example. Galai and Masulis [1976] have proven the propositions within the framework of the option- pricing model. Hirshleifer [1966] utilized state-preference theory to establish the validity of the MM propositions. As a synthesis, Hsia [1978] has shown that the MM propositions are consistent with the option pricing model and CAPM. 3The most important assumptions are: a perfect and competi- tive securities market, no restrictions on short-selling and borrowing, and a single-period horizon. See Hamada (1969), p. 14, for a detailed discussion. 4This same relationship was derived, using an alternate set of assumptions, in Hamada [1972]. 5Thomas E. Conine, Jr., "On the Theoretical Relationship Between Business Risk and Systematic Risk," Journal of Business Finance & Accounting (Summer 1982), 200. 6A8 risky debt in the manner of Conine [1980] is added to the mathematical formulation of systematic risk, the covariability of the debt return (financing risk) becomes an element of the accounting beta. As such, in the presence of risky debt, the accounting beta cannot be viewed as a pure measure of operating risk. CHAPTER 4 METHODOLOGY The empirical tests of this study are directly related to the systematic risk models formulated in expressions 3.15 and 3.17 of Chapter 3. These expressions provide the desired linkage of the firm's market-based beta with the corporate characteristics reflected in the production-financing-investing activities of the firm. As such, Model 1, expressed by equation 3.15, and Model 2, expressed by equation 3.17, are the foundation for the empirical tests described in this chapter. For explanatory purposes, expressions 3.15 and 3.17 may be rewritten V_u with the scaling factors Vu and Vm on the left hand side of the equa- tions.1 Accordingly, expression 3.15 (Model 1) may be rewritten as: DL BLVu = (P-VC)BQ(1 + :92). (4.1) In a similar manner, expression 3.17 (Model 2 may be expressed as: D Vu _ ._L BL VI; - er + SL). (4.2) An examination of the relationship between the scaled market- D L ’ _] 18 Q SL the major focus of the empirical tests of this study. As such, the based beta (8L) and its theoretical determinants [(PAVC), B empirical examination of Model 1 may be regarded as a test of syste- matic risk model with explicit theoretical underpinnings. In a general framework, Model 1 may be formulated as follows: 44 45 DL vueL = f[(P-VC), sq. -S—;]. (4.3) That is, the firm's market-based beta is a function of three firm— specific variables. Two of the variables [P-VC, 8Q] multiplicatively formulate the theoretical measure of business risk that was developed in Chapter 3. The measurement issues associated with each of the Model 1 variables will be discussed first. For comparative purposes, the relationship between the firm's market-based beta (BL) and the accounting beta as defined in footnote 6 of Chapter 1 was also examined. This association was formulated as the second risk model (Model 2) expressed in equation 3.17. Model 2 may be stated functionally as: D Vu L 34%;} fIBA. 75—]. (4.4) L The only variable unique to the formulation of Model 2 is the accoun- ting beta (BA)' Thus, the accounting beta will be the only variable discussed within the context of the second systematic risk model. The specific definitions for the accounting risk measures and market-based variables are detailed in Table 4.1 at the end of this chapter. Table 4.1 associates each of the elements of Model 1 and Model 2 with its specific data base. The first section of this chapter contains a description of the procedures used to select the two samples examined in this study. The estimation techniques needed to operationalize Model 1 are described in section 4.2. Section 4.3 contains a similar presentation for Model 2. An overview of the purpose of the empirical 46 investigations is contained in section 4.4. The last section, sec- tion 4.5, is a summary of the chapter. 4.1 Sample Selection Procedures Two samples of firms were used to examine the descriptive validity of the risk models formulated in expressions 3.15 and 3.17. To assure a broad test of the models, the first sample (NYSE firms) was randomly drawn fromt he annual Compustat data files without regard to firm industry classification. One hundred firms were examined for possible inclusion in the sample of NYSE firms. Of these initial firms, it was necessary to eliminate fifty-seven firms due to incom- plete data histories on one or more of the five data tapes used for the 1975-1980 study period. Two additional firms were eliminated because of merger activity during the test period. The final sample consisted of forty-one NYSE firms. These firms are listed in Appendix B. Several researchers have demonstrated the presence of an industry effect when relating systematic risk measures to accounting variables.2 An inter-industry effect implies differential risk across industry. The fit of the risk models within a homogeneous industry grouping could eliminate the possible shortcomings of not controlling for beta-financial data relationships that may differ by industry. Therefore, a second sample was drawn from the electric utility industry. The electric utility industry was selected because of homogeneity with regard to product, regulation environment, and accounting methodology, as well as the data availability of a physical output time series. All firms within the electric utility classification on the annual 47 Compustat tape were examined for possible inclusion in the electric utility sample. Thirty-eight firms survived the data availability criteria for the period 1971-1980. One additional firm was elimin- ated from the sample due to merger activity during the test period. The final electric utility sample consisted of thirty-seven firms. These firms are listed in Appendix C. 4.2 Estimation of the Components of Model 1 D All four variables 'BL’ (P-VC), BQ’ EL] needed to operation- L alize Model 1 have associated measurement issues which must be addressed. The estimation issues related to each variable will now be discussed. 4.2.1 Estimation of the Firm's Market-Based Beta (8L) The market-based beta of each firm was estimated using the market model relationship developed by Sharpe [1963]. The market model is a specification of the stochastic return-generating process on an individual security. This process may be represented mathemati- cally as follows: Rjtg j+ ijt+ejt (4.5) where Rjt = the return on security j in period t Rmt - the return on the market index in period t éjt - the individualistic factor representing the part of security's j return which is independent of R (assumed to have a zero mean, constant variance, and no serial correlation with R ) mt aj, B3 = the intercept and slope parameters associ- ated with the linear relationship. 48 The parameters (aj, B ) may be estimated using the ordinary j least-squares (OLS) statistical regression technique. The basic assumptions of the linear regression model (i.e., linearity, serial independence of error terms and homoscedasticity) have been tested and empirically supported.3 OLS regression was used in this study to estimate the market beta (BL) for each of the forty-one firms in sample one as well as the thirty-seven electric utility firms in sample two. For each of the NYSE sample firms, the seventy-two monthly returns (adjusted for divi- dends and other distributions) for the period from January 1975 through December 1980 were used as measures of the dependent variable ~ Rjt' For the electric utility sample, the monthly returns of each firm for the period January 1971 through December 1980 were used as measures of Rjt. Both the CRSP equal-weighted index and value-weighted indices were used to measure the independent variable Rmt. There are two measurement issues associated with the estimation of a firm's market-based beta: (1) The selection of a security market index to serve as a proxy for the unobservable market index. (2) The length of the historical estimation period. With regard to the first issue, the selection of a market index, Elgers and Murray [1982] have provided empirical evidence which suggests that the ability of accounting risk measures to explain cross— sectional variation among betas is highest when the firm's market betas are estimated using the CRSP equal-weighted market index. Many other capital market researchers (e.g., Roll [1977] and Foster [1978]), however, have suggested that value-weighted indices are 49 theoretically superior to equal-weighted indices. Due to the general uncertainty with regard to this issue, the market betas of both samples in this study were estimated using both the CRSP equal-weighted market index and the CRSP value-weighted index. The second issue involved in the estimation of the firms' mar- ket betas (BL) is the choice of an estimation time period. The research of Bogue [1972] and Gonedes [1973] suggests that 60-72 months is a reasonable estimation period for market model betas. According to the authors, the 60-72 month estimation period will insure a reason- able number of observations, yet avoid the problem of an increased likelihood of structural change in the generating process. In accord with this research, the market model betas of this study were, as previously indicated, estimated over a 72 month period (January 1975- December 1980) for the NYSE firms. A longer period of 120 months (January l97l-December 1980) was selected for the electric utility firms (sample 2). This choice was made in an effort to gain more degrees of freedom in the statistical procedures (time series regres- sion) used in the estimation of B , the theoretical output volatility Q measure derived from annual data. Quarterly output data were not available for the electric utility sample. In summary, the market-based beta (BL) of expressions 4.1 and 4.2 was estimated for each firm of both samples by using an OLS regression of the firm's monthly returns on the temporally correspond- ing market returns (value-weighted and equal weighted). This procedure yielded two market-based betas for each firm in both samples. 50 4.2.2 Estimation of the Contribution Mapgin Variable (P-VC) of the Business Risk Component In theory, the unit contribution margin (P-VC) is the price at the end of the period of the firm's output less the variable cost per unit of output for each product line. The data necessary to calculate the unit contribution margin cannot be obtained directly from the firm's publicly available financial statements. To estimate an average contribution margin for each firm, a time series regression of the following form was run: a. + 6. + e. yjt J 3th Jt where y.t = net operating income of firm; in time J period t Q’t = dollar volume of sales (both samples) and annual J kilowatt hours (KWHs) for the electric utility firms t ={1975-80 quarterly data (NYSE firms) 1971-80 annual data (electric utilities) Given stable inventory levels, the estimated slope coefficient, A dj, is an estimate of the average contribution margin ratio of the firm. It may be interpreted as an average contribution margin per dollar of selling price. As such, this ratio indicates the change in operating income induced by a unit change in sales. The statistical assumptions underlying the above OLS regression are linearity, serial independence of the error terms and a constant error variance. Some evidence of the appropriateness of these assumptions is presented in the discussion of the empirical results in Chapter 5. In the above formulation, operating income based on the 51 absorption costing method was regressed on sales dollars. To account for fixed indirect manufacturing costs, firms, for external reporting, use the absorption costing method. In this method, fixed overhead costs are allocated to production. Hence, these fixed costs appear on the financial statements as if they were variable. Using operating income based on absorption costing in the above regression is somewhat troublesome. However, this methodological decision was made in accord with the desire to use publicly-available data. If production of output is different than sales of output, the resultant slope coefficient is a gross margin measure rather than a contribution margin measure as specified in the theoretical model. However, when periodic sales equal production (i.e., no inventory changes), costs under the absorption method will equal those under the contribution margin method. It follows that, given stable inventories, both cost methods will yield the same operating income. There would then be no discrepancy in the contribution margin estimate. This measurement problem (gross margin or contribution margin) is an issue only in the NYSE sample. Under absorption costing with unstable inventory levels, the regression coefficient will be biased. The degree of the bias will depend on the magnitude of the inventory change. That is, the difference between operating income -- absorp- tion costing and operating income -- contribution margin method would be the unit inventory change multiplied by the unit manufacturing over- head rate (given a constant overhead rate). Accordingly, due to the lack of inventories, no bias is expected with respect to the electric utility sample firms. 52 4.2.3 Estimation of the Output Covariability Measure (8Q) The output demand beta (8Q) was defined on page ten of Chapter 3 as an output demand volatility measure. Specifically, 8Q is the covariability of the firm's output with the aggregated returns associated with a market index. The estimation of 6Q involved four separate estimation procedures for both samples. In the NYSE sample, the output variable (Q) necessary for the estimation of the theoretical 8 is not publicly available. There is Q no known empirical work which suggests a proxy for the firm's output level in a 8 measure. However, on a theoretical basis, it can be Q demonstrated that the covariance risk on any asset can be partitioned into two parts: the systematic risk of its revenue stream and the systematic risk of its cost structure.4 Theoretically, the covariance risk of sales will conform to the theoretical covariance risk of out- put only if price is held constant. With this assumption, then, total revenue (sales dollars) was used in the NYSE sample as a proxy for the output level. Since quarterly sales were used as a proxy for output in the NYSE sample, the first step in estimating 8Q involved the creation of quarterly market returns. Fama [1976, p. 260] suggests that, in general, returns over one time period may be related to returns over an intermediate period by the following expression: 1 + Rit = (1+r1)(1+r2) ... (1+rk) (4.7) where fiit = return on an initial investment of $1 for some period of time t (e.g., week, ~ month or years) I = returns for the intermediate period K = 1,2,3, 000K 53 Accordingly, the quarterly returns for each three month period (1975- 1980) were estimated as follows using monthly market returns obtained from the CRSP data tapes: 3 mt = [ H (1+rK)] - l, where (4.8) k=l Rmt = market return for quarter t EK = market return for month K A similar procedure was used to calculate the annual market returns (1971-1980) needed to estimate 8 (sales-based) in the electric Q utility sample. The B covariability measure may be stated functionally as: Q th = f(Rmt) (4.9) where Q = quarterly sales (NYSE sample or annual sales and KWH (electric utilities sample) ~ Rmt = quarterly (NYSE sample) or annual (electric utilities sample) market returns In the above functional relationship, the independent and dependent variables differ substantially in order of magnitude. OLS regression estimates tend to be sensitive to this condition. A sug- gested solution to this problem is to standardize both the independent and dependent variables and thereby reparameterize the regression model.5 Standardization makes the transformed variables fall between -1 and +1 with a mean of zero. This process involves expressing the mean deviations for each variable for each period in standard devia- tion units. The relationship between the estimated regression coeffi- cients of the original model (untransformed variables) and the 54 estimated regression coefficients of the reparameterized model involves a scalar, the ratio of the standard deviation of the depen- dent variable to the standard deviation of the independent variable.6 Accordingly, in the present research, the large difference in magnitude between sales (kilowatt hours) and market returns was remedied by a second data manipulation procedure. This procedure involved the standardization of the variables represented in the func- tional relationship of expression 4.9. After the aggregation of the monthly returns and the standard- ization of the variables, the third phase in the estimation of 8Q for the NYSE sample involved the process of extracting trend and season- ality factors from the sales variable. It is well known that dollar sales generally exhibit some form of predictable trend over time. The measurement of 8Q in this study will be based on variability unaccounted for by a constant trend. In both samples, the scatterplots of sales across time indi- cated a curvilinear trend was appropriate.7 A trendline with an adjustment for quarterly seasonality was then estimated for each firm: .t+O,t2+O x t g ' . Sa 9 13 23 33 02.: + O4ij3.:+ O53"Q4,c + Ejt (4 10) 3t OJ+0 where Sa' standardized sales for fixnlj in quarter t X g {I if period t is quarter 1 (i=2,3,4) Qi,t 0 otherwise 01,62 = OLS slope coefficients that indicate the rate of change in the level of sales according to a quadratic trend across time 03,04,05 = OLS slope coefficients that indiage the effect of additive seasonal variation in sales for each quarter 55 e! = the residual or unexplained sales variation 3t after accounting for trend and seasonality Since annual sales were used in the electric utility sample, the estimated trendline did not include a quarterly indicator vari- able: .. 2 .. 4.11 Sajt ¢0j + ¢ljt + ¢2jt1j+ cjt ( ) standardized annual sales (kilowatt hours) where Sajt ¢1.¢2 = estimated slope coefficients that indi- J cate the change in sales across time egt = residual or error term In both samples, several variations of curvilinear trend models were estimated. Coefficients of determination, t-values, Durbin-Watson statistics and residual plots were used to select the specific forms indicated above. 3 Q sales with the market return) was fitting of a second regression The final procedure used to estimate 8 (covariability of model for each firm. In that model, the standardized residuals from the trendline regressions were taken as a proxy for unexplained output variation. The following time series regression model was then run to S Q for each firm in the NYSE and electric utility samples: estimate 8 e! =A.R +8. (4-12) where E't = standardized residuals from the trend- 3 line regression for fixnnj in time t R' = standardized market return for time period t (value-weighted and equal- weighted) = the residual error term 56 The OLS estimated coefficient (Aj then used as an estimate of BS in the fit of the cross-sectional risk Q ) for each firm in both samples was models. As indicated, for comparative purpose, the sales covariability measure (83) was also estimated for the electric utility sample. In addition, a second 83 measure was estimated for the electric utility sample based on the physical output level of kilowatt hours. This variable was estimated for each electric utility firm using the four- step procedure detailed above for 88 Q In summary, the estimation of BS and 8 K Q for each sample in- volved four procedures: (1) Creation of quarterly/annual market returns from the monthly returns available on the CRSP tapes (2) Standardization of sales/kilowatt hours and the returns calculated in step 1 (3) Extraction of the trend and seasonality components from sales/kilowatt hours by OLS regression (4) Estimation of B by using the standardized residuals from the OLS regression in step 3 as the dependent variable and standardized market returns as the independent variable 8 Q and equal-weighted) for each firm in the NYSE sample. In the electric These procedures resulted in two 8 estimates (value-weighted utility sample, the estimation procedures resulted in four covari- ability measures, two 83 estimates (value-weighted and equal-weighted) and two BK estimates (value-weighted and equal-weighted). Q The theoretical business risk component of Model 1 presented in expression 4.1 was calculated by multiplying the estimated (P-VC), unit contribution margin as calculated in section 4.2.2., by the B Q variables generated above. The resultant business risk component, 57 (P-VC)8Q, was used in the cross-sectional fit of Model 1. 4.2.4 Estimation of the Financial Risk Leverage Component Another element needed to operationalize the risk models was the leverage ratio for each firm. Theoretically, the debt-to-equity ratio captures the financial risk of the firm and can be used to ex- plain part of the cross-sectional dispersion in market based betas. There were three measurement issues associated with the calculation of the debt-to-equity ratio. The first issue was associated with the measurement of the elements of the ratio. The theory developed in Chapter 3 indicates that the elements of the ratio should be measured at their market values. Several researchers have, however, conducted empirical tests that have incorporated book value (accounting) measures of the debt-to-equity ratio (e.g., Beaver, Kettler and Scholes [1970], Rosenberg and McKibben [1973], and Thompson [1976]) Although these studies found that leverage was a significant variable in assessing systematic risk, they did not address the issue of whether book value measurement of the leverage ratio was an adequate surrogation for the theoretical market value measurement. Undoubtedly, this was due in part to difficulties in estimating the market values of both the numerator and denominator of the leverate ratio. Bowman [1980b] did, however, provide direct empirical evidence on the sensitivity of systematic risk models to the use of book value and market value measurements in the leverage ratio. For a sample of ninety-two firms across seven industries, Bowman considered four forms of the debt-to-equity ratio in an association test of the effect of leverage on systematic risk. The four forms used by 58 Bowman were: A D (1) '1; S M D (2) '75 S A D (3) '3; S M D (4) '—A S where DA 8 book value of debt SA = book value of equity DM - market value of debt SM - market value of equity First, Bowman ran an OLS regression of the various forms of the debt-to-equity ratio on a market-based beta. In terms of explanatory power, the mixed ratio, 2;, performed somewhat better than the theoretical market-based ratio. SIn a second test, Bowman investi- gated the effect of the various forms of the leverage ratio on syste- matic risk in a fully-specified model (both business and financial components included). Bowman ran both the multiplicative and additive forms of the fully-specified model. He concluded that a mixed measure (book value of debt divided by market value of common equity) had explanatory power which was marginally greater than that of a pure market measure. Bowman stated this conclusion in his paper. The principal research finding is that, in the context of this study, accounting measures of debt were statistically indistinguishable from market value measures.8 More specifically, in the context of beta association studies, Bowman further concluded: This research indicates that the accounting measure may be a very good surrogate for the market value of debt in the leverage variable when used in association tests of risk. 59 Thus, in accord with Bowman's research, this study used a mixed book value and market value measure for the calculation of the debt-to-equity ratio of each firm. The market value measure of the equity component was obtained by multiplying the number of common equity shares outstanding by price (data obtained from the CRSP Master file tape). The book value of the debt element was calculated using data obtained from the Compustat tapes. The second measurement issue associated with the calculation of the leverage component involved the specific elements to include in the debt portion of the debt-to-equity ratio. Bowman [1978, 1980] and other prior researchers defined debt as total assets minus common stockholder's equity. Thus the debt of firm j would include current liabilities, long-term debt, deferred taxes, other noncurrent liabili- ties and preferred stock. The appropriateness of the inclusion of deferred taxes in the assessment of the firm's debt-to-equity ratio is an unresolved empirical question. It is unclear whether the market perceives or values the amount of deferred taxes as a liability. The analysis of this study measured the debt component without deferred taxes.10 Finally, the third measurement issue related to the calculation of the leverage component was the point in time at which the debt-to- equity ratio should be measured. This would not be a problematic issue if the firm's debt-to-equity ratio remained relatively stable over time. This, however, is generally not true for most firms, as the debt-to-equity ratio fluctures from one period to the next with increases/decreases in the firm's debt financing. Essentially, in beta association studies that are conducted over a specific period of 60 time, the potential measurement points for the leverage ratio are at the beginning of the test period, at the end of the test period, or some kind of average over the test period. An analysis conducted by Hamada [1972] has provided some empirical evidence on this issue. Using a sample of 102 firms over the time period 1947 to 1966, Hamada examined the propriety of using a beginning of the period debt-to-equity ratio, an end of the period debt-to-equity ratio, and a simple average for the period ratio in a cross-sectional association test of the rela- tionship between systematic risk and leverage. Hamada found that, in a beta association context, an average debt-to-equity ratio (rather than the single ratio calculated at the beginning or end of the sample period) more accurately represented the leverage component. Accordingly, in this study, the debt-to-equity ratio (2;)j for each firm was calcu- lated as an average over the test period :ssociated with each sample. Specifically, a debt-to-equity ratio was calculated at the end of each year. These period ratios were then used to calculate an average debt-to-equity ratio for each firm over the beta estimation period associated with each sample: A 1980 A D 1 D (—) = - Z (——) (4.13) SM j K t=i SM jt where K = number of years in the test period 1975 (NYSE firms) 1 = or 1971 (electric utilities) In summary, then, an average debt-to-equity ratio was calcu- lated for each firm. The debt element consisted of total current liabilities, long term debt, other liabilities (all measured at book value) as well as preferred stock (measured at liquidating value). 61 The equity element of the leverage ratio was measured at market value using year-end share and price data obtained from the CRSP tapes. 4.3 Estimation of the Components of Model 2 The systematic risk model presented in expression 4.2 was developed to examine the adequacy of using the accounting beta as a surrogate for business risk. As indicated in expression 4.2, Model 2 is a function of three variables. The methodology associated with A and 2M) is identical to the Model 1 estima- S tion that was discussed in previous sections of this chapter. The two of these variables (BL third variable (BA) is the only variable unique to the formulation of Model 2. The operationalization of BA will now be discussed. 4.3.1 Estimation of the Accounting Beta The firm's accounting beta, BA, as described in Chapter 1, footnote 6, is the covariance of the firm's accounting income with the average accounting income across all firms, divided by the variance of the average accounting income. As such, the accounting beta may be viewed as an earnings volatility measure. Previous research studies (e.g., Beaver, Kettler, and Scholes [1970], Rosenberg and McKibben [1973], Gonedes [1973, 1975], Beaver and Manegold [1975], and Hill and Stone [1980]) have defined the accounting beta in terms of a return series where earnings is deflated by a measure of the market value of the firm. This definition of the accounting beta has led to two basic specification questions. First, what is the appropriate accounting return series? Secondly, how should one construct the accounting income index? With regard to the first issue, the return metric most 62 consistent with the theory discussed in Chapter 3 would be the ratio of operating income divided by the total market value of the firm. However, on an empirical level, past researchers have considered many alternative forms of the return measure. Apart from the alterna- tives available for defining the numerator (earnings), there is the issue of what denominator (market value of the firm) should be used in the accounting return measure. Ball and Brown [1969] examined the relationship between the firm's security market beta and three speci- fications of the accounting beta based on three different measures of earnings (operating income, net income and income available for common). In the Brown and Ball study, the denominator of the accoun- ting beta return measure was based on market value (the number of the firm's outstanding common shares multiplied by share price). The Ball and Brown results, consistent with theoretical expectations, indicated that the return metric based on operating income was most highly cor- related with the firm's systematic risk measure. An analysis of this issue at the portfolio level was conducted by Beaver, Kettler, and Scholes [1970]. Beaver, 35 21., utilizing a return metric of net income for common divided by the market value of the firm, also found a significant association between the firm's market-based beta and the accounting beta. A controversial issue was then raised by Gonedes [1973]. Gonedes suggested that the observed correlation between the accounting beta and the market beta which had been reported in the previously-cited research could have been due to the stock price being common to the denominator of both the market beta and the accounting beta. Gonedes then recomputed the accounting beta with earnings deflated by the book value of total assets, and found the 63 degree of association between the market-based beta and the accounting beta to be greatly reduced. In a more extensive analysis, Beaver and Manegold [1975] used three alternative specifications of the return metric of the accounting beta (income per dollar of assets, income divided by the book value of common equity, and income divided by mar- ket value). In all three cases, Beaver and Manegold defined the numerator as income before extraordinary items. In contrast to the empirical work of Gonedes, Beaver and Manegold found a significant cor- relation with the market beta for all three forms of the accounting beta. Their results did, however, incorporate various statistical measures designed to reduce the measurement error inherent in the sample estimates of the accounting beta. Since the cited research studies have differed substanti- ally in terms of sample, time period of estimation and basic research design, it is difficult to discern from this work which specification of the accounting beta should be used in a risk asso- ciation study. However, certain recent research by Bowman [1980] has provided some additional evidence with regard to this issue. Bowman considered two forms of the return metric of the accounting beta.11 (1) BA - accounting beta based on income before extra- ordinary items over book value of common equity (2) B; - accounting beta based on income before interest and taxes (operating income) over total assets Bowman concluded that 8? had the highest explanatory power when used in his general model of systematic risk. Since the focus in the comparative analysis portion of this study is on the adequacy of using the accounting beta as a surrogate 64 I I for business risk vis-a-vis the competing theoretically-indicated business risk component of Model 1, the specification of the accoun- ting beta with the highest explanatory power was used. This would tend to bias the comparative analysis in favor of the alternative risk model (Model 2). Thus, in accord with the research of Bowman [1980], this study used an accounting beta based on the return metric of income before extraordinary items divided by the book value of common equity. With regard to the second issue involved in the measurement of the accounting beta, namely, the construction of the marketwide index of accounting returns for each year, there were several decisions to be made: (1) Use a value-weighted or equal-weighted index con- struction scheme; (2) Define the composition of firms in the market as all firms with available data on the Standard and Poor's Compustat tapes or use a subset of this group of firms; (3) Impose or not impose the condition that all firms used in the market index have a common fiscal year- end. Gonedes [1973] has provided some empirical evidence with regard to the alternative index construction schemes available for the accounting beta. Gonedes' research findings indicated that a value-weighting based on all firms in the sample with common fiscal year ends pro- duced a better specification of the accounting beta than the alterna- tives. More recently, additional empirical evidence consistent with Gonedes' results has been provided by Bowman [1980a, 1980b]. In accord with the aforementioned studies, the present research used an index construction scheme based on a value-weighting 65 of the accounting returns of all firms of the sample. Although alternative index formation procedures were examined, the indicated procedure produced the best specification of the accounting beta using standard t-values and R2 statistics as evaluative criteria. In addition to the specification issues associated with the accounting beta, various researchers have suggested several remedial statistical measures to deal with estimation measurement error12 in the accounting beta. Suggested procedures have included: (1) Transformation of the return metric by a first difference Operator or two-stage least-squares (Durbin technique13) (2) Bayesian adjustment procedures which incorporate cross sectional information into the estimation of the accounting beta associated with a specific firm14 (3) Portfolio level examination of the cross sectional risk association model (aggregation procedures) The use of these procedures involves assumptions about the nature and direction of the measurement error associated with the accounting beta. The propriety of using the statistical procedures listed above in an accounting beta context was investigated by Beaver and Manegold [1975]. The authors' results with regard to these procedures indi- cate that some of the techniques appear to be useful in reducing measurement error, while several others appear to be of very little value. With regard to the first procedure, data transformation, Beaver and Manegold expressed the following observations: It was expected that Durbin betas would outperform both regular and first difference betas. However there does not appear to be any overall superiority for any of the three types of beta.15 On the other hand, Beaver and Manegold found that: 66 The Bayesian adjustment procedure and aggregation into portfolios consistently produce results which suggest they are successful in removing a nontrivial portion of the measurement error.16 There has been little, if any, empirical research which examines the findings of Beaver and Manegold in other beta association settings. Similarly, the present research did not investigate the sensitivity of the cross-sectional model fitting to the various statistical mea- sures listed above. These procedures are, however, a significant issue and will be discussed further in Chapter 6 as a further exten- sion of the present study. In summary of this section, there are numerous measurement issues associated with the estimation of the acc0unting beta. Based on an examination of these issues, the following model was used to estimate the accounting beta used in Model 2: th jt where th = income before extraordinary items scaled by the beginning of the period book value of common equity of firm j in period t = the market index of the income return mt measure (as defined above), calculated as a value-weighted average of the income measures of all firms in the sample in year t That is, N C mt = lejt 633-], where j=l t C. = common equity beginning-of-the-period book Jt . value measure for firm j at time period t 2N: c - c t j=l jt = / Y1 + YZth + u. (4.14) 67 A first difference of the above index model was also run for compara- tive purposes. In the context of this study, the model indicated above (without differencing of the return series) was better specified, based on the magnitude of the t-values and R2 statistics. 4.4 Functional Form of the Models The preceding discussion of the methodological procedures has detailed the measurement issues associated with estimating the variables needed to fit the risk models expressed in equations 4.1 and 4.2. A multiple regression analysis of these models constitutes the principal statistical examination of the relationship between the market-based beta and the accounting risk measures. The use of multiple regression analysis requires a specification of the functional form of Model 1 and Model 2. In Chapter 3, the model development sec- tion, one notes that the theory indicates a multiplicative relation- ship between business risk and financial risk. Previous research, however, has treated the financial component as a separate additive term of the linear regression model. This assumption of additivity has led to the following criticism of the empirical work in the risk assessment area. From the viewpoint of the Hamada-Rubinstein formulas, the financial structure dependency used in the regression equ- ations of the studies surveyed above are all misspecified. Rather than expressing financial structure as a multipli- cative term scaling a measure of intrinsic operating risk, the test equations treat it as a separable, additive term or combination of terms.17 In this study, Model 1 and Model 2 were first operationalized according to the theory, by expressing the leverage component in a multiplicative relationship with the business risk measure. This 68 implies a logarithmic estimation for equations 4.1 and 4.2.18 Model 1: DL = — -———- * 1n 81 ol + a2 1n[E(P VC)BQ] + a3 ln(l + SL) + E Model 2: DL = -—— ** 1n BL 81 + 92 ln(BA) + 83 1n(l + SL) + E Alternatively, the following additive models were also fitted: Model 1: DL 0 BL = Y1 + Y2[E(P-VC)BQ] + Y3 (5;) + E Model 2: DL - m Using an additive model to combine variables representing business and financial risk is problematic. However, Bowman [1980a, 1980b] indicated that systematic risk models were not seriously weakened by specifying additive relationships. It is believed that a utilization of both functional forms of the risk models will permit a more complete examination of the relationships expressed in equation 4.1 and 4.2. 4.5 Purpose of the Empirical Investigation This study is an extension of the Rubinstein [1973] analytical work which linked accounting variables to the systematic risk measure of the firm's common equity securities. As indicated,the joint 69 purpose of this study is a test of a risk model and the operational- ization of that model with publicly available accounting data. As discussed in previous chapters, the analytically derived risk model (Model 1) of the present study is a mathematical reduction of the Rubinstein model in combination with the financial risk analysis of Hamada [1969, 1972]. As such, Model 1 addresses a common criticism of the previous beta association studies--empirical examination of risk models without theoretical underpinnings. In short, the formula- tion of Model 1 incorporates theoretically-derived components of both business and financial risk. The elements of Model 1 were then operationalized using publicly available accounting data that were manipulated by the various methodological procedures described in the previous sections of this chapter. The purpose of the first phase of the statistical tests was, then, to examine the relationship between the market-based beta and its theoretically indicated accounting risk measures. More specifically, the statistical tests were used to ascertain whether or not the operationalization provided empirical support for the derived theoretical model. As stated in Chapter 2, a finding of significant association between measures derived from accounting data and the market based beta would tend to support the joint hypothesis that accounting data do reflect information about the risk of capital assets and that such information is impounded in the market price of the securities. The second aspect of this joint hypothesis addresses the issue of the information content of accounting data. In this research, as well as in other beta association studies, a finding of empirical support for the systematic risk model may be viewed as providing evidence of the 70 information content of accoutning data at the aggregate level of the securities market. In the context of this study, an acceptance of the theory of market efficiency would imply an observable association between the market based systematic risk element (beta) and the accounting risk measures of Model 1. Therefore, as stated in Chapter 1, this study incorporated a joint test of the descriptive validity of a theoretical model of systematic risk and of the information con- tent of the accounting risk measures used to operationalize that model. The second phase of the empirical analysis of this study was an investigation of the comparative explanatory power of Model 1 and Model 2. In previous research studies, the accounting beta has been used as a surrogate for the business risk component in systematic risk models. As indicated in Chapter 3, the accounting beta is not a pure measure of business risk. Model 2 of the present study was developed by substituting the accounting beta for the theoretical business risk component of Model 1. Model 2 was then operationalized using available accounting data. A comparison of the explanatory power of Model 2 with Model 1 should provide some empirical evidence of the adequacy of using the accounting beta as a surrogate for busi- ness risk. The implication of empirically estimating Model 2 is subject to the same joint hypothesis that was discussed with regard to Model 1. 4.6 Summary This chapter has provided a description of the procedures used to estimate the business and financial risk components of Model 1 and Model 2 as expressed in equations 4.1 and 4.2. Section 4.1 71 contained a description of the sample selection procedures used in this study. The formulations of Model 1 and Model 2 were examined in two samples. Section 4.2 contained a description of the procedures needed to operationalize the theoretical risk model (Model 1). Included in this section was a discussion of the methodological proce- dures used to estimate the market-based betas 8L, the business risk components [(P-VC)BQ], and the debt to equity ratios (the financial risk component). The covariability measures of Model 1 were estimated using both an equal-weighted and a value-weighted market index proxy. The estimation procedures needed to operationalize Model 2 were discussed in section 4.3. The levered beta and debt-to-equity ratios of Model 2 are common to both models. Hence, both these variables of Model 2 were estimated in the same manner as discussed for Model 1 in section 4.2. The major focus in section 4.3 was on the methodological issues associated with the estimation of the accounting beta, a vari- able unique to the formulation of Model 2. Section 4.4 presented the functional forms of the cross-sectional risk models fitted in this study. Each model was estimated eight times (two formulations with two indices across two samples). Section 4.5 contained a discussion of the joint purpose of this research. This joint purpose involves an examination of the descriptive validity of a theoretical model of systematic risk and the assessment of the information content of the accounting data used to operationalize that model. The results of the empirical investigations and a discussion of the implications of these results are presented in Chapter 5. 72 Chapter 4 Footnotes 1This mathematical operation is consistent with the methodology of past beta association studies (e.g. Bowman [1980]). In this study, the scalar vectors Vu (the total value of the firm's equity) and Vm the total value of the equity of all firms in the market) will not be estimated empirically. 2For a complete discussion of the analysis of differential industry risk, see Reilly and Drzycimski [1974]. 3Fama, Fischer, Jensen, and Roll [1969] is an example of a research study that empirically investigated many of the statistical properties of the market model. For a discussion of the theoretical support for the market model, see Fama [1965b]. 4See Appendix A (equation 32). Both Sullivan [1978] and COpe- land and Weston [1979, p. 260] present decompositions of unlevered systematic risk into systematic revenue and cost components. 5Roundoff errors tend to enter into the OLS estimations pri- marily when the inverse of the X'X matrix is taken. The estimated slope coefficient tends to become large and unstable. For a complete discussion, including the reparameterized model derivations, see Neter and Wasserman, [1974, pp. 347-351]. 6Ibid. 7A linear trend was also fitted for each firm but the best results were obtained with the curvilinear model. 8Robert G. Bowman, "The Importance of a Market-Value Measure- ment of Debt in Assessing Leverage," Journal of Accounting Research, 91bid. 10Given the objectives of this study, as stated in Chapter 1 (page 4), an examination of the market assessment of deferred taxes was not conducted. This is, however, an issue that merits investi- gation in a model designed to capture all tax effects. The risk models of the present research abstract from corporate and personal taxation issues. 11The examination of these two specific forms of the accoun- ting beta was based on theory and known measurement problems asso- ciated with the estimation of the accounting beta. For a complete discussion of this issue see the dissertation of Robert Bowman, "An Empirical Investigation of the Debt Equivalence of Leases," Stanford University, 1978, pp. 60-61. 73 12 To the extent that measurement error exists in the accoun- ting beta, correlations between the measured accounting and market betas will be biased downward and estimated slope coefficients will be inefficient and biased downward. 1 3In the Durbin technique, the autoregressive correlation coefficient is estimated in the first stage. This correlation coefficient is used to transform the data. Estimates of the accounting beta are obtained by fitting a second regression on the transformed variables. 4In general, Bayesian adjustment procedures involve computing an adjusted sample estimate of the firm's accounting beta using the prior (cross-sectional accounting beta) and the sample (firm-specific accounting beta) weighted by the precision of each. There are several alternative versions of this method based on the specification of the prior mean. Several researchers have suggested that the adjustment procedure will be more efficient if the prior mean is chosen to more closely approximate the underlying parameters of the specific firm (e.g., an industry beta). For another variation of the Bayesian adjustment procedures, see Maier, Peterson and Vanderweide [1982]. 15William Beaver and James Manegold, "The Association Between Market-Determined and Accounting-Determined Measures of Systematic Risk: Some Further Evidence," Journal of Financial and Quantitative Analysis (June 1975), p. 261. 16Ibid., p. 266. 17 Ned C. Hill and Bernell K. Stone, "Accounting Betas, Systematic Operating Risk and Financial Leverage: A Risk Composition Approach to the Determinants of Systematic Risk," Journal of Financial and Quantitative Analysis, XV (September 1980), p. 599. 18 An alternative procedure to reflect multiplicative effects is to scale the debt-to-equity ratio by the business risk component as a single element of the cross-sectional risk models. However, according to Bowman [1980], given the potential measurement error in the BA element, this alternative procedure may not be the proper empirical specification of a multiplicative model and hence was not used in the present study. TABLE 4.1 Definitions of Market-Based and Accounting Risk Measures Variable Samplea Sourceb Formula/Description Market Variables ~, n and n CRSP #1 Monthly security returns for jt 1 each firm j ~mt n1 and n CRPS #2 Monthly returns on value- weighted and equal-weighted NYSE market portfolio (ii .11 ) B n andn - cov ——-j——-———t~ mt L l 2(R ) 0 mt Accountinngariables. Sal n1 Quarterly Sales, net Compustat Item #2 Dp1 n1 Quarterly Depreciation and amortization Compustat Item #5 y1 n1 Quarterly Operating income Compustat Item #21 [(Yl'DP1)csa] E(P-VC) n . . cov( ) l 2 2 0 Sa Sa n Annual Sales, net 2 2 Compustat Item #12 Dp2 n2 Annual Depreciation and amortization Compustat Item #14 Y n Annual Operating Income 2 2 Compustat Item #13 TABLE 4.1--Continued Variable Samplea Sourceb Formula/Description [(3, ”DP )!38 ] E(P-VC)2 n2 ... cov( 2 2 2 ) o Sa2 e' n ... Standardized residuals after jt l the extraction of seasonality and trend from Sa1 RS: n1 . . Standardized aggregated ~ quarterly returns based on Rmt (value weighted and equal- weighted) (5' ofiQ ) 881 n cov —J-E-—£F— Q 1 02(RQ ) mt svt n2 Standardized residuals after 3 the trend extraction from Sa2 ~A . R n .. Standardized aggregated annual mt 2 c returns based on Rut (value- weighted and equal-weighted) ~A H 82 (Ejt’Rmt) 8Q n2 . . . cov __—02(fiA ) mt KWHjt n2 Moody's Annual kilowatt hours for Public electric utility j in time Utilities period t Manuals egé' n2 Standardized residuals after the trend extraction from K v v v ”A KWH (Ejt ’Rmt) 8Q n2 ... cov 2 ~A o (R ) TABLE 4.l--Continued Variable Samplea Sourceb Formula/Description CL nl and n Annual Total current liabilities-- Compustat liabilities due within one Item #5 year, including the current portion of the long term debt D nl and n Annual Total book-value of long term Compustat debt due more than one year Item #9 from the company's balance sheet date 0L nl and n Annual Includes all liabilities that Compustat are not debt, deferred taxes, Item #75 minority interest, primarily contingent liabilities, cus- tomer deposits, etc. PF n1 and n Annual Preferred stock at liquidating Compustat value, represents the number Item #10 of preferred shares at year end times the involuntary liquidating value per share (carrying value was used when liquidating value was not reported) DL 111 and n ... CL + DB + OL + PF SN CRSP #3 The number of common equity shares outstanding at year end PS CRSP #3 The year end price of each common equity share * SL nl and n ... SN PS lKDL 1E}E(§—)j 111 and n Average debt to equity ratio . L for firm j over the test period (K = the number of periods) ygt nl and n Annual Income before extraordinary Compustat items and discontinued opera- Item #20 tions less preferred dividend requirements (adjusted for additional dollar savings due to common stock equivalents) TABLE 4.1--Continued Variable Samplea Source Formula/Description C.t 1 and n Annual Beginning of the period book J Compustat value of common equity of firm Item #11 j in time period t N Ct 1 and n .. 23C3t where N = number of j=l firms c 311 Z’t l and n C J jt N C t and n .. [z -1—] mt 1 j=1 jt CT 8 and n cov (2 t’zmt) A l 2 o 2 mt Notes: a n1 = NYSE firms n2 = electric utility firms b CRSP #1 8 return tape CRSP #2 I index tape CRSP #3 = master file tape CHAPTER 5 RESULTS The methodological procedures used to estimate the elements of the systematic risk models formulated in expressions 4.1 and 4.2 were described in Chapter 4. For Model 1, these procedures provided two estimates of the market-based beta and six estimates of the busi- ness risk component across two samples. In addition, the estimation procedures resulted in the calculation of an average debt to equity ratio and an accounting beta for each firm in both samples. Various statistical tests were then used to examine the Model 1 association between the market based beta and its theoretical determinants. Finally, in the comparative analysis, other statistical tests were used to focus on the explanatory power of Model 2 relative to Model 1. The operational aspects of Model 1 and Model 2 involved various data manipulation procedures that were conducted prior to the examination of the relationships expressed in equations 4.1 and 4.2. These procedures were described in detail in Chapter 4. Now, to facilitate the discussion of the statistical analysis, Section 5.1 contains a summary of the results of the preliminary data manipulation procedures. Next, a discussion of the statistical analysis conducted in this study is presented in Section 5.2. Finally, Section 5.3 con- tains a summary of the empirical results. 78 79 5.1 Results of the Preliminary Data Manipulation The preliminary data manipulations involved four procedures: (1) the use of OLS regression to estimate the market-based betas for each firm; (2) the use of data transformation techniques and OLS re- gression procedures to estimate the business risk component; (3) the utilization of Compustat and CRSP data to calculate an average debt- to-equity ratio for each firm. In addition, the comparative analysis of this research required the estimation of a second model. As indi- cated, Model 2 was formulated by substituting the accounting beta for the business risk component of Model 1. Hence, phase (4) of the data manipulation procedures involved the estimation of an accounting beta. All of the aforementioned data manipulation procedures were performed on both the NYSE sample and the electric utility sample. A discussion and interpretation of the summary statistics associated with each phase of the preliminary procedures follows. Phase 1: As indicated above, the first phase of the data manipulation procedures involved the estimation of the market-based betas of each firm using the market model relationship developed by Sharpe [1963]. As previously described in section 4.2.1, the seventy- two monthly returns of each firm from the period January 1975 through Rjt’ for the NYSE sample firms. The CRSP equal-weighted and value-weighted December 1980 were used as measures of the dependent variable, market return indices were used as the measures of the independent ~ variable, R mt' This resulted in two measures of the market-based beta for each firm of the NYSE sample. The slope of each regression equation were taken as an empirical estimate of the systematic risk component of Model 1 and Model 2. The results of the market model 80 regressions for the NYSE sample are presented in Table 5.1. The summarized statistics indicate that the results of this study are comparable to the findings reported by prior researchers.l It may be recalled that the NYSE firms were drawn randomly from all firms listed on the Compustat data tapes. This common statistical procedure was used to obtain sampled firms representative of the popu- lation of market firms. The expected beta of the market portfolio of common equity stocks is equal to 1.0. Based on a value-weighted mar- ket index, the average market-based beta of 1.1394 indicates that the NYSE sample stocks were, on the average, marginally more risky than the expected average of the market portfolio. In contrast, the aver- age market-based beta using an equal-weighted market index was .90690, a magnitude closer to the expected beta for the market portfolio. In general, then, there appears to be little bias in the market-based betas arising from the sample selection procedures. Firms across all risk classes appear to be represented in the NYSE sample. Average t ratios of 6.12 and 6.64 (value-weighted and equal-weighted respectively) for the NYSE sample indicate that statistical reliance can be placed on the market beta estimates. Specifically, the null hypothesis that the mean market model beta for either index equals zero can be rejected at the .01 level of significance.2 The market based risk measures were also estimated for the electric utility sample firms by using the same market model regres- sion techniques that were used for the NYSE firms. The monthly returns of each electric utility firm for the period January 1971 through December 1980 were used as measures of R . The contempora- jt neous returns associated with both the CRSP equal weighted and 81 value-weighted indices were used to measure the independent variable, ~ mt' Thus a value-weighted and equal-weighted market based beta was estimated for each firm in the electric utility sample. The summary statistics associated with the electric utility sample firms are also presented in Table 5.1. The average market-based betas for the electric utility sample were .63170 and .51770 (value-weighted and equal-weighted respectively). These results are comparable to the calculated industry betas reported by Rosenberg and Guy [1976]. Rosenberg and Guy estimated betas for various industries by using monthly security returns from April 1966 to August 1974. The authors reported an average industry beta for the electric utility industry of .60. The results of this study are clearly very close in magnitude to the Guy and Rosenberg electric utility beta. Furthermore, the overall t-ratios and adjusted R2 for the electric utility sample lend statistical support to the estimated market based betas. In a formal manner, if we assume that the calcu- lated mean firm betas of .63170 (value-weighted) and .51770 (equal- weighted) follow a normal distribution with an estimated standard deviation of .020073 and .015937 (value-weighted and equal-weighted respectively), we can reject the null hypothesis that either average electric utility firm beta equals zero at the .01 level of significance. Phase 2: The second phase of the preliminary data manipula- tion involved a two step technique to estimate the business risk component [(P-VC)BQ] of Model 1. The first step in estimating this risk component involved the use of an OLS time series regression to estimate the unit contribution margin (P-VC). For the NYSE sample, the quarterly dollar volume of sales for the period January 1975 82 TABLE 5.1 Summary Statistics--Market Model Regressions Value-weighted Market Index Equal-weighted Market Index éj s(§j) i éj s(§j) i2 NYSE sample Lites; Mean 1.13940 .20610 33.20 .90690 .1428 36.90 (6.12)* (6.64)* Median 1.11620 .18350 32.40 .83201 .1259 39.00 Standard deviation .39880 .06660 12.70 .36117 .0430 12.58 Range: High 2.28560 .36960 68.30 1.76780 .0735 61.10 Low .26310 .11150 9.30 .24280 .2352 3.90 Electric utility sample firms: Mean .63170 .10870 21.80 .51770 .08292 27.72 (5.85)* (6.84)* Median .60970 .10610 21.30 .49840 .07503 27.02 Standard deviation .12220 .01680 4.88 .09694 .05783 7.39 Range: High 1.01050 .15420 37.00 .73815 .41442 40.60 Low .38690 .08260 11.50 .33840 .00442 8.60 Note: *indicates the average t-ratio across all firms and 8(8.) represents the standard deviation of the estimated regression coefficients. 8 j’ 83 through December 1980 was used as the independent variable, while the concurrent amounts of net operating income were used as the dependent variable. The estimated slope coefficient provided an estimate of the firm's average unit contribution margin. The summary statistics asso- ciated with the estimation of this variable are presented in Table 5.2. The average contribution margin ratio for the NYSE sample was .12146. The mean adjusted R2 across firms in the NYSE sample was 60.97%. This indicates that variation in sales accounted for a very large share of the total variation in operating income. Other relevant summary statistics associated with the contribution margin ratio are reported in Table 5.2. The range of this ratio was from .01003 to .42424. Generally a high contribution margin would indicate a larger amount of revenue available for the fixed costs and income of the firm. The range of the unit contribution margin ratios in the NYSE sample seems to indicate the inclusion of firms representative of many diverse industries, a fact consistent with the attributes of the NYSE sample. In the electric utility sample, the average contribution margin was .20282 with an associated range from .06846 to .34318. This range is smaller than the indicated range for the NYSE sample and may be attributed to the homogeneity of the industry. Table 5.2 also in- cludes the average t-ratios, standard deviations and other summary statistics associated with the average contribution margin ratio for the electric utility sample. The estimation of the second element of the business risk com- ponent of Model 1, (B ), required four basic steps for each sample: Q 84 TABLE 5.2 Summary Statistics--E(P-VC) Regressions 3 5(3) fiz NYSE sample firms: Mean .12146 .02115 60.97 (14.14)* Median .10115 .01878 64.50 Standard deviation .09514 .01383 24.20 Range: High .42424 .06856 96.00 Low .01003 .00360 26.60 Electric utility sample firms: Mean .20282 .02311 84.18 (10.31)* Median .19578 .02238 89.75 Standard deviation .06398 .00992 18.15 Range: High .34318 .04992 99.00 Low .06846 .00879 52.70 Note: *indicates the average t-ratio across all firms for 6, the estimated regression coefficient. 85 (l) The aggregation of monthly firm returns into quar- terly returns (NYSE sample)/annual returns (electric utilities sample) (2) Standardization of quarterly sales (NYSE sample), annual sales (electric utilities sample), annual kilowatt hours (electric utilities sample), and the aggregated returns (both samples) (3) Extraction of the trend and seasonality components from the quarterly sales, annual sales, and annual kilowatt hours by OLS regression (4) Estimation of the output covariability measure by regressing the residuals from the first OLS regres- sion (step 3) on the standardized market returns The above methodological procedures resulted in two measures of 8Q for the NYSE sample (value-weighted and market-weighted). These same procedures yielded four output covariability measures for the electric utility sample (value-weighted and equal-weighted for annual sales and annual kilowatt hours). The summary statistics based on sales for both samples are presented in Table 5.3. The summary statis- tics based on kilowatt hours in the electric utility sample are reported in Table 5.4. In the NYSE sample, the average output volatility measure based on sales was .28119 with an average t-ratio of 2.72. Assuming the sample statistic 8Q follows a normal distribution with a mean of .28119 and a standard deviation of that mean of .11565l/zzi.01806, a t-test of the hypothesis that the mean output volatility measure (value-weighted) equals zero would be rejected at the .01 level of significance. The range of the magnitude of the output covariability measures for the NYSE sample (value-weighted) was from .02450 to .45550. Similar results are reported in Table 5.3 for the NYSE equal-weighted covariability measure. 86 TABLE 5.3 Summary Statistics--Output Volatility Measure Based on Sales (8 Q ) Resgression Value-weighted Market Index Equal-weighted Market-Index S S BQ (8Q) 8Q (8Q) NYSE sample firms: Mean .28119 .1156 .20746 .1078 (2.72)* (3.02)* Median .27520 .1161 .21770 .0919 Standard deviation .11565 .0167 .09243 .1222 Range: High .45550 .1418 .37434 .1912 Low .02450 .0864 .02430 .0485 Electric utility sample firms: Mean .29031 .2971 .32160 .2925 (2.89)* (3.74)* Median .28920 .3230 .32100 .3171 Standard deviation .03912 .0467 .03986 .0442 Range: High .36480 .3370 .40550 .3395 Low .20620 .2249 .20900 .2171 t-ratio 1.54870 1.57150 Note: *indicates the average t-ratio across all firms. 87 The mean output covariability measure based on sales for the electric utility sample was .29031 (value-weighted). A t-test of the hypothesis that the mean 8 estimate is equal to zero based on a Q normal distribution with a standard deviation of .039120//37¥.00643 would be rejected at the .01 level of significance. The statistical results are similar for the mean 8 measure (equal-weighted). Finally, Q it should be mentioned that there is no known empirical work that attempts to estimate an output covariability measure for a firm. As such, it is not possible to compare the 8 results of this study with Q prior research. Table 5.4 presents the summary statistics associated with the electric utility sample for the output volatility measure based on actual output units (annual kilowatt hours). On a value-weighted K Q 1.0008. The range on BE (kilowatt based) was from -.03690 to -4.7300 basis the average 8 is -1.4l74 with an average standard error of (value-weighted). Similar results are reported for the qual-weighted 83 estimate. As indicated by the average t-ratio of 1.36, the covari- ability measures based on kilowatt hours are not as well estimated as the same measures based on sales. Measurement error is one possible explanation for this result. As indicated in the methodology chapter, various data manipulation procedures were used prior to the estimation of this measure. Another possibility which has not been empirically explored in this study is that the output volatility measure should be defined as the covariability of output with the average covari- ability of the market's output rather than with the market return.3 The actual measurement of the market's output would, however, pose some difficult estimation issues. 88 TABLE 5.4 Summary Statistics--Output Volatility Measure Based on KWHs (85) Value-weighted Equal-weighted Market Index Market Index “K “K “K “K 8 S S Q (8Q) 8Q (8Q) Electric utility firms: Mean -1.4l74 1.0008 -l.1514 .70826 (1.36)* (1.629)* Mean -.8053 .77650 -.67830 .60210 Standard deviation 1.3704 .89930 1.11300 .60491 Range: High -4.7300 .00017 -4.09300 .00010 Low -.0369 3.49000 -.05410 2.51800 Note: *indicates the average t-ratio across all firms. Although the standard errors are large, a t-test of the null K Q level of significance. This result is based on the assumption of a hypothesis that the estimated mean 8 = 0 may be rejected at the .01 normal distribution of the estimated mean covariability measures of -l.4l74 and -l.1514 (value-weighted and equal-weighted respectively) with calculated standard deviations of .2253 and .1829. The unit contribution margin and the output covariability mea- sure multiplicatively provide the theoretical business risk component, [(P-VC)BQ]. Table 5.5 presents several summary statistics associated with this component. The mean business risk components of the NYSE sample firms were .031384 and .023147 (value-weighted and equal-weighted 89 TABLE 5.5 Summary Statistics for Business Risk Component E(P—VC)B Q Value-weighted Equal-weighted Market Index Market Index Sales Based NYSE sample firms: Mean .031384 .023147 Median .029020 .017839 Standard deviation .025373 .020059 Range: High .109390 .086723 Low .000158 .001079 Electric utility sample firms: Mean .070339 .065796 Median .064915 .068034 Standard deviation .036967 .021401 Range: High .163720 .105070 Low .021654 .019929 Actual Output Based Electric utility firms (output KWH): Mean -.24783 -.l7108 Median -.15897 -.14273 Standard deviation .20714 .16374 Range: High -.00925 -.01097 Low -.68088 -.69659 90 respectively). In the electric utility sample, the average sales- based business risk component was .070339 and .065796 (value-weighted and equal-weighted respectively). Other summary statistics associ- ated with this measure are provided in Table 5.5. Phase 3: The third phase of the preliminary data manipulation involved the calculation of an average debt-to-equity ratio for each firm in both samples. As discussed in section 4.2.4, Compustat and CRSP data tapes were used to estimate a debt-to-equity ratio with a book value debt element and a market value equity element. Summary statistics with regard to the average debt-to-equity ratios are pro- vided in Table 5.6. TABLE 5.6 Summary Statistics--Debt-to-Equity Ratios NYSE sample £15m: Mean 2.2615 Median 1.1348 Standard deviation 2.8572 Range: High 12.7270 Low .0676 Electric utility sample firms: Mean 2.6720 Median 2.5579 Standard deviation .7093 Range: High 3.9007 Low 1.3632 91 As indicated, the average debt-to-equity ratios reported in Table 5.6 represent mixed measure (book value and market value) ratios. As such, they cannot be compared to the leverage ratios based on book values that were reported in most of the previous beta-associ- ation studies. However, Bowman [1978, 1980b] and Mohr [1981] have provided some empirical evidence with regard to the ratios examined in this research. With respect to Bowman's analysis, certain summary statistics can be used to determine that his mixed measure mean debt- to-equity ratio was 2.26. It is noted that this ratio did, however, include deferred taxes as a part of the debt component. In addition, Mohr [1981], in a beta association study, reported a mean mixed debt- to-equity ratio of 2.1469 for a sample of single industry firms. In the present research, the average debt-to-equity ratio (mixed-measure) was 2.2615 for the NYSE sample and 2.6720 for the electric utility sample, results quite consistent with the previous research of Bowman [1978, 1980b] and Mohr [1981]. Phase 4: The final phase of the data manipulation involved the estimation of the accounting beta, a variable needed for the examination of the descriptive validity of Model 2. The accounting beta was estimated using an OLS index model. Table 5.7 presents sum- mary statistics with regard to the accounting beta. The average accounting betas were .8186 and 1.4530 for the NYSE and electric utility samples respectively. These results are consistent with previous research utilizing the same return metric (income available for common/common equity) as used in the present research. Gonedes [1975] reported an average accounting beta of .9573 for 316 firms over the time period 1946-1969. Similarly, Summary 92 TABLE 5.7 Statistics BA Regressions “ “ -2 BA 3(8A) R NYSE sample firms: Mean .81859 .4089 31.14 (2.14)* Median .82549 .3949 27.80 Standard deviation .73870 .2184 18.67 Range: High 2.17900 .8674 68.40 Low -l.29800 .0950 5.00 Electric utility sample firms: Mean 1.4530 1.0934 26.127 (2.06)* Median 1.3960 1.0030 20.450 Standard deviation 1.3379 .4543 18.363 Range: High 4.4130 2.3280 78.800 Low -2.0505 .4616 2.400 Note: *Average t-ratio across all firms for SA. the estimated regression coefficient. Bowman [1978, 1980a] reported .8700 as the average accounting beta for 92 firms over the period 1963-1973. Although the accounting beta of the electric utility sample is greater than 1.0 and somewhat higher than reported in Gonedes [1975] and Bowman [1978, 1980], its magnitude is not inconsistent with values of the accoutning beta that have been reported by other researchers (e.g., Beaver and Manegold [1975]). The estimation of the accounting betas for both samples 93 represented the last phase of the preliminary data manipulation. The accounting beta in conjunction with the average debt to equity ratios (phase 3) and the market-based betas (phase 1) for both samples were the elements needed for the cross-sectional fitting of Model 2. The theoretical Model 1 expressed in equation 4.1 was operationalized using the theoretical business risk component (phase 2) and the aver- age debt-to-equity ratios (phase 3) with the market based betas (phase 1). The statistical testing and analysis of Model 1 and Model 2 are discussed in the next section of this chapter. Statistical Testing and Analysis of the Systematic Risk Models The systematic risk models formulated in expressions 4.1 and 4.2 were the central focus of the empirical analysis of this study. Several alternative forms of these models were discussed in Chapter 4. Specifically, the multiplicative models tested in this research were estimated as: Model 1: D L In BL a1 + o21n[E(P VC)BQ] + o3 ln(1 '§;) ( ) Model 2: DL = __. ** 5.2 1n 82 91 + (92 1n(BA) + 93 1n(1 + SL) + E ( ) Alternatively, the following additive models were also fitted: Model 1: D BL — Y1 + YZIHP VC)BQ] + Y3(SL) + E (5 ) 'Model 2: DL m BL - (>1 + ¢2(BA) + ¢3(§{) + E (5.4) 94 The relationships in the above expressions were operational- ized as described in Chapter 4 and section 5.1. The data manipulation procedures provided an estimation of the elements of Model 1 and Model 2. In this section, the results of the statistical analysis as applied to each model will be discussed. 5.2.1 Multiple Regression Analysis Multiple regression analysis (MRA) was the principal statis- tical tool used to test the relationships expressed in the four equ- ations listed above. Multiple regression analysis is a statistical methodology that examines the relationship between two or more vari- ables. As such, it was used to examine the descriptive validity of Model 1 and Model 2. Specifically, MRA.was used to examine the con- temporaneous association between the market risk measures and accoun- ting risk measures as formulated in equations 5.1, 5.2, 5.3, and 5.4. The present application of this statistical procedure is consistent with the methodology employed in prior beta association studies. It is a logical choice since regression analysis can be used to examine both the nature and the strength of the relationship between accoun- ting and market risk measures. Prior to presenting the results of the cross-sectional regres- sion analysis, it should be recalled that Model 1, as formulated in expressions 5.1 and 5.3, is a theoretical model that provides the desired linkage of the firm's market-based beta with the corporate characteristics reflected in the production-financing-investing activities of the firm. As discussed in Chapter 4, Model 1 was operationalized using several estimates of the theoretical business 95 risk component (sales and actual output with both value-weighted and equal-weighted market return indices). These estimates were tested in two samples (NYSE firms and electric utility firms). When possible, both an additive and multiplicative functional form were considered. The results of the empirical examination of Model 1, an analytically derived model of systematic risk that includes both business and financial risk components, is the subject of the following paragraphs. Correlation matrices associated with this examination are presented in Tables 5.11 and 5.12. The results of fitting an additive functional form of the cross-sectional linear regression model to the operationalized speci- fications of Model 1 are presented in Table 5.8 for both samples. Table 5.8 contains six different specifications of Model 1, two of these specifications are associated with the NYSE sample firms and four are associated with the electric utility firms. The statistical support for each of the relationships presented in Table 5.8 may be examined by reviewing the calculated F-statistic. The magnitude of the F-statistic indicates whether or not the null hypothesis that the estimated regression coefficients equal zero can be rejected at a specified level of significance. As such, in regression analysis, the F-statistic is used to evaluate whether any of the independent variables are statistically related to the dependent variable. In the context of this study, an evaluation of the F statistics indicates whether the relationship expressed between the market based beta and its theoretical determinants can be statistically supported. As indicated in Table 5.8, only one of the two NYSE sample estimations exhibited a linear relationship that was statistically significant. 96 Specifically, for the NYSE sample, the additive formulation of the theoretical model was statistically supported in the case which used an equal-weighted market index to estimate the covariability measures. In this case, the F-statistic indicates that the null hypothesis Yl=yz=y3=0 can be rejected at the .05 level of significance. The strength of the association as measured by the adjusted R2 is .145. This indicates that, in the NYSE sample, only 14.5% of the variation in the market-based beta could be explained by the business risk com- ponent and the debt-to-equity ratio when utilizing an additive func- tional form. Also included in Table 5.8 are the summary statistics associ- ated with the fit of Model 1 in the electric utility sample when using the additive functional form (equations 5.1 and 5.3). There were four specifications of the fitted model in the electric utility sample, since the business risk component was estimated using both actual output and sales across two market return indices. Of these four cases, the F-statistics indicate that three are statistically significant. Two of the cases are associated with the covariability measures estimated on a sales basis (value-weighted and equal-weighted), while the third case is associated with covariability measures esti- mated on the basis of actual output (kilowatt hours), when using an equal-weighted market return index. The adjusted R2 are high for the equal-weighted index in the electric utility sample, 49.8% (sales) and 47.7% (kilowatt hours). This indicates that, relative to the NYSE sample, a higher percentage of the market-based beta is explained by the theoretical business risk component and debt-to-equity ratio in the electric utility sample. 97 In addition to the hypothesized existence of a linear rela- tionship between the market risk measures and the accounting-based variables, the theoretical model also asserts that the intercept term should be equal to zero and that the estimated slope coefficients should be positive. An indication of the positive nature of the observed linear relationship is provided by an examination of the signs of the estimated slope coefficients, while a standard t-test may be used to examine the statistical significance of the estimated magnitude of the regression coefficients. Of the four statistically significant specifications of Model 1 indicated in Table 5.8, t-tests performed on the estimated slope coefficients, indicated that the null hypothesis that 72-0 and 73=O could be rejected for all cases at the .05 level of significance. These results suggest that both the business risk components and the debt-to-equity ratio are statistically related to the market-based beta. In addition, the signs of the slope coefficients for three of the significant cases are in the expected positive direction. However, with regard to the fourth significant case (NYSE sample and equal— weighted index), the sign on the estimated regression coefficient of the business risk component is negative. The economic interpretation of this result is troublesome as the empirical result is not supportive of the theoretical model hypothesized in expression 4.1. It may be that the operational procedures used to estimate Model 1 in the NYSE sample firm resulted in more measurement error than in the electric utility sample. Also, it will be recalled that sales dollars were used as a surrogate for the output measure in the business risk com- ponent. This surrogation may be inadequate in a sample of diverse firms. 98 .mpm: movnaocfi uoc mum muHsmmu monsoon unmoalwouswwo3 onu .vofiaaem was masooooua HmfivoEou menu noumm co>o u:do«maawfimaw Hagan mos umoulm may modem .osvwcnomu moumoum ammoa mounwfios m wean: voumefiumonmu mus done many .aowuaasmmm uouuo ucmumcoo onu mo sowumH0fi> oaofimmoa m oomUAvcH .uo>oso: .vwm mmaomfium> wouowmoua new oHomfium> ucovconmvcfi may mamum> mamnvfimou was we muoaa onu .AHmoOE m>fiufivwm mouswfimzleHm> .oHaEmm mmwzv ommu oco cH .mommu somuuaom 0:» mo uao coouufizu cw maOHuQESmmm scammouwou may Bonn maovoe wouuwm onu mo mounuumawm macauom o: mo~mm>ou mousmmoe amuse .mamnvfimou may no uoaa >ufiafiomooua Hmeuos osu cam .oanmaum> ucovconow nouowvoua ocu msmuo> mam odomwum> usoosoaovsfl osu msmuo> mHmnvamou ecu mo muOHd was .Ewuw lemma: Hmsmwwou osu mo cowumcfismxw no mo woumfimcoo mHm%Hmcm comm .Aoa.m mam .a.m .m.m oHanV mHovoE Hmcofiuommnmwouo wouufiw coouunom osu mo sumo now wouosvcoo mos mammfimcm Hmsofimou < .HHoB mm Ho>oa Ho. osu um unmowmacwfim wagon o.~ coca Houmouw mafiumunu Suva .Hm>oH mo. osu um ousmofiMficwfim moumofivcw on one .A>vm\> co momma ohm mowumulu voumasoamo paw .moumsfiumm omonu mo mowumulu osu uaomoumou moumefiumo cosmmmuwou osu summons mononucmumd cfi so>fiw madman: use .mfinmcofiumaou Hamada uchAMchHm m mo o>wumowucw ma mam .onm>uN>uH> umsu mfiwocuoa%n Hana mSu mo coauuohou m 0» ucoam>fisvw ma mowumaumumsm onu mo mocmofiMfiawfim .Ho>oH mo. o:u um oUGmUAMHcmfim Hmofiumaumum moumoavafiex AmV Amv Aav "0H.m mam m.m mmHan ou oHomoHHaam omam mum mouo: wafisoaaom one .Amm.sv .Aoa.Hv .Aon.sv Asa.ev Aa~.1v Amm.sv amass manages»: ..ss.~e A.as asso. Home. mmAN. mm.H H.m ammo. HwNo.u sacs. usuuumam Amoammv .AmH.nV .Aac.mv .Amm.mv .Aam.ev .Asm.HV .Aes.sv meanness: ..ma.ma m.ms cowao. momH.H same. .«mm.m o.HH ammo. mama. «mos. unusuwam .AHe.Hv .Aas.muv oamo.HHv Asa.v Ao~.~-v Aeo.HHv Aooaumv pause ..am.s n.4H cosmo. owoo.m- ammsa. oa.~ a.w ommeo. o-.nu oooN.H meaaam mmsz smouum m s N» H» ummsnm m m» N» H> NI mix ( < NI. < < < Rows“ uoxums mmucwfioB Honom News“ umxuma vouswfioa osam> A Amnem> + Hamao>umvmams + H» u Am ”Have: ambush a < muaomom moumsvm momma humsfivuo m.n mqm om m o N H Am:.+_HV:H a + m_Au>-ame=H a + a a mufismom moumsam ammoq humcfiouo $.m mqm "Hope: amused mufismmm mwumscm ammo; >pmcfivuo OH.m mgm¢H mofiuwawus oauuooam maufim oaaamm mmwz 105 TABLE 5.11 Correlation Matrix NYSE Sample N=4l v E 0 v Variables 8L BL BA IE (-)BQ(Sa1es) E BL .918 8A .162 .234 D/E .157 .252 .006 (-)BX(Sales) -.340 -.349 -.139 -.058 (-)Bg(Sales) -.381 -.364 -.146 -.O48 .983 where (-)=E(P-VC) TABLE 5.12 Correlation Matrix Electric Utility Sample N=37 Variables B: 8: BA %' (.)83 (.)83 (“)82 (Sales) (Sales) (KWH) BE .713 8A .297 .235 D/E .287 .683 .172 (-)Bg(Sa1es) .279 .312 .272 -.031 (')Bg(Sales) .064 .395 .235 .231 .389 (°)BX(KWH) .006 .157 .097 .180 -.016 -.068 (-)8§(KWH) .116 .478 .151 .437 .044 .101 .763 where (-) = E(P-VC) 106 It is noted, however, that the difference in explanatory power of the two models is very small. 5.3 Summary In summary, the objectives of the empirical analysis of this study were twofold: (1) To empirically test a theoretically derived model of systematic risk (2) To use comparative analysis to determine the adequacy of using an accounting beta as a surrogate for busi- ness risk in theoretically based risk models With regard to the first objective, Model 1 was fitted in two func- tional forms across two samples utilizing various specifications of the business risk components. The empirical results of this research evidenced, in general, a significant positive association between the market-based beta and the operationalized theoretical specifications of the accounting determinants of systematic risk. The explanatory power of the model was greatest when fitted within the electric utility sample with an equal-weighted market return index used in the estimation of the covariability measures. The incorporation of sales into the model as a surrogate for the actual output measure in the electric utility sample did not detract from the power of the model. Finding empirical support for Model 1 has important implications for various groups that utilize accounting-based risk measures. The second objective of the study focused on the adequacy of using the accounting beta in systematic risk models. The results of the comparative analysis indicated substantial similarity between models incorporating the theoretically-determined elements and those utilizing the accounting beta. This result also has implications for 107 various user groups interested in security risk assessment based on accounting reports. 108 Chapter 5 Footnotes 1For example, Beaver, Kettler and Scholes [1970] reported a mean systematic risk estimate of .991 with a .336 standard deviation and associated range of .17 to 2.15. 2Formally, if we assume the average beta estimates of the NYSE sample follow a normal distribution with means of 1. 13940 and .90690 (value-weighted and equal-wei hted respectively) and associ- ated standard deviations of .39884/v41- .06228 and .36117/VT= .056406 (value-weighted and equal-weighted respectively), a t-test of the null hypothesis that 8j=0 would be rejected at the .01 level of statistical significance. 3The suggested Bj=cov(Q ,Qm) may be mathematically derived within the theory of Chapter 3 And essentially involves a decomposi- tion of Rm . 4There are a number of recent studies that have provided evi- dence of security return anomalies. These anomalies (size, dividend payout, and price-earnings ratio) are persistently significant when related to market risk measures, although they cannot be explained on a theoretical level. A good discussion of the price earnings versus size effect is provided in Reinganum [1981]. 5It is noted that Bowman [1980] also examined his general model of systematic risk by controlling for industry membership with intercept dummy variables. Bowman reported that this industry con- trol model explained 70% of the variation in market risk. CHAPTER 6 CONCLUSIONS The results of this study should be of interest to various groups or constituencies in the financial reporting environment. As indicated in the introductory chapter, these groups include investors, financial information intermediaries, management, and financial reporting regulators. In this chapter, the implications of the present research findings for these four groups are discussed. In addition, the final segment of this chapter includes a discussion of possible extensions of the present research. The interest of the investment community in security risk assessment is based upon a desire to understand the linkage of the firm's beta with its security market risk, and ultimately, with the firm's market-determined return. Risk assessment models can aid investors in this activity. In the present study, a theoretical model was derived which related accounting measures of the firm's financing and operating characteristics to the firm's market-based beta. In addition, this research empirically examined the theoretical model and provided some evidence of empirical support. Thus, this research indicates that the analytical model can provide investors with a theoretically-derived basis for assessing risk effects of certain fundamental firm activities (.e.g, changes in product lines, changes in costs of the input mix, etc.). 109 110 Closely aligned with the interest of the investor group in beta assessment is the interest of financial information intermedi- aries. Financial intermediaries are interested in models that provide estimates of the risk levels of equity instruments since a major aspect of their work is to pass on such risk information to individual and institutional investors. It is suggested that the model of the present study might be useful to financial intermediaries as a basis for understanding the relationship between accounting microeconomic risk measures and the market-based measures of equity risk. It should also be noted, however, that this study did not investigate the predictive ability of the theoretical model examined. Such a focus would necessitate an extension of the present research beyond the beta association level and would include a comparison of the predictive performance of Model 1 with the performance of other beta prediction models. It is believed, however, that the beta asso- ciation methodology employed in this study is a necessary exploratory step before moving to the predictive setting. The empirical results of this study indicate that further research in the predictive mode may in fact be warranted. A third group, the managers of the firm, are also concerned with risk assessment. Models which relate accounting measures of the firm's operating and financial structure to systematic risk can assist managers in evaluating the influence of corporate policy decisions on the firm's risk level. The theoretical model examined in this study provides such a framework and should be of interest to corporate management. Specifically, the model examined in this study indicates the relationship between some managerial decision variables and the lll firm's market based beta. It is suggested that the model examined in this study can aid managers in assessing the impact of their decisions (production, investment, and financing) on the firm's per- ceived risk level. With regard to the production decision, the model explicitly allows for an assessment of the impact of alternative pro- duction levels on the firm's market-based beta. In a related manner, the capital investment and financing decisions might also be enhanced by the risk assessment model developed and tested in the present research. That is, the risk assessment model of the present study incorporates the effect of cost structure and debt financing on the firm's market based beta. As such, it should be of interest to managers who must estimate the appropriate capitalization rate for alternative investment projects. The final group which may be interested in the results of this study were identified as accounting regulators or policymakers. The primary regulators in the financial reporting environment are, as stated earlier, the FASB and the SEC. These policymakers have indi- cated two concerns over the impact of financial reporting require- ments on the public. One concern is expressed at the level of the individual user and the other concern is expressed at the level of the aggregate market. Specifically, policymakers are concerned that inequities may befall investors because of informational deficiencies. In addition, policymakers appear to be concerned over the effects of fuller disclosure on resource allocation and capital formation. Although the model of the present study does not empirically examine the effect of alternative reporting disclosures on market-based risk, it is suggested that the model does provide a theoretical framework 112 for evaluating the efficacy of certain required disclosures. In addition, the model examined within could be used to examine the economic consequences of a regulation once that regulation has been adopted. In concluding the discussion of the implications of the present research, some comments will be made regarding possible extensions of the present research. First, there are certain unresolved methodo- logical issues which might represent logical extensions of the present study. In addition, there are major theoretical aspects that represent areas of future consideration. On a methodological basis, it is believed that an important extension of this study is an investigation of the explanatory power of the theoretical model at the portfolio level. It would also be of interest to investigate the robustness of the findings of this study to alternative estimations of the output covariability measure as well as the impact of controlling for certain market anomalies (size, dividend yield, etc.). Other research extensions of interest might include a consid- eration of the effects of risky debt, personal and corporate taxes, and also stochastic prices. It is suggested that these elements might theoretically enhance the explanatory power of the model of the present research and, as such, represent a potential area for further empirical analysis. U) l" < t" :34?" APPENDIX A following notation will be employed in this Appendix: an expectations operator a variance operator with o = standard deviation a covariance operator with p = correlation coefficient random variable; the rate of return on a levered firm L random variable; the rate of return on an unlevered firm u (an all equity firm with the same asset base as firm L) total market value of firm L debt total market value of firm L common stock total market value of firm L risk free rate of return random variable; rate of return on the market portfolio of risky securities positive constant = E (RM) - RF / 02 (RM) 10' (RM) 3 random variable, dollar value of earnings before interest and tax (net operating income) total fixed cost of the firm variable cost per unit (superscript T, total variable cost) random variable output level of the firm price per unit of output Q 113 APPENDICES 114 APPENDIX A Integration of the Single Period Theoretical Market Risk Models The first major analytical work in the risk assessment area was accomplished by Hamada in 1969. Hamada's primary purpose, in his 1969 paper, was to derive the three Modigliani-Miller (M-M) propositions in the general equilibrium setting of CAPM. In this context, Hamada demonstrated that: E(RL) = E(RU) + [E(RU) - RF] g— (1) The E(RL) as defined by CAPM is: E(RL) = R1: + [E(RM) - RFJBL (2) The E(RU) as defined by CAPM is: 120111) = RF + [E(RM1 - RF]BU (3) The substitution of Eq. (3) into Eq. (1) reveals: D map = RF + (mu) - RF18U + {(13F + [E(RM) - RFDBU} g1“- (4) L Simplifying: DL E(RL) = RF + [E(RM) - RFJBU 1 + g— (5) 115 And setting Eq. (5) equal to Eq. (2): DL RF + [E(RM) - RF]BL = RF + (”“11 - RF]BU> 1 + g- (6) L By elimination and simplification we obtain Hamada's 1972 result: DL &=%1+r m L The next contribution in the risk assessment area was made by Rubinstein in 1973. Rubinstein derived the nature of BU’ the busi- ness risk component, in terms of microeconomic firm level variables. The CAPM may be formulated as: E(RL) = R1, + A cov (RURM) (8) Using 1* = 10(RM) and the definition of covariance the CAPM becomes: E(RL) = RF + 1*p(RL.RM) c(RL) (9) Under appropriate assumptions and acceptance of MM proposition 1 we can state: 0(RL9R-M) = po(RU> g1”- (13) L The second component on the right-hand side of Eq. (13) represents operating risk while the third component represents financial risk. Rubinstein [1973] then developed a theoretical model of the operating risk component. Allowing demand (Q) to be a stochastic variable, Rubinstein demonstrated that the operating risk component may be decomposed as follows: A 0(R-U.RM)Q(RU) = g [aaa1 mam“) 3:7, (14) This expression results from the following definitions: >< II (P - v0) 808 - F3 (15) 56 II [(P - VC)aQa — Fa] /va , (16) where a represents an individual product line or activity. By assuming a one segment firm, aa = 1. This implies a single product line and allows us to abstract from the weighting factor. We may also assume F (fixed costs) do not covary with the market return, which leads to the following: O' 0(RU.RM)U(RU) = p (P - VC)UQU ’RM (RU) (17) VU In covariance structure, the right-hand side of (17) is: 117 9(RU.RM)O(RU) = cov (P - VC)UQU’ RM' O'RU) vU am”) 001,!) (18) Assuming that (P - VC)U is a constant and simplifying we obtain: 0(RU.RM)0(RU) = (P - VC)U cov(QU.RM) (l9) VU °(RM) Multiplying Eq. (19) by 0Q/0Q gives: p(RU.P.M)o(RU> = (P - VC)u cov (911.81,) “U mum“) 771; (21) The linkage of Rubinstein's model to the work of Conine (1982) can be demonstrated with a rearrangement of Expression (l9). Recall that p (correlation) is preceded by 1* in Rubinstein's formulation of CAPM Expression (9). This implies that Expression (19) can be multiplied by 1/0 (RM): 0(RU.RM) 0(RU) = (P - VC)U cov (QU.RM) (22) The definition of ()(correlation) then implies: 118 cov (RU,RM) o (RU) (P - VC)U cov (QU.RM) mu) 0701“) vU 6701”) (23’ or, in terms of covariability (beta) measures, BU = (P -' VC)UBQ (24) VU The result in Eq. (24) is one component of the Conine model, a fact which will be made apparent in the derivations which follow. Conine (1982) defined business risk by allowing the VC, P, and Q to be random variables. Recall that Rubinstein's model allowed for stochastic demand (Q) only. Given the definitions of XU and RU’ and again, the assumption that F (fixed costs) do not covary with the market return, we obtain: ~ 8U = cov (P - v0) 01,3“) (25) 1. 02(RM) VU Applying the operational rule for the product of two random vari- ables:1 B U ='% [E(P‘TVC)U cov (QU’RM) + E(QU) cov[(P - VC)U,RM]]|02 (RM) U (26) 1Bohrnstedt and Goldberger (1969) demonstrate1that if X, Y and U are jointly distributed random variables with expectations E(X), E(Y) and E(U),variances 02(X), 02(Y) and 02(U), and covariances cov (X, Y), cov (X, U) and cov (Y, U), then the covariance of the product XY with U (assuming multivariate normality) is given by: cov (XY, U) = E(X) cov (Y, U) + E(Y) cov (X, U) 119 In terms of beta measures, this expression becomes: 1 8 =-— U VU ~ ~ [E(P - VC)U 8Q + E(QU) 8(P _ v04 (27) The results in Eq. (27) may be compared to Eq. (24) to show the exact linkage between the Conine and Rubinstein models. Another systematic risk model that can be compared to the Rubinstein model is Lev (1974). Lev defined before-tax earnings as total revenues (rU) less total variable costs (VCE) and total fixed costs (FCU): X0 = rU - v0: - FU (28) Then, by assuming a direct relationship between accounting net income and security returns, Lev obtained: RU = [Xu (1 - a) + ng / vU (29) where Ag = change in the capitalized growth rate and 1 = the corporate tax rate. If we recall that systematic risk is: 86 = cov (RU.RM) (30) U2(RM) Then, substitution of Eq. (29) into Eq. (30) and dropping Ag (given a one period context), we obtain: = cov ((rU - v03 - FU) (1 - 1)).RM (31) vU BU 02(RM) 120 And since (by assumption) F does not co-vary with the market return: BU = cov (rU (l - 1), RM) - cov (VCE, RM) (32) 02(RM) 92(RM) Lev considers firms in homogeneous industries with similar revenues. For such firms, only the second term on the right-hand side of Eq. (32) will differ. Essentially, in the specified environment, Lev's model stated that an inverse relationship existed between BdBT h T VT) U an VC , w ere BVC -cov ( CU’RM ’ U U 2 0 (RM) Thus, both Rubinstein [1973] and Lev [1974] developed theoret- ical models of systematic risk that allowed for stochastic demand. Lev's analysis, however, rests on two restrictive assumptions: (1) The industry of interest is homogeneous. This implies that differences in operating leverage are reflected in variable unit costs and that the average product price is identical across firms. (2) The output pattern is identical across the group of homogeneous firms. 121 APPENDIX B NYSE SAMPLE FIRMS n=4l DNUM* CNUM** Firm 2000 33609 Anderson, Clayton & Co. 2600 793453 St. Regis Paper Co. 2600 809877 Scott Paper Co. 2600 500602 Koppers Co. 2890 252165 Dexter Corp. 2911 48825 Atlantic Richfield 2911 190441 Coastal Corp. 2911 977385 Witco Chemical 3079 781088 Rubbermaid Inc. 3221 219327 Corning Glass Works 3310 912656 U.S. Steel Corp. 3330 761763 Reynolds Metals 3449 150033 Ceco Corp. 3520 576216 Massey Ferguson Ltd. 3520 627151 Murray Ohio Mfg. Co. 3573 848355 Sperry Corp. 3651 835699 Sony Corp. 3651 989399 Zenith Radio Corp. 3662 620076 Motorola Inc. 3714 99725 Borg-Warner Inc. 3714 278058 Eaton Corp. 3714 872649 TRW Inc. 3740 513696 Lamson & Sessions Co. 3861 277461 Eastman Kodak Co. 4210 522066 Leaseway Transportation Corp. 4511 276191 Eastern Airlines 4511 693602 PSA Inc. 4511 760274 Republic Airlines Inc. 4811 171870 Cincinnati Bell Inc. 4922 835415 Sonat Inc. 4923 624029 Mountain Fuel Supply Co. 4940 30411 American Water Works 5140 561280 Malone & Hyde Inc. 5411 501044 Kroger Co. 5411 716544 Petrolane Inc. 5712 859145 Sterchi Bros. Stores Inc. 6798 443444 Hubbard Real Estate Inc. 6798 575421 Massmutual Mfg. & thy. Ins. 6798 804396 Saul (B.F.) Real Estate Inv. 7011 947423 Sebb (D.E.) Corp. 8911 861572 Stone & Western Inc. *Compustat Industry Classification Code **Compustat Company Identification Code 122 APPENDIX C ELECTRIC UTILITIES SAMPLE DNUM 4911 n-37 CNUM* Firm 17411 Allegeny Power Sys. Inc. 48303 Atlantic City Elec. Co. 100599 Boston Edison Co. 144141 Carolina Power & Lt. Co. 152357 Central & Southwest Corp. 154051 Central Me. Power Co. 186108 Cleveland Elec. Illum. Co. 202795 Commonwealth Edison 250847 Detroit Edison Co. 264399 Duke Power Co. 266228 Duquesne Lt. Co. 277173 Eastern Utils. Assoc. 291641 Empire Dist. Elec. Co. 341109 Florida Progress Corp. 370550 General Puv. Utils. Corp. 40255010 Gulf Sts. Utils. Co. 485260 Kansas Gas & Elec. Co. 491674 Kentucky Utils. Co. 595832 Middle South Utils. 641423 Nevada Power Co. 6444001 New England Elec. Sys. 664397 Northeast Utils. 677347 Ohio Edison Co. 678858 Oklahoma Gas & Elec. Co. 709051 Pennsylvania Power & Light 736508 Portland Gen. Elec. Co. 737679 Potomac Elec. Pwr. Co. 744465 Public Suc. Co. Ind. Inc. 744482 Public Suc. Co. N.H. 745332 Puget Sound Power & Lt. 842400 Southern California Edison Co. 842587 Southern Co. 882848 Texas Utils. Co. 889175 Toledo Edison Co. 898813 Tucson Elec. 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