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The Journal of Financial Research • Vol. XXVI, No. 2 • Pages 179–189 • Summer 2003

SYSTEMATIC RISK AND REVENUE VOLATILITY

Harry F. GriffinSam Houston State University

Michael T. DuganThe University of Alabama

Abstract

We introduce the degree of economic leverage (DEL) as an extension of the ex-isting method of decomposing beta and assess its incremental explanatory powerthrough empirical testing. The DEL is defined as the percentage change in thefirm’s sales resulting from a unit percentage change attributable to an exogenouseconomic disturbance. The exogenous economic disturbance employed is the ra-tio of long-term T-bond rates to short-term T-bill rates. The evidence supports theDEL’s role in explaining systematic risk at both the industry and portfolio levels.However, we find mixed results at the firm level.

JEL Classification: G30

I. Introduction

To better understand the role of sales variability minimization in manag-ing the firm’s systematic risk, the multiple dimensions of systematic risk must beconceptually analyzed. Hawawini and Viallet (1999) provide such an analysis inFigure I by illustrating financial risk as the relation between earnings after taxes(EAT) and earnings before interest and taxes (EBIT), and operational risk as therelation between EBIT and sales. Hawawini and Viallet further specify that salesvary as a result of the uncertainties in the economic, political, social, and compet-itive environment in which firms operate. Hence, they characterize economic riskas the risk faced by all firms and interpret the combined effect of economic riskand operational risk as business risk.

Mandelker and Rhee (1984) demonstrate that both operational risk andfinancial risk can be proxied through the respective use of the degree of operatingleverage (DOL) and the degree of financial leverage (DFL). In this article weextend that original work by separating economic risk from business risk, and we

We thank Anup Agrawal for his early constructive comments. We also extend our thanks to bothRichard Lord and Ghon Rhee (the referee) for their insightful and worthwhile comments.

179

180 The Journal of Financial Research

Hawawini and Viallet 1999: From Finance for Executives (1st ed.), by G. Hawawini and C.Viallet © 1999.Reprinted with permission of South-Western College Publishing, a division of Thomson Learning.Fax (800) 730-2215.

Figure I. Analysis of Multiple Dimensions of Systematic Risk.

empirically represent the economic risk construct through the use of the term,degree of economic leverage (DEL). We explain the fundamental determinants ofsystematic risk via beta decomposition by extending Mandelker and Rhee to includethe explicit relation between economic leverage and economic risk.

Given the assumption of perfect competition, all firms in the market facethe same risk from an exogenous economic disturbance. An economic disturbance isan unforeseen event that possesses the power to disturb the equilibrium of the modeland hence the equilibrium of firm operations. Chen, Roll, and Ross (1986) describesuch events as systematic variables that affect the economy’s pricing operator orinfluence dividends, or any variable necessary to complete the description of a stateof nature. Their research suggests that the spread between long- and short-terminterest rates, expected and unexpected inflation, monthly growth rate in industrialproduction, and the spread between high- and low-grade bonds have a significanteffect on systematic risk.

Chen, Roll, and Ross (1986) describe the spread between the long- and theshort-term interest rates as

UTSt = LGBt − TBt−1, (1)

whereUTSt = the difference between the long- and short-term interest rates;LGBt = returns on the long-term government bonds at time t ; andTBt−1 = end-of-month return on the one-month Treasury bill at time t−1.

The selection of the interest rate spread as the DEL proxy is not tautological.This proxy is chosen because the inverse relation between the market portfolio valueand interest rates is well accepted in finance. If our proposed theory is valid, theempirical test results should be consistent with the anecdotal incidences alreadyobserved in the capital markets.

Systematic Risk and Revenue Volatility 181

Ferson and Harvey (1991) concur with the findings of Chen, Roll, andRoss (1986), finding significant the yield-to-maturity difference between the ten-year and three-month government instruments, as well as the spread between thecorporate and government bonds. They do not test the monthly growth rate ofindustrial production, but do test and find significant the monthly growth rates ofpersonal consumption.

Mandelker and Rhee (1984) observe that neither Hamada (1972) norRubinstein (1973) explicitly demonstrates how operating and financial leverage arerelated to operating risk and financial risk.1 The Mandelker and Rhee investigationcorroborates the joint impact of the degrees of operating and financial leverageon systematic risk by demonstrating analytically and empirically how operatingleverage and financial leverage relate to operating risk and financial risk.

Rhee (1986) is the first to decompose systematic risk into a three-component model: business risk, operating risk, and financial risk. Rhee suggeststhat the business risk component is determined by the market-related portion ofdemand uncertainty, as evidenced by sales variability.

Blazenko (1999) recognizes the susceptibility to and impact of economicshocks on sales and earnings. Given the information value of firm earnings,Blazenko hypothesizes a relation between trading of the firm’s shares and firmsales and adds an “economic perturbance” term to his model to account for thisrelation.

II. The Degree of Economic Leverage

We begin with the existing Mandelker and Rhee (1984) analytical modelof the determinants of systematic risk and extend their approach and develop theDEL theory. Finally, we test the incremental explanatory power of the DEL usingthe method employed by Mandelker and Rhee.

The Mandelker and Rhee (1984) approach permits the presentation ofsystematic risk as an explicit multiplicative function of the degree of operatingleverage, the degree of financial leverage, and the degree of economic leverage.

1Hamada (1972) first decomposes the systematic risk of the levered firm, thus allowing beta to bewritten as a function of operating risk and financial risk. Rubinstein (1973) expands Hamada’s work byallowing the firm to have multiple product lines, and the output of each line is stochastic. Defining operatingleverage as the difference between price and variable cost, Rubinstein is the first to demonstrate that thesystematic risk of the levered firm could be written as a function of operating risk. By allowing for stochasticoutput while holding price and variable costs constant, Rubinstein shows that the levered firm’s beta is afunction of operating risk, the variance of sales per dollar of assets, and a term that reflects the influenceof economywide events. The last term is the correlation coefficient between the firm’s quantity of productssold and the return on the market. Thus, Rubinstein is the first to establish the interplay between economicshocks and systematic risk.


The degree of economic leverage is the percentage change in the firm’s sales re-sulting from a unit percentage change attributable to an exogenous economic dis-turbance (Zt). Using the Mandelker and Rhee notation:

DEL = %�Q

%�Z=

(Q j,t

Q j,t−1− 1

)(

Z j,t

Z j,t−1− 1

) , (2)

and rearranging and solving for

(Q j,t

Q j,t−1− 1

)

yields

(Q j,t

Q j,t−1− 1

)=

(Z j,t

Z j,t−1− 1

)(DEL). (3)

Inclusion of the DEL term in the Mandelker and Rhee decomposed β j functionyields

β j = (DEL)(DOL)(DFL)β0j , (4)

where

β0j =

Cov

[(π j,t−1

Z j,t−1

)(Z j,t

E j,t−1

), Rm,t

]

σ 2m,t

. (5)

The first term within the covariance is a constant that represents lastperiod’s earnings after taxes (π j,t−1) that already reflect the economic disturbance(Z j,t−1) that may have occurred in that period. The second term within the covari-ance includes an expectation that the firm’s equity market value (E j,t−1) alreadyreflects anticipated future economic disturbances (Z j,t ). It is the covariance of theproduct of these two terms with the market return that represents the intrinsic busi-ness risk faced by the firm. This β0

j is different from similar terms expressed inthe analytical models of Rhee (1986) or Mandelker and Rhee (1984). The Rheeβ0

j represents the firm’s intrinsic risk after the business, operating, and financialrisks are isolated. The Mandelker and Rhee β0

j represents the firm’s intrinsic risk


in the absence of operating and financial leverage. Accordingly, in our extensionof the Mandelker and Rhee analytical model, the DEL may be considered the lensthat maps the financial effect of the economic disturbance onto the firm’s sales.Because the extension explicitly demonstrates that systematic risk may now bewritten as a multiplicative function of DOL, DFL, and DEL, the importance of theDEL is tested in an empirical investigation of its relation with systematic risk. Thenonlinear multiplicative effect of financial structure on operating risk is avoidedby employing a logarithmic transformation of expression (4).

III. The Data

The data consist of 183 manufacturing firms that reported not only twentyyears of continuous data but also strictly positive EBIT and EAT2 from January1, 1980, to December 31, 1999. The fundamental data for these firms are fromthe Compustat database, and the monthly pricing data for these firms are from theCenter for Research in Security Prices (CRSP) database.3

The degrees of operating, financial, and economic leverage of the samplefirms using the two-stage approach suggested by O’Brien and Vanderheiden (1987)are now estimated. Straightforwardly extending the O’Brien and Vanderheidenmethod, we determine the DEL estimate as follows:

ln(Salest ) = ln(Sales0) + gSales t + µSalest , (6)

and

ln(Zt ) = ln(Z0) + gZ t + µZt . (7)

This produces the series µSalest and µZ

t . We then estimate the following model:

µSalest = (DEL)µZ

t + φt , (8)

2We recognize that by limiting the fundamental financial data to firms with strictly positive EBIT andEAT there may be some loss of generality.

3Only the most recent ten years’ data are used in this analysis because of a stationarity issue. Followingthe stationarity test of Mandelker and Rhee (1984), the data are grouped by CUSIP into two ten-yearsubperiods. Six coefficients are estimated for each CUSIP; three for each subperiod in all SIC codes. Wefind that at the α = .05 significance level that almost 60% of the DOL coefficients, more than 38% of theDFL coefficients, and more than 95% of the DEL coefficients estimated were not stationary over the twoten-year subperiods tested. On this account, we continue the analysis using only the most recent ten years’data, from December 31, 1989, to December 31, 1999.


TABLE 1. Industry Averages of the Beta (β), Degree of Operating Leverage (DOL), Degreeof Financial Leverage (DFL), and Degree of Economic Leverage (DEL) Estimates.

Industry Code Number of Firms Beta DOL DFL DEL

20 Food and Kindred Products 21 .622 1.578 1.412 0.00326 Paper and Allied Products 11 .124 2.351 0.997 −0.17729 Petroleum and Coal Products 07 .226 2.411 1.342 −0.11133 Primary Metal Industries 08 −.135 2.154 1.312 −0.20235 Industrial Machinery and Equipment 18 .580 2.167 1.122 −0.13536 Electrical and Electronic Equipment 22 .322 1.163 1.311 −0.09937 Transportation Equipment 11 .326 2.148 0.941 −0.12649 Electric, Gas, and Sanitary Services 85 .684 0.750 0.056 −0.007

whereφt = the error term; and∧

DEL = the degree of economic leverage estimate.

The DEL estimation depicts the average sensitivity of the percentage changes insales from its trend relative to the percentage deviation of the economic disturbancefrom its trend. Following Lev (1974), we use firm sales as a proxy for quantity soldbecause sales information is available on the income statement, whereas quantityof product sold is not.

We use the market model to estimate the beta of each common stock. Themarket portfolio monthly rates of return are based on the S&P 500 value-weightedindex compiled from the CRSP database. The monthly returns of both the index andof each firm are annualized to compare returns with each firm’s financial statementdata. The returns are annualized using twelve-month geometric moving averages.Table 1 summarizes the market estimates of beta and the leverage estimates ofDOL, DFL, and DEL for the 183 firms distributed over eight industries under thetwo-digit Standard Industrial Classification (SIC) code.

Table 1 reflects the effects of an interest rate generated economic shock atthe industry level. An inspection of Table 1 provides some economic inferences. SICCodes 20 and 49 have the two DEL coefficient estimates closest to zero. Theoreti-cally, consumption decreases as the cost of consumption increases, and consumptionremains relatively unchanged only if an interest rate change affects supply and de-mand equally. The DEL coefficient estimates closest to zero suggest that the foodand kindred products and the utilities industries will be least affected by an economicshock in the form of an unanticipated shift in the term structure of interest rates. Thisresult is consistent with a low degree of demand inelasticity for those products. Thegreatest absolute-valued DEL coefficient estimate suggests that the paper and alliedproducts industries and the primary metals industries would be the most highly af-fected by this economic shock. This result is consistent with a high degree of demandelasticity for those products. These implications also are consistent with anecdotalinstances observed in the security prices of firms in each of the respective industries.


IV. Results

The incremental explanatory power of the DEL is tested at the industrylevel4 using the expression

β j = A + B + C ,

whereβ j = the beta of the firm j where j = 1, 2, . . . , 183;

A = γ0 + γ1 X1 + γ2 X2 + γ3 X3; (9)

γ = the estimated coefficients;X i = the DOL, DFL, and DEL estimates where i = 1, 2, 3;

B = γ4 I1 + · · · + γ10 I7; (10)

I = seven industries (SIC 20, 26, 29, 33, 35, 36, 37) indicator variables; and

C = γ1,1 I1 X1 + γ1,2 I1 X2 + γ1,3 I1 X3 + · · · + γ7,3 I7 X3, (11)

the combination of interaction variables of all three leverage estimates with eachof seven industries.

Table 2 provides the regression results at the industry level. Limitationsof this test notwithstanding, the DEL offers a degree of incremental explanatorypower at the industry level.

We next examine the explanatory power of DEL at the portfolio level.The coefficient estimates are sorted three times according to the Mandelker andRhee (1984) method: first by ascending DOL estimates, then by ascending DFLestimates, and finally by ascending DEL estimates. The first five observations areplaced into the first portfolio, the second five observations are placed into the secondportfolio, and the last three observations are placed into thirty-seventh portfolio.The portfolio coefficients are averaged, and these averages are twice tested, usingexpression (12) as the basic test vehicle.

ln β j = γ0 + γ1 ln(DOL j ) + γ2 ln(DFL j ) + γ3 ln(DEL j ) + e j , (12)

4Because there were only eight observations at the industry level of analysis, and because each industrycontributes a different variance to the beta (Y ) estimation, it is appropriate to test the DEL at the industrylevel using a method that equally weights all firms in the sample. Using this method, we can test the entiresample set. We determine that neither term B nor C contributes to the explanation of beta, leaving only theA term, which is twice tested, once with and once without the DEL term.


TABLE 2. Industry-Level Regression Results.

Model γ 0 γ 1 γ 2 γ 3 R2% F-statistic

Restricted model 0.699 −0.088 −0.096 (−) 8.9 8.77(0.000) (0.006) (0.007) (0.000)

Full model 0.722 −0.079 −0.098 0.554 12.2 8.29(0.000) (0.011) (0.005) (0.010) (0.000)

Note: Figures in parentheses are p-values; (−) indicates the term is suppressed. The variables are definedas follows:

γ = the estimated coefficients;R2% = the measure of the proportion of the variance of the dependent variable about its mean that

is explained by the independent variable; andF-statistic = ratio used to measure the significance of the overall model—as the p-value decreases, the

significance of the overall model increases.

wheree j = the error term;

j = the number of portfolios in this analysiswhere j = 1, 2, . . . , 37;

β j = the beta of each portfolio in this analysis; andβ j , DOL j , DFL j , and DEL j = the respective portfolio-level beta, and the

respective portfolio-level degrees of operating,financial, and economic leverage.5

The results are displayed in Table 3.From the DOL sort, the DOL and DFL coefficients estimated are significant

in both trials, and the DEL estimate is not significant. From the DFL portfoliosort, the constant and DOL coefficient estimate decline in statistical significancewhen the DEL term is included. Nevertheless, the DEL coefficient is statisticallysignificant with a p-value of .050. The R2 increases, and the overall F-statistic issignificant at the .01 level. From the DEL portfolio sort, the statistical significanceof the constant term declines slightly, and the DOL and DFL coefficients remainstatistically insignificant. The DEL term is statistically significant at the .000 level.The R2 and overall F-statistic both experience a large increase, and the overallF-statistic is significant at the .001 level.

5Many of the coefficients estimated are negative, and as such, are transformed because of the lin-earization construct requirement. The required transform also has to maintain the informational contentof the data. This requirement eliminates the squaring transform because squaring causes a loss of bothmonotonicity and ordering. The transform selected is a constant of sufficient magnitude added to the coef-ficient estimate to transform all negative estimate values into positive values. This transform maintains notonly both monotonicity and order but is also tractable in application. The firm-level inquiry constant valueselected is 10, the portfolio level inquiry constant is 4, and the industry level inquiry constant is 2.


TABLE 3. Regression Results for 37 Portfolios.

Model γ 0 γ 1 γ 2 γ 3 R2% F-stat

DOL sort 1.93 −0.104 −0.167 (−) 33.9 8.73(0.000) (0.006) (0.035) (0.001)

Full model 1.520 −0.097 −0.182 0.311 34.9 5.89(0.017) (0.019) (0.029) (0.489) (0.002)

DFL sort 1.890 −0.185 −0.0516 (−) 24.6 5.55(0.000) (0.040) (0.057) (0.008)

Full model 0.766 −0.145 −0.0514 0.769 33.0 5.42(0.186) (0.098) (0.048) (0.050) (0.004)

DEL sort 1.64 −0.0268 −0.0567 (−) 1.60 0.28(0.000) (0.734) (0.552) (0.758)

Full model 0.620 0.0234 −0.0598 0.686 39.9 7.31(0.025) (0.713) (0.431) (0.000) (0.001)





Next, we examine the explanatory power of DEL at the firm level.6 Weanalyze the combined effects of leverage on systematic risk faced by the firm usingthe following regression equation:

ln β j = γ0 + γ1 ln(DOL j ) + γ2 ln(DFL j ) + γ3 ln(DEL j ) + e j (13)

wheree j = the error term;

j = the number of firms in this analysis wherej = 1, 2, . . . , 183;

β j = the beta of each firm in this analysis; andβ j , DOL j , DFL j , and DEL j = the respective firm-level beta, and the

respective firm-level degrees of operating,financial, and economic leverage

The firm-level test results are presented in Table 4.When the total sample of 183 firms is tested for incremental significance

of DEL, the full-model DEL coefficient is statistically significant at the .011 level,

6We acknowledge that the coefficient estimates are cross-sectionally constant and that SIC 49 mayassert an inappropriate amount of influence in this analysis, given its size relative to the entire sample. Thus,we administer the test twice; first over the entire sample set and then with SIC 49 suppressed. No loss ofgenerality or reliability is expected arising from the decrease in the degrees of freedom.


TABLE 4. Firm-Level Regression Results.

Model γ 0 γ 1 γ 2 γ 3 R2% F-stat

183 firms 2.810 −0.103 −0.090 (−) 8.5 8.41(0.000) (0.006) (0.010) (0.000)

Full model 1.580 −0.094 −0.0917 0.530 11.8 8.00(0.002) (0.012) (0.008) (0.011) (0.000)

91 firms: SIC 49 suppressed 2.930 −0.112 −0.130 (−) 7.6 3.90(0.000) (0.046) (0.063) (0.024)

Full model 1.880 −0.103 −0.131 0.447 8.9 3.08(0.041) (0.069) (0.060) (0.238) (0.031)





though its economic significance is questionable. The DOL and DFL coefficientsare only slightly differentiated, ostensibly indifferent to the inclusion of the DELvariable. The test is repeated with the SIC 49 utilities omitted, and again the sameresult is observed. Thus, we are unable to determine whether this result is attributableto industry sensitivity or insensitivity to this type of economic shock. Table 1suggests that the utilities industry is insensitive to an interest rate shock. Thus,eliminating utilities from the sample should increase the explanatory power of theDEL variable, but it does not. Hence, the results at the firm level are mixed.

V. Summary and Conclusions

The objective of this study is to demonstrate the degree of economic lever-age as a determinant of systematic risk and to assess the incremental explanatorypower of the DEL through empirical testing. The Mandelker and Rhee (1984) modelprovides the theoretical framework for the DEL through their explicit deconstruc-tion of beta into its component parts of intrinsic business risk and operating andfinancial leverage.

The regression results suggest legitimacy of the DEL as a driver of system-atic risk. This research show that the DEL provides incremental explanatory powerat the industry and portfolio levels, and mixed results at the firm level.

The DEL is not without its limitations. The exogenous shocks must bemacroeconomic in nature and reduced to a logarithmic transform. If the shocks areeither infrequent or rare in occurrence, or of zero magnitude, adequate modelingis difficult. Notably, the data used in this study were screened to include only


manufacturing firms with positive EBIT and EAT. This restriction may result insome degradation in generality.

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journal of financial research volume 26 issue 2 2003 [doi 10.1111%2f1475-6803.00053] harry f....

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