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Determinants of market beta: the impacts of firm-specific accounting figures and market conditions


This article examines and extends research on the relation between the capital asset pricing model market beta, accounting risk measures and macroeconomic risk factors. We employ a beta decomposition approach that nests competing models with different business risk proxies and allows to frame cross-model comparison. Because model tests require estimated independent variables resulting in measurement error, we empirically estimate three comparable model specifications with instrumental variable estimators and for the first time provide thorough instrument diagnostics in this setting. Correcting for the heretofore neglected weak instruments problem we find that growth risk (i.e., the risk of firm sales variations that are inconsistent with the market wide trends), is the business risk that explains cross-sectional variations in market beta best.

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  1. Although we acknowledge that prior studies such as Francis et al. (2004, 2005) have investigated the relation between earnings quality and cost of equity and debt capital, our research question is distinct, because we want to analyze how to appropriately capture and measure business risk, which is different from information risk, as main determinant of the cost of equity capital. Based on the work of, e.g., Griffin and Dugan (2003), Mensah (1992), Chung (1989) and most notably Penman (2010a, p. 668 et seq.), this is an important and different question. (See also Penman (2010b, p. 221), who states that his framework is untested). However, in the robustness section we also investigate whether earnings quality (i.e., information risk) subsumes our construct of intrinsic business risk, which is not the case.

  2. Penman (2010a, p. 668) denotes growth risk as “operating risk 2”.

  3. See, for example Mandelker and Rhee (1984), Chung (1989) and Mensah (1992). A step-by-step illustration of the derivation process and how this formula incorporates prior model specifications is available upon request.

  4. The decomposition of formula (1) indicates that the macroeconomic variable has to be market-wide sales. One might suggest that it should be market-wide earnings, so that in robustness tests we use the latter option to estimate income risk and obtain equivalent results.

  5. Because all of our final models equal the CAPM market beta, the models are equivalent.

  6. See Chung (1989) Eq. (11), p. 347. Note that the factors \( \left( {dS_{M,t} /S_{M,t - 1} } \right) \cdot (E_{M,t - 1} /dNI_{M,t} ) \cdot (Var(dS_{M,t} /S_{M,t - 1} ))^{ - 1} \cdot Cov(dIS_{t} /IS_{t - 1} ,dS_{M,t} /S_{M,t - 1} ) \) and \( (dS_{M,t} /S_{M,t - 1} ) \cdot (E_{M,t - 1} /dNI_{M,t} ) \) are not firm specific and thus are captured by constants in the regression analysis.

  7. Griffin and Dugan (2003) require data to be non-missing from 1980 onwards which results in a smaller sample than ours. However, their main analysis is based on the 1990 until 1999 time period.

  8. See also “Appendix 3”.

  9. Our robustness tests include varying time intervals for alternative 10-year time spans, which support our findings for 1990 to 1999. Further time intervals are 1965 to 1974, 1980 to 1989, 1985 to 1994, 1995 to 2004 and 1998 to 2007. In conducting an estimation using 10 years of annual data, we are consistent with the prior literature.

  10. Our results are robust to the inclusion of financial firms, but we recognize that the estimated risk proxies should be treated with care when comparing financial and non-financial firms.

  11. All of our conclusions remain qualitatively unchanged if we use the S&P 500 equal-weighted index returns.

  12. We would like to note suggestions by O’Brien and Vanderheiden (1987) and Dugan and Shriver (1992), who propose the inclusion of a time trend for detrending the risk proxies’ estimate.

  13. We apply aggregate market sales data provided by Reuters.

  14. See also Mensah (1992) and Ismail and Kim (1989).

  15. For details regarding accounting flow calculations, see “Appendix 2”.

  16. In unreported but available upon request robustness tests, we also re-estimate our results for the FFOP, WCOP, and CFOP variables for various time intervals. All results remain valid.

  17. In unreported robustness tests we perform this transformation and re-estimate the models on the enlarged data sample. The results reveal a better model fit for growth risk if compared to the other competing models. However, the point estimates vary due to the chosen absolute amount of the arbitrary chosen constant.

  18. Recall that financials (included in Fama and French’s classification code 11) are dropped.

  19. See in particular Vuong (1989, Sect. 6) and Cameron and Trivedi (2005) for overlapping models. In addition, a self-contained description of the derivation to perform the discrimination test for overlapping models is available from the authors upon request.

  20. We refer to the sum of all income figures as the market income.

  21. In addition to the OLS results for the second income risk model, we present IV estimations of that model in Table 4. In unreported robustness checks, we estimate the modified income risk model for all other presented estimations and find that the growth risk model performs better.

  22. The first stage results of the modified income risk model resemble the result of the main income risk model based on market-wide sales figures. Results are not tabulated.

  23. As outlined by Baum et al. (2007), the Sargan-Hansen test is a test of over-identifying restrictions. The joint null hypothesis is that the instruments are valid instruments, i.e., uncorrelated with the error term, and that the excluded instruments are correctly excluded from the estimated equation.

  24. In addition, we re-estimated (unreported, but available up on request) our specifications for the periods 1965–1974 yielding 302 observations and 1998–2007 based on 500 observations again supporting our results.

  25. Note that we include 11 industry indicator variables. The industry classifications are obtained from Kenneth French's website, available at

  26. We are grateful to an anonymous referee for suggesting this analysis.

  27. We employ the logarithm of the earnings quality metrics to be in line with the other independent variables. However, the results do not vary if we do not employ the logarithmic transformation.

  28. See Section 3, and see Chen et al. (1986) and Fama and French (1993) for further reading.

  29. See Chen et al. (1986).

  30. The data on TBill returns are provided by the H.15 Federal Reserve Statistical Release; the data for inflation rates are published by the Bureau of Labor Statistics.

  31. All data are provided by the H.15 Federal Reserve Statistical Release.

  32. See also Ismail and Kim (1989) and Mensah (1992).


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This paper has benefited from the comments of participants in the VIII Workshop on Empirical Research in Financial Accounting 2011 in Spain, the European Accounting Association Annual Congress 2011 in Italy, 7th Accounting Research Workshop 2011 in Switzerland, WHU Campus for Finance Research Conference 2012 in Germany and the research seminar at the University of Cologne. The authors gratefully acknowledge funding from the Department of Banking, University of Cologne. We also owe thanks to Christian Mueller for valuable comments.

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Appendix 1

Data requirements for the model specification based on the ‘Net income from operations’ (NIOP) accounting flow

We obtain the following items from COMPUSTAT:

Data item number

Item name




Total assets (mm$)



Property, plants and equipment-total (net) (mm$)



Long-term debt-total (mm$)



Common equity-tangible (mm$)



Sales (net) (mm$)



Interest expenses (mm$)



Dividends-preferred (mm$)



Income before extra items-adjusted for common stock equivalents (mm$)



Adjustment factor (cum.) by ex-date



Debt in current liabilities (mm$)



Common shares for basic eps (mm)



Common equity-total (mm$)

  1. We obtain annual data during the period from 1990 to 1999 for these Compustat items

We obtain the following items from the Center for Research in Security Prices (CRSP):

Item name



Returns—incl. dividends


Value-weighted returns—incl. dividends


Shares outstanding


Price or bid/ask average

  1. We obtain monthly data from CRSP. We require firms to have a minimum of 60 observations for the period from 1990 to 1999

Appendix 2

2.1 Calculation of accounting flows

The following table reports the formulas for our four employed accounting flows.Footnote 32 Detailed data requirements for our preferred formula, ‘net income from operations’ (NIOP), are given in Appendix 1 for firms with and without financial leverage. Throughout the analysis we also employ ‘fund flows from operations’ (FFOP), ‘working capital from operations’ (WCOP) and ‘cash flow from operations’ (CFOP).

We calculate each accounting flow using firm-level data from 1990 to 1999 as follows:







CFOP_l = ((IBADJ + DP + TXDI) − (ACT − CHE − LCT) + (L1.ACT − L1.CHE − L1.LCT))/(CSHPRI · AJEX)

CFOP_u = ((IBADJ + DP + TXDI + DVP + (1-TAX) · XINT) − (ACT − CHE − LCT) +(L1.ACT − L1.CHE − L1.LCT))/(CSHPRI · AJEX)

  1. The subscripts ‘l’ and ‘u’ refer to a firm with and without financial leverage, respectively. ‘TAX’ accounts for the tax rate. We set TAX to 0.4. Our results are robust to a wide range of variations in ‘TAX’
  2. We list the description of the variables used for NIOP in “Appendix 1”. For the other three accounting flows, we also require non-missing financial statement data for ‘depreciation and amortization’ (DP), ‘income taxes-deferred’ (TXDI), ‘current assets-total’ (ACT), ‘cash and short-term investments’ (CHE) and ‘current liabilities-total’ (LCT). The operator ‘L1’ is the lag operator. These additional data requirements create differing numbers of observations, as presented in Table 6. Our results are robust if the data for all accounting flows are required simultaneously

Appendix 3

3.1 Instrument definition

Since the independent variables of our models are not observable and must be estimated first, creating measurement error, we use the instrumental variable approach to reduce the potential bias in the OLS regressions. We use the following instruments for each variable:




IV growth risk (1)

= standard deviation of sales

Chung (1989)

IV growth risk (2)

= average growth of total assets

Beaver et al. (1970)

IV spread risk (1)

= standard deviation of the ratio of debt in current liabilities to total assets


IV spread risk (2)

= standard deviation of interest expenses


IV spread risk (3)

= average growth of total assets


IV income risk (1)

= standard deviation of the ratio of net income to sales


IV productivity risk (1)

= standard deviation of the ratio of net income to average sales growth


IV operating risk (1)

= average of the ratio of property, plant and equipment to total assets

Mandelker and Rhee (1984)

IV operating risk (2)

= standard deviation of net income

Chung (1989)

IV financial risk (1)

= average ratio of total long-term debt to total assets

Mandelker and Rhee (1984)

IV financial risk (2)

= average ratio of interest expenses to operating income after depreciation

Chung (1989)

IV financial risk (3)

= average ratio of total long-term debt to common tangible equity

Chung (1989)

IV financial risk (4)

= average of the ratio of total long-term debt to total common equity

Chung (1989)

  1. This table states the definitions of the instruments used. The abbreviation “IV” stands for ‘instrumental variable’. The instruments are computed on a firm-level basis using annual data from 1990 to 1999. Most estimated risk proxies are instrumented using more than one instrument. We therefore show the number of each instrument belonging to the risk proxy of interest. The ‘Definition’ column specifies how we calculated each instrument. The ‘source’ column states each instrument’s original use in the related literature. The instruments labeled ‘*’ are newly proposed in this study based on the reasoning provided in the main text. Instrument motivation is presented in Sect. 4

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Schlueter, T., Sievers, S. Determinants of market beta: the impacts of firm-specific accounting figures and market conditions. Rev Quant Finan Acc 42, 535–570 (2014).

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  • CAPM
  • Cost of capital
  • Accounting beta
  • Intrinsic business risk
  • Growth risk
  • Instrumental variables

JEL Classification

  • C36
  • G11
  • G12