Abstract
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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Notes
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.
Penman (2010a, p. 668) denotes growth risk as “operating risk 2”.
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.
Because all of our final models equal the CAPM market beta, the models are equivalent.
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.
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.
See also “Appendix 3”.
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.
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.
All of our conclusions remain qualitatively unchanged if we use the S&P 500 equal-weighted index returns.
We apply aggregate market sales data provided by Reuters.
For details regarding accounting flow calculations, see “Appendix 2”.
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.
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.
Recall that financials (included in Fama and French’s classification code 11) are dropped.
We refer to the sum of all income figures as the market income.
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.
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.
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.
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.
Note that we include 11 industry indicator variables. The industry classifications are obtained from Kenneth French's website, available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
We are grateful to an anonymous referee for suggesting this analysis.
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.
See Chen et al. (1986).
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.
All data are provided by the H.15 Federal Reserve Statistical Release.
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Acknowledgments
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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Appendices
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 | Description |
---|---|---|
#6 | AT | Total assets (mm$) |
#8 | PPEQT | Property, plants and equipment-total (net) (mm$) |
#9 | DLTT | Long-term debt-total (mm$) |
#11 | CEQT | Common equity-tangible (mm$) |
#12 | SALE | Sales (net) (mm$) |
#15 | XINT | Interest expenses (mm$) |
#19 | DVP | Dividends-preferred (mm$) |
#20 | IBADJ | Income before extra items-adjusted for common stock equivalents (mm$) |
#27 | AJEX | Adjustment factor (cum.) by ex-date |
#34 | DLC | Debt in current liabilities (mm$) |
#54 | CSHPRI | Common shares for basic eps (mm) |
#60 | CEQ | Common equity-total (mm$) |
We obtain the following items from the Center for Research in Security Prices (CRSP):
Item name | Description |
---|---|
RET | Returns—incl. dividends |
VWRETD | Value-weighted returns—incl. dividends |
SHROUT | Shares outstanding |
PRC | Price or bid/ask average |
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:
NIOP_l = IBADJ/(CSHPRI · AJEX) |
NIOP_u = (IBADJ + DVP + (1 − TAX) · XINT)/(CHSPRI · AJEX) |
FFOP_l = (IBADJ + DP)/(CSHPRI · AJEX) |
FFOP_u = (IBADJ + DP + DVP + (1-TAX) · XINT)/(CSHPRI · AJEX) |
WCOP_l = (IBADJ + DP + TXDI)/(CSHPRI · AJEX) |
WCOP_u = (IBADJ + DP + TXDI + DVP + (1-TAX) · XINT)/(CSHPRI · AJEX) |
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) |
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:
Label | Definition | Source |
---|---|---|
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) |
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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). https://doi.org/10.1007/s11156-013-0352-1
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DOI: https://doi.org/10.1007/s11156-013-0352-1
Keywords
- CAPM
- Cost of capital
- Accounting beta
- Intrinsic business risk
- Growth risk
- Instrumental variables
JEL Classification
- C36
- G11
- G12