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Using accounting earnings and aggregate economic indicators to estimate firm-level systematic risk

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Abstract

We revisit the literature on using accounting earnings to estimate firm-level systematic risk, using macroeconomic indicators rather than listed-firm indexes to measure aggregate risk. Conventional listed-firm indexes reflect an unrepresentative subset of aggregate assets and thus are expected to substantially mismeasure aggregate and systematic risk (J Financ Econ 4, 129–176, Roll 1977). That choice dictates using earnings rather than returns to measure firm-level outcomes. Earnings and macroeconomic indicators both are primarily realized annual outcomes and thus are better aligned in time than forward-looking returns for capturing the contemporaneous co-movements that underlie systematic risk. Our macroeconomic indicators are chosen to reflect shocks to aggregate supply and demand, providing a parsimonious model that incorporates the two fundamental determinants of aggregate risk. We find that firms’ earnings-based sensitivities (betas) to aggregate supply and demand shocks are negatively correlated and explain the cross-section of returns better than conventional “index” betas. The earnings-based sensitivities are correlated with firm characteristics employed in empirical asset pricing models and explain one quarter of the explanatory power of those characteristics.

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Notes

  1. See also Mayers (1972).

  2. The phenomenon of prices leading returns was first documented by Ball and Brown (1968) and measured more precisely by Ball and Shivakumar (2008).

  3. A formal model of how earnings and returns differ in incorporating forward-looking information is provided by Ball et al. (2013, Section 2).

  4. Kamara et al. (2016) document that asset risk depends on investment horizon.

  5. We offer our estimates of earnings-based supply betas and demand betas as instruments for CAPM systematic risk. Both are based on individual firm co-movement with aggregate undiversifiable outcomes. We do not offer them as yet another set of empirical asset pricing factors. The case is quite the opposite: we report evidence that these admittedly imperfect estimates of CAPM systematic risk displace some of the explanatory power of empirical factors.

  6. A related literature studies stock returns and macroeconomic variables such as industrial production, default risk premium, and growth in income per capita (e.g., Chen et al. 1986; Fama & French 1989; Jagannathan & Wang 1996).

  7. We use market capitalization in the end of year t − 2 rather than t − 1 as a deflator to avoid a mechanical relation with return momentum when we sort firms into portfolios based on stock returns in year t − 1.

  8. Both the macroeconomic indicators and annual earnings are nominal values, avoiding the potential price-level mismatch discussed in Konchitchki (2011).

  9. For example, Chen (1991) and Sadka and Sadka (2009), and Ball et al. (2009).

  10. Konchitchki and Patatoukas (2014a, b), find that quarterly earnings predict future quarterly GDP and other macroeconomic indicators. In annual data, we do not find that annual ΔEarnings predict future annual ΔGDP, ΔTFP, or ΔWealth.

  11. This result is consistent with the Andersen et al. (2005) finding that the covariance between portfolio market beta and lagged industrial production growth increases from the low B/M portfolio to the high B/M portfolio.

  12. The result of earnings wealth betas increasing in return momentum is potentially driven by recoveries from economic downturns. Firms’ market capitalizations are low in downturns, and earnings growth increases in recoveries. Deflating earnings change \(\left [ Earning_{t,p}-Earning_{t-1,p}\right ] \) by lagged market value Pt− 2,p thus could amplify high return momentum firms’ sensitivities to wealth shocks. The result is not observed when deflating by book assets or book equity, which are less depressed in downturns, or by smoothed market capitalization (e.g., a three-year or five-year average).

  13. Unlike a “market model” regression in which the independent variable (the “market” index) is the mean of the dependent variables and hence the mean beta is unity, the means of our two systematic risk instruments are not constrained.

  14. More precisely, \(\widehat {\upbeta }_{MKT,t,i},\widehat {\upbeta }_{Wealth,t,i}\), and \(\widehat {\upbeta }_{TFP,t,i}\) are earnings betas for firm i in year t − 1 because we use firm characteristics in year t − 1 to assign earnings betas to individual firms. We then examine their relation with the twelve monthly returns from July of year t to June of year t + 1. We use year t in the subscript in the equation for brevity.

  15. The “risk premiums” for TFP and wealth betas are not the traditional tradable premiums, because both TFP and wealth betas are unlikely to be observable in real time. Therefore, we are not able to construct factor mimicking portfolios. Our objective is not to document a new trading factor but rather to understand the nature of the risk information contained in accounting earnings.

  16. We thank an anonymous reviewer for these helpful suggestions.

  17. Because we use twelve-month cumulative returns from December of year t-2 to November of year t-1 to identify return momentum and then link with monthly returns from June of year t + 1 to July of year t + 2, cumulative returns start presenting long-run reversal (i.e., negative risk premiums). This is consistent with De Bondt and Thaler (1985, 1987) and Chopra et al. (1992), who document long-term reversal over 2- to 5-year horizons, and with Jegadeesh and Titman (1993, 2001), Rouwenhorst (1998, 1999), and Chui et al. (2000), who document short-run momentum over 3- to 12-month horizons.

  18. We thank Stephen Penman for bringing this possibility to our attention.

  19. These results are for specifications in which TFP is lagged (i.e., observed prior to stock returns). İmrohoroğlu and Tüzel (2014) find that TFP is positively correlated with contemporaneous returns, which is hardly surprising. TFP here is a firm-level relation between inputs and outputs, and structurally related to earnings. Specifically, they measure TFP based on operating income before depreciation and labor expenses, then adjust it for the number of employees and the net book value of property, plant, and equipment. It is well known that earnings are correlated with contemporaneous returns (Ball & Brown, 1968).

  20. Requiring a positive number of employees (Compustat: EMP) loses 27 percent of the observations because many firms do not disclose that information. Requiring positive values for sales revenue, total assets, capital expenditure, gross PP&E, and accumulated depreciation (Compustat: REVT, AT, CAPX, PPEGT, DPACT) loses another 11 percent.

  21. We report additional results in our Online Appendix. It is available at: https://personal.utdallas.edu/~gxs143630/AppendixBST.pdf.

  22. Specifically, Ahn et al. (2009, Figure 3) show that Sharpe ratio bias increases with the number of basis asset portfolios.

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Authors and Affiliations

  1. Booth School of Business, University of Chicago, 5807 South Woodlawn Avenue, Chicago, IL, 60637, USA

    Ray Ball

  2. University of Texas at Dallas, 800 West Campbell Rd, Richardson, TX, 75080, USA

    Gil Sadka

  3. Indiana University, 1309 E 10th Street, Bloomington, IN, 47401, USA

    Ayung Tseng

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We thank Valeri Nikolaev, Stephen Penman and two referees for their helpful comments. Ball gratefully acknowledges research support from the University of Chicago, Booth School of Business. All errors remain our own.

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Ball, R., Sadka, G. & Tseng, A. Using accounting earnings and aggregate economic indicators to estimate firm-level systematic risk. Rev Account Stud 27, 607–646 (2022). https://doi.org/10.1007/s11142-021-09594-9

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