This paper investigates differences in value relevance of predictive stock return models depending on which firm size proxy (or proxies) is used, these being market value (MV), total book assets (TBA) and market value of total book assets (MVTA). Over the 27 year period of 1989–2015, MV provides higher value relevance in predicting future returns, while TBA provides higher value relevance when limited to large firms. Moreover, results reveal incremental explanatory power of approximately 27% when TBA are added to a one-year-ahead returns model already containing MV. The increase is 60% when examining only the last 10 years of the sample period. The findings of this study will help future accounting and finance research that uses predictive return models and potentially allow investors to make better resource allocation decisions leading to higher risk adjusted returns. In addition, the findings related to TBA will add to the debate on whether standard setters should place more emphasis on the valuation of assets and liabilities relative to earnings.
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Bujaki and Richardson (1997) present firm size proxies used in five major accounting journals. For expected returns, they report all articles to have used MV. From examination of more recent articles in major accounting journals, I find that this is largely still the case. In addition, recent empirical articles in the Journal of Finance almost always use MV as the size proxy.
Although firm size proxies are commonly used as control variables, they also represent general characteristics of the firm. TBA ae likely going to be negatively related to expected returns due to their association with lower bankruptcy risk and better earnings quality, and these two firm characteristics have been shown to be negatively related to expected returns (e.g., Griffin and Lemmon 2002; Lambert et al. 2007; Chava and Purnanandam 2010). MVTA have been used as the numerator in Tobin’s Q as a firm valuation proxy (e.g., Moeller et al. 2004; Thomsen et al. 2006).
The control variables for the main predictive returns model used in this paper are dividend yield, CAPM beta and the book-to-market ratio. By adding individually or jointly the natural log of debt-to-total assets, return on assets or sales, earnings yield, current returns, accruals, and asset growth, the incremental value relevance and statistical significance of TBA is robust in all cases. Also, TBA provide the highest incremental value relevance to a model that already contains MV compared to these additional variables.
Financial reporting should provide information about an entity’s resources (assets) and the claims to those resources. Information about the effects of transactions and other events are indicated as “also” essential (Preliminary views in Financial Accounting Series NO. 1260–001, 2006). However, recent papers by Watts and Zuo (2016) and Dichev (2017) still purport the income statement as being primary.
Banz (1981) uses a generalized asset pricing model, which includes a variable for the market value of a firm less the average value of NYSE stocks, all divided by the average value of NYSE stocks, to determine a relationship between market value and returns of common stocks. Even after controlling for the market beta, size was negatively related to returns. Banz notes that the size effect is not linear and is more concentrated in small firms. The findings of the current study reveal that this is still the case.
He obtains a coefficient of −0.099 on TBA with a p value of 0.067 when TBA is used as the sole size proxy in a univariate predictive returns model. However, in the same working paper, regressing returns on the residuals of MV that are orthogonal to TBA provided a stronger relationship than just regressing returns on MV, thus indicating that TBA do not provide any information on future returns. The sample firms used in the Berk (1996) working paper are restricted to firms on the NYSE. The current paper uses firms on the NYSE, AMEX, and NASDAQ stock exchanges.
Although, in 2001, FASB required goodwill to be checked for impairments annually to increase the accuracy of the balance sheet (Cheng et al. 2017).
Two exceptions are Berk (1996) and Badertscher et al. (2011). As presented in sub-section 2 (ii) of the literature review, Berk (1996) gets inconclusive evidence on the statistical significance of TBA. Badertscher et al. (2011) use TBA in a model that examines cumulative market adjusted returns’ relation to accounting restatements 60 days after the announcement, but obtain statistically insignificant results for size proxy TBA. However, neither papers assess the value relevance of using TBA in a one-year-ahead predictive returns model.
The arguments for TBA used in hypotheses 1 and 2 are the same for MVTA.
Value relevance has also been determined by the value and statistical significance of the coefficient on an independent variable (e.g., Easton et al. 1992; Jenkins et al. 2009; Jones and Smith 2011). This determinant of value relevance is positively related to the adjusted R2. Nevertheless, in this study I only use the adjusted R2 as the determinant of value relevance because of its superiority when examining more than one variable and because it is not influenced by the scale of the variables.
The predicted direction of the BTM ratio with future stock returns is positive. Lakonishok et al. (1994) provide a behavioural explanation for the positive relationship. Investors are overly pessimistic about low-growth stocks, proxied by the BTM ratio, but as the growth rates mean revert in the future, investors are surprised by the positive performance, resulting in higher returns. A risk based explanation, provided by Fama and French (1992), is that high BTM ratio stocks have a higher probability of bankruptcy relative to high-growth stocks. Nevertheless, they do not rule out the above behavioural explanation.
Fama and MacBeth (1973) regressions are used to allow equal weights for all fiscal years and the means of all variables to change yearly, which helps to reduce any survivorship bias (Fama and French 2002, p. 15). However, to be consistent with prior research evaluating value relevance (e.g., Jenkins et al. 2009; Balachandran and Mohanram 2011), I also perform the same relative and incremental value relevance testing using pooled cross-sectional regressions with clustered standard errors by firm and year to adjust for both cross-sectional and serial correlation. The results are very similar to using annual Fama-Macbeth regressions.
“Berk (1995) analytically shows that the relationship of future returns with MV is due to an endogenous relationship rather than some firm-level factors. Since TBA are highly correlated with MV, the reader is cautioned of a potential endogenous relationship of future returns with TBA. In section 6, robustness testing is performed by including a battery of additional variables known to be related to stock returns. The findings obtained using these extra variables are qualitatively similar to the main findings set out in Table 2.
For computing Vuong’s Z-statistic, the predicted values for each model are obtained using the MLE procedure MIXED in SAS. The SAS code used for calculating the Vuong statistics was obtained from the SAS Institute and can be found at http://support.sas.com/kb/42/addl/fusion_42514_6_vuong.sas.txt.
To test the statistical significance of this difference or incremental value relevance, I do not use the Vuong (1989) test because it is not recommended for comparing nested models and should not be used for nested models that are correctly specified (Wooldridge 2010, p. 506). Equation (1) with only LnMV is a nested model of Equation (1) with LnTBA added to it. Therefore, I test the statistical significance of the increase in explanatory power by using a simple F statistic that compares the two adjusted R2s, as presented in Gujarati (2003 p. 263). The F statistic is [(R2new – R2old)/df1] / [(1- R2new)/df2], where “new” is the model with the additional variable and df1 is the number of new regressors and df2 is the sample size less the number of parameters in the new model.
Near multicollinearity does not violate the OLS BLUE properties, in which case the regression estimators are unbiased but with large standard errors (Pearce and Reiter 1985; Gujarati 2003). However, if one of the size variables is dropped, then a more serious problem of misspecification may lead to biased estimators.
LnDTAT is the natural logarithm of total debt to tangible assets, ROA is earnings before interest and taxes (EBIT) divided by average TBA, ROS is EBIT divided by TBA, Eyld is earnings per share divided by prior year price, and RETlag is one year lagged returns. LnDTAT ratio is included because I suspect that the book-to-market ratio, in Equation (1), is not fully controlling for leverage since that ratio can vary even for a firm with no debt. The logarithm of ROA, ROS, and Eyld is not taken because they are often negative.
Badertscher B, Hribar SP, Jenkins NT (2011) Informed trading and the market reaction to accounting restatements. Account Rev 86(5):1519–1547
Balachandran S, Mohanram P (2011) Is the decline in the value relevance of accounting driven by increased conservatism? Rev Acc Stud 16(2):272–301
Ball R, Brown P (1968) An empirical evaluation of accounting income numbers. J Account Res 6(2):159–178
Ball R, Shivakumar L (2005) Earnings quality in U.K. private firms: comparative loss recognition timeliness. J Account Econ 39(1):83–128
Banz RW (1981) The relation between return and market value of common stocks. J Financ Econ 9:3–18
Bell TB, Landsman WR, Shackelford DA (2001) Auditors' perceived business risk and audit fees: analysis and evidence. J Account Res 39(1):35–43
Berk J (1995) A critique of size related anomalies. Rev Financ Stud 8(2):275–286
Berk J (1996) An empirical re-examination of the relation between firm size and return. University of Washington, Working Paper
Berk J (1997) Does size really matter. Financ Anal J 53(5):12–18
Bernard V (1995) The Feltham-Ohlson framework implications for empiricists. Contemp Account Res 11(2):733–747
Biddle G, Seow S, Siegel A (1995) Relative versus incremental information content. Contemp Account Res 12(1):1–23
Biddle G, Bowen R, Wallace JS (1997) Does EVA beat earnings? Evidence on associations with stock returns and firm values. J Account Econ 24:301–336
Brown LD, Sivakumar K (2003) Comparing the value relevance of two operating income measures. Rev Acc Stud 8:561–572
Bujaki ML, Richardson AJ (1997) A citation trail review of the uses of firm size in accounting research. J Account Lit 16:1–27
Callen J, Khan M, Lu H (2013) Accounting quality, stock Price delay, and future stock returns. Contemp Account Res 30(1):269–295
Campbell JY, Thompson SB (2008) Predicting excess stock returns out of sample: can anything beat the historical average? Rev Financ Stud 21(4):1509–1531
Chava S, Purnanandam A (2010) Is default risk negatively related to stock returns? Rev Financ Stud 23(6):2523–2559
Chen Y, Chang K (2010) Analyzing the nonlinear effects of firm size, profitability, and employee productivity on patent citations of the US pharmaceutical companies by using artificial neural network. Scientometr 82:75–82
Cheng S (2004) R&D expenditures and CEO compensation. Account Rev 76(2):305–328
Cheng Y, Peterson D, Sherrill K (2017) Admitting mistakes pays: the long term impact of goodwill impairment write-offs on stock prices. J Econ Financ 41:311–329
Cochrane J (1999) New facts in finance. Econ Perspect 23:36–58
Collins D, Gong G, Hribar P (2003) Investor sophistication and the mispricing of accruals. Rev Acc Stud 8(2–3):251–276
Cooper MJ, Gulen H, Shchill MJ (2008) Asset growth and the cross-section of stock returns. J Financ 63(4):1609–1651
Dechow P (1994) Accounting earnings and cash flows as measures of firm performance: The role of accounting accruals. J Account Econ 18:3–42
Defond M, Raghunandan K, Subramanyam K (2002) Do non-audit service fees impair auditor independence? Evidence from going concern opinions. J Account Res 40(4):1247–1274
Demerjian P (2011) Accounting standards and debt covenants: has the “balance sheet approach” led to a decline in the use of balance sheet covenants? J Account Econ 52:178–202
Dichev I (2017) On the conceptual foundations of financial reporting. Account Bus Res 47(6):617–632
Docherty P, Chan H, Easton S (2013) Australian evidence on the implementation of the size and value premia. Account Finance 53(2):367–391
Easton P, Harris T, Ohlson JA (1992) Aggregate accounting earnings can explain most of security returns. J Account Econ 15:119–132
Ecker F, Francis J, Kim I, Olsson P, Schipper K (2006) A returns-based representation of earnings quality. Account Rev 81(4):749–780
Erkens DH, Bonner SE (2013) The role of firm status in appointments of accounting financial experts to audit committees. Account Rev 8(1):107–136
Fama EF, French KR (1992) The cross-section of expected stock returns. J Financ 47(2):427–465
Fama EG, French KR (1995) Size and book-to-market factors in earnings and returns. J Financ 50(1):131–155
Fama EF, French KR (2002) Testing trade-off and pecking order predictions about dividends and debt. Rev Financ Stud 15(19):1–33
Fama E, MacBeth JD (1973) Risk, return and equilibrium: empirical tests. J Polit Econ 81(3):607–636
Financial Accounting Standards Board (2006) Preliminary views: conceptual framework for financial reporting. Financial Accounting Series 1260–001, Available at: http://www.fasb.org/jsp/FASB/Document_C/DocumentPage?cid=1218220340119&acceptedDisclaimer=true. Accessed 1 Aug 2019
Francis J, LaFond R, Olsson P, Schipper K (2005) The market pricing of accruals quality. J Account Econ 39:295–327
Givoly D, Hayn C, Katz S (2017) The changing relevance of accounting information to debt holders over time. Rev Acc Stud 20(1):64–108
Goh B, Krishnan J, Li D (2013) Auditor reporting under section 404: the association between the internal control and going concern audit opinions. Contemp Account Res 30(3):970–995
Gompers P, Ishi J, Metrick A (2003) Corporate governance and equity prices. The Q J Econ February 118:107–155
Griffin JM, Lemmon M (2002) Book-to-market equity, distress risk, and stock returns. J Financ 57(5):2317–2336
Gujarati DN (2003) Basic econometrics, 4th edn. McGraw-Hill/Irwin, New York, NY
IFRS Foundation (2010) The conceptual framework for financial reporting. A21-A52. Available at: https://www.ifrs.org/issued-standards/list-of-standards/conceptual-framework/. Accessed 1 Aug 2019
Ince U, Owers JE (2012) The interaction of corporate dividend policy and capital structure decisions under differential tax regimes. J Econ Financ 36:33–57
Jenkins DS, Kane GD, Velury U (2009) Earnings conservatism and value relevance across the business cycle. J Bus Financ Acc 36(9–10):1041–1058
Jones D, Smith K (2011) Comparing the value relevance, predictive value, and persistence of other comprehensive income and special items. Account Rev 86(6):2047–2073
Kang T, Lobo G, Wolfe M (2017) Accounting Conservatism and Firm Growth Financed by External Debt: The Role of Debt Maturity. J Account, Auditing and Financ 32(2):182-208
Knez PJ, Ready MJ (1997) On the robustness of size and book-to-market in cross-sectional regressions. J Financ 52:1355–1382
Lakonishok J, Shleifer A, Vishny RW (1994) Contrarian investment, extrapolation, and risk. J Financ 49(2):1541–1578
Lam FY, Wei KC (2011) Limits-to-arbitrage, investment frictions, and the asset growth anomaly. J Financ Econ 102:127–149
Lambert R, Leuz C, Verrecchia R (2007) Accounting information, disclosure, and the cost of capital. J Account Res 45(2):385–420
Lara JMG, Osma BG, Penalvac F (2014) Information consequences of accounting conservatism. Eur Account Rev 23(2):173–198
Moeller S, Schlingemannb FP, Stulz RM (2004) Firm size and the gains from acquisitions. J Financ Econ 73:201–228
O'Brien PC, Bhushan R (1990) Analyst Following and Institutional Ownership, J Account Res 28(supplement):55–76
Palmon D, Sudit E, Yezegel A (2008) The accruals anomaly and company size. Financ Anal J 64(5):47–60
Pearce DK, Reiter SA (1985) Regression strategies when multicollinearity is a problem: a methodological note. J Account Res 23(1):405–407
Penman S (2011) Accounting structure, specification, and inference in empirical accounting research. Working paper, Columbia University, referenced by permission. Available at: https://business.sydney.edu.au/__data/assets/pdf_file/0003/89562/Penman_MEAFA_2011.pdf. Accessed 1 Aug 2019
Perez-Quiros G, Timmerman A (2000) Firm size and cyclical variations in stock returns. J Financ 55(3):1229–1262
Powell J, Shi J, Smith T, Whaley R (2009) Common divisors, payout persistence, and return predictability. Int Rev Financ 9(4):335–357
Rapach D, Zhou G (2013) Econ forecast 2A:330. North Holland, Amsterdam
Sloan R (1996) Do stock prices fully reflect information in accruals and cash flows about future earnings? Account Rev 71(3):289–315
Thomsen S, Pedersen T, Kvist HK (2006) Blockholder ownership: effects on firm value in market and control based governance systems. J Corp Finan 12:246–269
van Dijk MA (2011) Is size dead? A review of the size effect in equity returns. J Bank Financ 35:3263–3274
Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econom 57:307–333
Watts RL, Zuo L (2016) Understanding practice and institutions: a historical perspective. Account Horiz 30(3):409–423
Wooldridge JM (2010) Econometric analysis of cross section and panel data, 2nd edn. The MIT Press, Cambridge, Massachusetts
I thank Douglas Hannah, Merridee Bujaki, Sarah Dyce, Eric Johnson, Raj Mashruwala (discussant), Bruce McConomy, Steven Murphy, Karin Petruska, Robert Resutek (discussant) and Ralph Winter for their valuable suggestions. The paper has also benefited from comments received at the 2015 Telfer (U. of Ottawa) annual conference on accounting and finance, the 2014 Canadian Academic Accountants Association annual conference, the 2013 AAA annual conference and the 2013 AAA Mid-Atlantic region conference. Any errors or omissions are my own.
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Wakil, G. Firm size proxies and the value relevance of predictive stock return models. J Econ Finan 44, 434–457 (2020). https://doi.org/10.1007/s12197-019-09491-7
- Firm size
- Value relevance
- Accounting assets