Firm size proxies and the value relevance of predictive stock return models

Abstract

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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Notes

  1. 1.

    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.

  2. 2.

    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).

  3. 3.

    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.

  4. 4.

    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.

  5. 5.

    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.

  6. 6.

    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.

  7. 7.

    Although, in 2001, FASB required goodwill to be checked for impairments annually to increase the accuracy of the balance sheet (Cheng et al. 2017).

  8. 8.

    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.

  9. 9.

    The arguments for TBA used in hypotheses 1 and 2 are the same for MVTA.

  10. 10.

    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.

  11. 11.

    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.

  12. 12.

    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.

  13. 13.

    “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.

  14. 14.

    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.

  15. 15.

    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.

  16. 16.

    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.

  17. 17.

    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.

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Acknowledgements

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

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Keywords

  • Firm size
  • Value relevance
  • Accounting assets

JEL classification

  • G12
  • G17
  • M410