Connecting book rate of return to risk and return: the information conveyed by conservative accounting

See Voulteenaho (2002), Fama and French (2006), Novy-Marx (2013), Ball et al. (2015), for example. Chen and Zhang (2010), Hou et al. (2015), and Fama and French (2015) build asset pricing models that include a book rate-of-return factor.

As ROE is highly persistent, current ROE₀ is usually applied as an estimate of ROE₁ in the research.

See also Greenball (1969), Livingstone and Salamon (1970), Fisher and McGowan (1983), Brief and Lawson (1992), Johansson and Östman (1995), and Beaver and Ryan (2000). Penman (2013, Chapter 17) and Penman and Reggiani (2018) demonstrate with examples, and the Rajan et al. (2007) four quadrants depict the effects well.

We recognize that “risk” is sometimes distinguished from “uncertainty,” the term mainly used in the accounting literature. We make no distinction, treating them as equivalent in this paper. Risk, as we use the term, is simply the possibility of variation of outcomes from expectation.

In justifying the immediate expensing of R&D under FASB Statement No. 2, the FASB focused on the “uncertainty of future benefits.” In IAS 38, the IASB applied the criterion of “probable future economic benefits” to distinguish between “research” (which is expensed) and “development” (which is capitalized and amortized). Both the deferral of revenue recognition and the expensing of investment result in lower earnings and lower book rates of return, ceteris paribus. Note that the aforementioned papers on conservative accounting typically deal with the second aspect, the expense side of earnings measurement. But revenue recognition also determines earnings, and both the earlier revenue recognition standards and the new ones (ASC 606 and IFRS 15) require the accountant wait until specific realization criteria are satisfied.

Research reports that R&D investment is associated with higher stock returns, in Lev and Sougiannis (1996), Lev et al. (2005), and Eberhart et al. (2004), for example. There are differing interpretations of the result, with Chambers et al. (2002) attributing the returns to risk and Chan et al. (2001) attributing them to investor misunderstanding of the accounting. Donelson and Resutek (2012) see the returns as part of the value-growth spread phenomenon.

Wu et al. (2009) introduce accounting effects on ROE to explain expected returns. Their work differs substantially from this paper. First, they focus on explaining the accrual anomaly rather than the effect of conservative accounting. Second, “investment” is defined as working capital accruals, excluding much of the investment on which we focus. Third, they connect ROE (and the accruals involved) to expected returns under q-theory. That posits a positive (unconditional) relation between ROE and returns that we challenge.

As equation (1) is an identity, then, for a given P₀ and thus a given expectation of life-long earnings, a lower Earnings₁ means higher future earnings, that is, expected earnings growth.

Johansson and Östman (1995, pp. 118–120) lay out the effects of conservative accounting on earnings and book values and demonstrate the special case of cancelling errors.

Case 3.2, with cancelling errors and E[Δ(P₁ – B₁)] = 0, is that where both (a) and (b) are operating. That is, it conveys the “steady state,” where realization of earnings from past investments are exactly offset by further delayed earnings recognition and expensing of new investments. For example, new R&D expenditure depresses earnings but past R&D is now producing offsetting earnings, as in a steady-state mature pharmaceutical company.

The \( {\mathrm{NFO}}_{\mathrm{t}}={\mathrm{P}}_{\mathrm{t}}^{\mathrm{NFO}} \) condition is not precisely met under GAAP but is approximately so, except when there is a significant change in interest rates or credit risk.

This C-score captures the effect on unconditional conservatism on the balance sheet, in contrast to that of Khan and Watts (2009), which is designed to capture unconditional conservatism. However, unconditional conservatism is also captured as it writes down NOA. McNichols et al. (2014) calculate a measure to correct for conservative accounting, but that measure aims to adjust book value to replacement cost as prescribed by Tobin’s q.

The empirical results in the paper are similar when \( \Delta {\mathrm{C}}_{\mathrm{it}}=\frac{{\mathrm{ER}}_{\mathrm{it}}}{{\mathrm{NOA}}_{\mathrm{it}}+{\mathrm{ER}}_{\mathrm{it}}} \), that is, with ER compared to the amount of NOA that would have been on the balance sheet without conservative accounting. Note that the deferred revenue component refers only to deferred revenue recorded on the balance sheet (for which the customer but not the firm has performed), not to revenue anticipated in prices more generally but not yet recognized in the accounts.

Results with quarterly ROE and quarterly returns indicate some positive relationship between ROE and (short-term) returns.

We thank a reviewer for the suggestion.

Further analysis shows that the ranking on ROE within E/P portfolios is not just a further ranking on E/P. Also, high-low differences in returns are more negative with 10 ROE portfolios within each E/P portfolio.

The high-low mean returns for the ΔC ranking were (in percent) 4.51, 4.23, 4.43, 6.23, and 6.03 for the positive E/P portfolios 1–5, respectively, and 8.16% for the negative E/P portfolio. All were significant at the 1 % level.

Regressions of returns on both ROE and ΔC within each E/P portfolio (not reported) find that there is still some explanatory power in ROE after controlling for ΔC. However, our ΔC measure may not capture all the effects of conservative accounting on ROE. Indeed, many contend that a good deal of selling, general and administrative expense (SG&A) is expensed investment―on employee training, software, start-up costs, customer development, distribution, and supply chain development, for example―and this we have not captured.

There is already some evidence in the literature that conservative accounting is associated with higher variance in outcomes. Kothari et al. (2002) and Amir et al. (2007) find that the variance of earnings from R&D investment is higher than that from other capital expenditure. In what has become known as the Bowman paradox, the strategy literature has found a negative relationship between book rate of return and the variance of book rate of return, although the finding has been called into question. See Bowman (1980) and Brick et al. (2015).

Because added investment in the first year ahead adds to earnings growth two years ahead, we also calculated the residual earnings growth rate two years ahead to subtract for the added investment. Residual earnings was calculated as Earnings_t + 2 – (r_f × Book Value_t + 1), where r_f is the yield on the U.S. 10-year Treasury note for the year. Results were similar.

Earnings growth two-years ahead is not sufficient for realized “long-run” earnings growth (which is unobservable). Results are similar for growth three years ahead, but survivorship bias significantly limits the inferences from longer-term ex post growth. We investigated one-year-ahead earnings growth: regressions of one-year-ahead earnings growth on E/P and ROE returned a mean coefficient of −0.18 on ROE, significant at the 1% level.

These results are supported by a regression of the absolute value of growth rates on ROE: the estimated coefficient on ROE was −0.40, significant at the 1% level. Results were similar for one-year-ahead growth rates and three-year-ahead growth rates. When the analysis here was repeated for the portfolios in Panel C of Table 5 (where ΔC and ROE are interacted), the association with risky outcomes was similar.

For the negative E/P portfolio, expected growth rates in Panel A of Table 6 and the dispersion of growth rate outcomes in Panels B and C align with the returns in Panel A of Table 5 but not in the direction implied by conservative accounting operating on the ROE. This reinforces the earlier interpretation that temporary realized losses swamp any effect of conservative on earnings for these firms.

Results are similar when market earnings are calculated as the average earnings yield for all stocks in the relevant year.

Results were similar when up-markets and down-markets were identified as years in which the stock market return in excess of the risk-free rate was positive or negative.

The analysis in this section involves only firms that survived up to the period investigated. There are differences in the frequency of bankruptcy between high and low ROE portfolios. For positive E/P portfolios, there is a significantly higher frequency of bankruptcy in low ROE portfolios (relative to high ROE) within one year for two of the five E/P portfolios. For bankruptcy within five years, the differences are significantly different for three of the five E/P portfolios. There is a significant difference in O-scores (which indicate the probability of bankruptcy) between low and high ROE portfolios for positive E/P portfolios 1–3. The direction of these differences indicates that conservative accounting and ROE indicate the risk of bankruptcy.

For example, see Fama and French (2006), Novy-Marx (2013), and Ball et al. (2015). Some of these papers use alternative measures of profitability to ROE. Lyle and Wang (2015) and Chattopadyhay et al. (2015) also report a positive relationship between log ROE and returns with log B/P in regressions.

The regressions in Table 8 do not incorporate modified book return metrics that have been in investigated by Novy-Marx (2013), Ball et al. (2015), and Ball et al. (2016), for example. While the return regressions in these papers also include log B/P, it remains an intriguing question whether these metrics differ in their association with returns, because they exclude some effects of conservative accounting (they exclude R&D and other expensed investments though maintain deferred revenue recognition). It is quite possible that firms with high gross margins in Novy-Marx (2013) invest in more advertising, R&D, etc., to gain more future sales and that this is not captured in the measure—an omitted variable that is required under clean-surplus accounting. Issues of denominators (also affected by conservative accounting) and value-weighted versus equally weighted returns also come into play. That said, the tests to follow in Table 9 use the “operating profitability” factor of Fama and French (2015).

We also estimated intercepts (alphas) for each of the ROE portfolios in Panel A of Table 5 with positive E/P and for the five high-low “hedge” portfolios in the bottom row of the Panel A. The alphas for the five hedge portfolios, 1 to 5, were − 0.341, −0.412, −0.457, −0.083, and − 0.443, respectively. With the exception of portfolio 4, these intercepts were significantly different from zero.