The role of diversification in the pricing of accruals quality

Abstract

Prior studies suggest that accounting information risk, primarily idiosyncratic in nature, can be diversified away. I show that accounting information risk, proxied by accruals quality, is priced even if it is entirely idiosyncratic. Building on a model developed in the ambiguity literature, I predict that, (1) in an under-diversified market, idiosyncratic information risk is priced even if it is diversifiable, and (2) in a well-diversified market, idiosyncratic information risk is priced when information is subject to managers’ discretion and thus ambiguous. The empirical results corroborate the predictions from the model. An association is observed between (unambiguous if risky) innate accruals quality and cost of capital. This association can be largely mitigated through diversification. However, diversification has little impact on the association between (ambiguous) discretionary accruals quality and cost of capital.

Appendices

Appendix 1: Earnings quality models

This appendix describes two commonly used models to estimate accruals quality. The first model is a modified Dechow and Dichev (2002) model as follows:

$$\begin{aligned} TCA_{j,t}&=:\phi _{0,j}+ \phi _{1,j}CFO_{j,t-1}+ \phi _{2,j}CFO_{j,t}+\phi _{3,j}CFO_{j,t+1}+ \phi _{4,j}\Delta Rev_{j,t} \\&\quad +\,\phi _{5,j}PPE_{j,t}+v_{j,t}, \end{aligned}$$

(8)

where $TCA= (\Delta CA-\Delta Cash)-(\Delta CL-\Delta STDEBT)$, $TA= TCA-Dep$, $\Delta CA= {\text {change in current assets}}$, $\Delta Cash= {\text {change in cash/cash equivalents}}$, $\Delta CL= {\text {change in current liabilities}}$, $\Delta STDEBT= {\text {change in short-term debt}}$, $\Delta Dep={\text {depreciation and amortization expense}}$, $NIBE= \text {{net income before extraordinary items}}$, $CFO= NIBE-TA$, $\Delta Rev={\text {change in revenue}}$, $PPE= {\text {gross property, plant, and equipment}}$

All variables are scaled by average total assets. Equation (8) is estimated for each of Fama and French’s (1997) 48 industry groups with at least 20 firms in year t. Annual cross-sectional estimations yield firm- and year-specific residuals. $DD_{j,t}=\sigma (v_j)_t$ is the standard deviation of firm j’s residuals, $v_{j,t}$, calculated over years t − 4 through t. Larger standard deviations of residuals indicate poorer accruals quality.

The second model is a modified Jones (1991) model as follows:

$$\frac{TA_{j,t}}{Asset_{j,t-1}}= \kappa _1\frac{1}{Asset_{j,t-1}} +\kappa _2\frac{(\Delta Rev_{j,t}-\Delta AR_{j,t})}{Asset_{j,t-1}}+\kappa _3\frac{PPE_{j,t}}{Asset_{j,t-1}} +\epsilon _{j,t}.$$

(9)

where $\Delta AR_{j,t}$ is firm j’s change in accounts receivable between year t − 1 and year t. Equation 9 is estimated for each of Fama and French’s (1997) 48 industry groups with at least 20 firms in year t. The resulting measures of normal accruals and abnormal accruals are $NA_{j,t}=\hat{\kappa _1}\frac{1}{Asset_{j,t-1}}+ \hat{\kappa _2}\frac{(\Delta Rev_{j,t}-\Delta AR_{j,t})}{Asset_{j,t-1}}+ \hat{\kappa _3}\frac{PPE_{j,t}}{Asset_{j,t-1}}$, and $AA_{j,t}=TA_{j,t} - NA_{j,t}$. $|AA_{j,t}|$ is the absolute value of $AA_{j,t}$ with a greater number indicating poorer accruals quality.

Appendix 2: Implied cost of capital models

This appendix describes five accounting valuation models that are used to estimate the implied cost of capital in this paper.

Claus and Thomas (2001):

$$P_{i,t} =bps_{i,t}+\sum ^4_{\tau =1}{\frac{(ROE_{i,t+\tau }-r)\times bps_{i,t+\tau -1}}{(1+r)^{\tau }}}+\frac{(ROE_{i,t+5}-r)\times bps_{i,t+4}\times (1+\gamma )}{(r-\gamma )\times (1+r)^4}.$$

(10)

This is a special case of the residual income valuation model. It is assumed that residual income grows at rate $\gamma$ after T = 5. bps is book value per share, $ROE_{i,t+\tau }=eps_{i,t+\tau }/bps_{i,t+\tau -1}, eps_{i,t+\tau }=eps_{i,t+2}\times (1+ltg_i)^{\tau -2}$ for $\forall \tau >2, ltg_i$ is IBES consensus long term growth rate, $bps_{i,t+\tau }=bps_{i,t+\tau -1}+eps_{i,t+\tau }\times (1-K)$, K is the payout ratio, and $\gamma$ is the 10-year government bond rate less 3 %. r or $COC_{CT}$ is solved via an iterative procedure.

Gebhardt et al. (2001):

$$P_{i,t}=bps_{i,t}+\sum ^{11}_{\tau =1}{\frac{(ROE_{i,t+\tau }-r)\times bps_{i,t+\tau -1}}{(1+r)^{\tau }}}+\frac{(ROE_{i,t+12}-r)\times bps_{i,t+11}}{(r-\gamma )\times (1+r)^11}.$$

(11)

This is a special case of the residual income valuation model. It is assumed that residual income converges to industry-specific median return from T = 3 to T = 12. From T = 12 on, residual income is assumed to remain constant. $ROE_{i,t+\tau }=eps_{i,t+\tau }/bps_{i,t+\tau -1}$ for $\tau =1,2, ROE_{i,t+\tau }=ROE_{i,t+\tau }-fade \, \forall \tau >2, fade=(ROE_{i,t-2}-HIROE_t), HIROE$ is the industry median from ROE t − 4 to t, $bps_{i,t+\tau }=bps_{i,t+\tau -1}+eps_{i,t+\tau }\times (1-K)$, and K is the payout ratio. r or $COC_{GLS}$ is solved via an iterative procedure.

Gode and Mohanram (2003):

$$P_{i,t}=\frac{eps_{i,t+1}}{r}+\frac{eps_{i,t+2}+r\times dps_{i,t}-(1+r)\times eps_{i,t+1}}{r\times (r-\Delta agr)}.$$

(12)

This model uses 1-year-ahead forecasted earnings and dividends per share as well as forecasts of short- and long-term abnormal earnings growth. It is assumed that dividends (dps) are a constant fraction of forecasted earnings. Long-term growth rate $\Delta agr$ is set to be the 10-year government bond rate less 3 %. Solving r in this equation yields $COC_{GM}$.

Easton (2004):

$$P_{i,t}=\frac{eps_{i,t+2}-eps_{i,t+1}}{r^2}.$$

(13)

This model is a special case of the Gode and Mohanram (2003) model when T = 2 and $\gamma =0$. It embeds the assumption that growth in abnormal earnings persists in perpetuity after the initial period. Solving for r in this equation yields $COC_{PEG}$.