## Abstract

We hypothesize that earnings downside risk, capturing the expectation for future downward operating performance, contains distinct information about firm risk and varies with cost of capital in the cross section of firms. Consistent with the validity of the earnings downside risk measure, we find that, relative to low earnings downside risk firms, high earnings downside risk firms experience more negative operating performance over the subsequent period, are more sensitive to downward macroeconomic states, and are more strongly linked to earnings attributes and other risk-related measures from prior research. In line with our prediction, we also find that earnings downside risk explains variation in firms’ cost of capital, and that this link between earnings downside risk and cost of capital is incremental to several earnings attributes, accounting and risk factor betas, return downside risk, default risk, earnings volatility, and firm fundamentals. Overall, this study contributes to accounting research by demonstrating the key valuation and risk assessment roles of earnings downside risk derived from firms’ financial statements, also shedding new light on the link between accounting and the macroeconomy.

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## Notes

The asymmetry in the earnings distribution cannot be attributed to accounting conservatism. Conservatism may enhance the left skewness of earnings distribution but not that of cash flows distribution. The fact that cash flows are also asymmetrically distributed suggests that there are fundamental factors other than conservatism that affect the asymmetry in the earnings distribution.

The link between EDR and cost of capital also relates to the notion of information acquisition. When high expectations exist about a value-relevant signal, such as an earnings downward pattern, investors are likely to engage in information acquisition to better understand it. This results in high investor marginal cost under the common assumption of increasing marginal cost to information acquisition. Accordingly, that cost can vary in the cross section such that it is positively associated with EDR, and investors who obtain the costly information need to be compensated by higher expected returns. This is the essence of Grossman and Stiglitz (1980).

Examples of return downside risk studies are those by Chen et al. (2001) and Kim et al. (2011), who investigate conditional skewness in the distribution of stock returns (i.e., the negative coefficient of skewness) as well as stock price crash risk (i.e., the down-to-up volatility); Bali et al. (2009), who focus on extreme stock downside risks such as tail risk; and Jin and Myers (2006), Hutton et al. (2009), and Lang and Maffett (2011), who focus on stock price crashes.

The basic idea is that news about earnings, which are persistent, alters perceptions regarding long-term expected growth rates and economic uncertainty (i.e., consumption volatility) and that this channel is important for explaining long-term risk and equity premia.

Earnings information can lead returns because of, for example, the gradual information assimilation that stems from complexity, market segmentation, information costs, and investor attention constraints. For the theoretical front of this research, see, for example, Merton (1987), Hong and Stein (1999), Lee (2001), Hirshleifer and Teoh (2003). For the empirical front, see, for example, Cohen and Frazzini (2008), Menzly and Ozbas (2010). See also Miller (1977) and Mashruwala et al. (2012). Studies also show predictable returns for other reasons (e.g., Sloan 1996; Kang et al. 2010; Konchitchki 2011, 2013; DeFond et al. 2013; Konchitchki and Patatoukas 2014b) or suggest the macro role in the setting of equilibrium prices as the major function of accounting data (e.g., Beaver 2015).

We note that (a) Equation (2) requires 3 years of input variables, (b) the independent variables are lagged by 1 year, of which the standard deviation of earnings requires at least 3 years of data, (c) and Eq. (3) requires a minimum of 3 years of residuals from Eq. (2). For example, estimating

*EDR*for the fiscal year-end of 1975 requires residuals from the earnings expectation model from at least fiscal year 1973. The 3-year rolling-window requirement and 1-year lagged independent variables for estimating the residuals from Eq. (2) require regressor data as early as fiscal year 1970, and one of the inputs,*STD_ROA*of fiscal year 1970, requires*ROA*data from fiscal year 1968 (because we use*ROA*spanning three to 5 years to compute*STD_ROA*). Thus, a minimum of 8 fiscal years, from 1968 to 1975, are involved to obtain the*EDR*estimate for 1975. Similar to the restriction of Francis et al. (2005) that only firms with at least 7 years’ accrual quality data could enter their sample, our estimation procedure requires at least 8 years of accounting data to obtain annual*EDR*estimates. Nevertheless, when we alternatively estimate our earnings expectation model using regressions by industry and for each fiscal year, which reduces the required minimum number of years to six, our main inferences are unchanged. Furthermore, we repeat our main tests after calculating*EDR*using 10 (rather than 3–5) earnings residuals following Eq. (3) and find similar inferences to those we report in the text.Because we allow a 6-month lag after the fiscal year-end for assimilation of accounting information when we examine subsequent stock returns, according to Compustat’s fiscal year definition, the earliest month with a valid match between EDR and returns is January 1976, with correspondence to the fiscal year of 1975 with a June fiscal year-end.

The effects of

*EDR_ibes1*,*EDR_ibes2*, and*EDR_ibes3*on the cost of capital appear stronger than those of*EDR_ind*and*EDR_neg*. However, analysts’ forecast data are only available for about half of our sample, and hence we do not adopt these measures in our main tests.We also consider earnings skewness as an additional variable when relevant in our correlation and regression analyses (specifically in Table 4, Panels B and C, and in Tables 5, 6). We measure earnings skewness using the skewness coefficient of earnings for every firm-year in our sample, calculated over 10-year rolling windows. We find significantly positive contemporaneous correlation between EDR and earnings skewness and unchanged inferences about EDR when earnings skewness is added in the regressions. Because earnings skewness is not commonly used as a risk measure in the literature, while we focus on the incremental information in EDR relative to common risk measures from prior research, we do not tabulate these findings.

This lower partial moment is a special case of Stone’s (1973) three-parameter risk measure \(L\left( {\tau ,\alpha ,\eta } \right) = \int_{ - \infty }^{\eta } {\left| {\tau - \gamma } \right|^{\alpha } f(\gamma )d\gamma }\) (where α ≥ 0), by setting the range parameter

*η*equal to the reference level*τ*(also see Fishburn 1977).

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## Acknowledgments

We appreciate helpful comments and suggestions from Yakov Amihud, Mary Barth, Sunil Dutta, Peter Easton, Jennifer Huang, Scott Joslin, Henry Laurion, Alastair Lawrence, Laura Liu, Gustavo Manso, Alexander Nezlobin, Topseht Nonam, Jim Ohlson, Panos Patatoukas, Andy Rose, Richard Sloan, Steve Tadelis, Vicki Tang, Rodrigo Verdi, Annika Wang, Joanna Wu, Hong Xie, Jenny Zha, Weining Zhang, Yong Zhang, three anonymous referees, and seminar participants at University of California at Berkeley’s Haas School of Business, Cheung Kong Graduate School of Business, Dalhousie University, Memorial University of Newfoundland, York University, and Canadian Academic Accounting Association Student/Junior Faculty Workshop. Yaniv Konchitchki acknowledges financial support from Berkeley’s Hellman Fellows Research Excellence Fund. Yan Luo acknowledges financial support from the National Natural Science Foundation of China (NSFC Project Number 71402032).

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## Appendices

### Appendix 1: Root lower partial moments

A long line of research spanning decades has studied cases where there is a possibility for realizing an outcome that is worse than some specified level. For example, Markowitz (1952, 1959) suggests semi-variance as a risk measure. Another example is Tobin (1958) who investigates conditions under which variance is a valid risk measure. Other authors (e.g., Fama 1965a; Samuelson 1967) object to variance in the area of portfolio selection if security prices are distributed according to a non-normal stable Paretian distribution for which variance is undefined (also see, e.g., Stone 1973; Laughhunn et al. 1980).

Relatedly, according to Stone’s (1973) generalized risk measure, the lower partial moment for a variable with value *γ* can be expressed as \(\int_{ - \infty }^{\tau } {\left| {\tau - \gamma } \right|^{\alpha } } f\left( \gamma \right)d\gamma\), where *α* ≥ 0, *τ* is the reference (target) level, and *f*(*γ*) is the probability density function for *γ*. The moment indicator *α* reflects the relative importance of the magnitude of the deviation from below the reference level.^{Footnote 13} For *α* = 2, this moment corresponds to the lower partial second moment, with its discrete case equals to \(\left( {\frac{1}{N}} \right)\sum\nolimits_{\gamma < \tau } {(\tau - \gamma )^{2} }\) where *N* is the number of sample observations.

The lower partial moment allows flexible target levels and is applicable to any arbitrary distribution, which differs from semi-variance where the reference level is fixed at the sample mean (e.g., Markowitz 1959). Prior research across different areas has employed the lower partial moment framework. For example, in an experimental study on individual investors’ risk perception in a financial decision-making context under two different modes of information presentation (or framing), Unser (2000) finds that symmetrical risk measures like variance can be dismissed in favor of shortfall measures like lower partial moments.

Several other empirical and simulation studies also show the superiority of portfolio selection criteria based on mean lower partial moments relative to those based on the traditional approach based on mean–variance, under the assumption of shortfall-risk oriented investors (e.g., Nawrocki and Staples 1989; see also Unser 2000). Even for symmetric distributions, the lower partial moment can differ from semi-variance and variance if the reference level is not equal to the sample mean. Also see Biddle et al. (2015).

In addition, Stone (1973) introduces root lower partial moment that is homogeneous of degree one and thus more suitable for economic analysis. Unlike traditional moment estimations, the root lower partial moment calculates moments by including observations only in the downside fraction below a reference level rather than over the entire distribution, with the following expression for the discrete case with *α* = 2: \({\text{Lower}}_{2} \left( \tau \right) = \left[ {\left( {\frac{1}{N}} \right)\sum\nolimits_{\gamma < \tau } {(\tau - \gamma )^{2} } } \right]^{1/2}\), where the subscript 2 refers to the second-moment case in the general lower partial moment formula. Thus, this expression represents the square root of the lower partial second moment, that is, the square root of \(\left( {\frac{1}{N}} \right)\sum\nolimits_{\gamma < \tau } {(\tau - \gamma )^{2} }\), indicating volatility below the reference level *τ*. Similarly, the root upper partial moment, which measures the moment when a variable value deviates above the reference level is (for the square root in the discrete case): \({\text{Upper}}_{2} \left( \tau \right) = \left[ {\left( {\frac{1}{N}} \right)\sum\nolimits_{\gamma \ge \tau } {(\gamma - \tau )^{2} } } \right]^{1/2}\). To construct our EDR measure, we use the relative root lower partial moment metric (LowerUpper), which deflates the root lower partial moment by its upper counterpart, as follows:

The rationale of the relative root lower partial moment metric follows from the fact that, although risk-averse agents dislike downside states and favor upside states, higher root upper partial moment usually accompanies higher root lower partial moment. Using Upper to scale Lower controls for firm-level differences in the upside states and thus refines the comparison of downside risk across firms. Also, the relative root lower partial moment incorporates cases where investors have asymmetric reactions to downside versus upside states (for more information also see, e.g., Markowitz 1952, 1959; Tobin 1958; Fama 1965a; Samuelson 1967; Stone 1973; Fishburn 1977; Laughhunn et al. 1980; Nawrocki and Staples 1989; Unser 2000).

### Appendix 2: Results from estimating earnings expectation model

Table 7 presents results from estimating unexpected (i.e., residual) earnings from the earnings expectation model in Eq. (2), using the sample data described in Sect. 4. The estimated residuals are used in the EDR construction according to Eq. (3) and following Sect. 2. Panel A reports summary statistics for the input (dependent and independent) variables in the model. Panel B reports average estimated coefficients as well as average adjusted R^{2} for the regressions estimated by industry and using 3-year rolling windows.

The average estimated coefficients on lagged *ROA* and *SALE* are significantly positive, consistent with Dechow et al. (1998). *SIZE* is also significantly positively associated with earnings, consistent with prior research and the notion that big firms have competitive advantages (e.g., Hall and Weiss 1967; Fiegenbaum and Karnani 1991; Feng et al. 2015). In addition, the average adjusted R^{2} is 41.8 %, demonstrating that there is a significant portion of earnings that is unexplained, which indicates a source of risk in firms’ fundamentals. Our EDR measure is designed to capture this risk in the downward fraction of firms’ unexpected earnings.

Panel C shows that unexpected earnings have a standard deviation of 0.25 and a mean of zero. The zero mean is consistent with the regression validity, in that the residual mean is expected to be zero under the OLS estimation. The lower quartile of unexpected earnings is about 0.08 standard deviation below its mean, whereas those of expected earnings (in Panel C) and total earnings (in Panel A) are about 0.06 and 0.03 standard deviation below their means, respectively. These findings indicate that the downside volatility of residual earnings is relatively large.

### Appendix 3: Variable definitions

### 3.1 Earnings downside risk measure

*EDR*
_{
it
}: Proxy for earnings downside risk. We calculate it for firm *i* at the fiscal year-end *t* as the natural logarithm of the ratio of one plus the root lower partial moment of earnings (Compustat: IB) over total assets (Compustat: AT), which is denoted as Lower, to one plus the root upper partial moment of earnings over total assets, which is denoted as Upper, according to Eqs. (2) and (3) in the text.

### 3.2 Operating performance measures

*DLOSS1*
_{
it
}: An indicator variable that is equal to one if annual income before extraordinary items (Compustat: IB) is negative for firm *i* in fiscal year *t* and zero otherwise.

*DLOSS2*
_{
it
}: An indicator variable that is equal to one if annual net income (Compustat: NI) is negative for firm *i* in fiscal year *t* and zero otherwise.

*IBM*
_{
it
}: The ratio of annual income before extraordinary items (Compustat: IB) to total revenues (Compustat: SALE) for firm *i* in fiscal year *t.*

*NIM*
_{
it
}: The ratio of annual net income (Compustat: NI) to total revenues (Compustat: SALE) for firm *i* in fiscal year *t.*

*OPM*
_{
it
}: The ratio of annual operating income after depreciation (Compustat: OIADP) to total revenues (Compustat: SALE) for firm *i* in fiscal year *t.*

*GPM*
_{
it
}: Annual gross profit margin ratio, calculated as the difference between total revenues (Compustat: SALE) and cost of goods sold (Compustat: COGS) divided by total revenues (Compustat: SALE) for firm *i* in fiscal year *t.*

### 3.3 Sensitivities to downward macroeconomic states

*beta_negshock_g*
_{
t+1} − *g*
_{
t
}: The sensitivity of a firm’s earnings scaled by total assets (Compustat: IB/AT or NI/AT) to future negative GDP changes defined as year-over-year drops in the growth of real GDP by 1 % or more, estimated by regressing scaled earnings on subsequent-year real GDP growth during periods of negative macro changes using a 5-year rolling window.

*beta_negshock_g*
_{
t+1} − *E*
^{SPF}_{
t
}
(*g*
_{
t+1}): The sensitivity of a firm’s earnings scaled by total assets (Compustat: IB/AT or NI/AT) to future unexpected negative GDP shocks defined as the realizations of GDP growth falling by 3 % below expectations using SPF consensus forecasts, estimated by regressing scaled earnings on subsequent-year real GDP growth forecast errors during periods of negative macro shocks using a 5-year rolling window.

*beta_recession*: The sensitivity of a firm’s earnings scaled by total assets (Compustat: IB/AT or NI/AT) to real GDP growth during recession periods as defined by the NBER at http://www.nber.org/cycles.html.

### 3.4 Measures for return downside risk, default risk, and earnings volatility

*DUVOL*
_{
it
}: Proxy for return downside risk for firm *i* in year *t* and calculated as the natural logarithm of the ratio of standard deviation of residual returns below the mean to standard deviation of residual returns above the mean. The residual return is the natural logarithm of one plus the residual estimated from an expanded market model using monthly stock returns over a 5-year rolling window (e.g., Kim et al. 2011).

*NCSKEW*
_{
it
}: Proxy for return downside risk for firm *i* in year *t* and calculated as negative one times the third moment of residual returns divided by the standard deviation of residual returns raised to the third power. The residual returns and estimation windows are the same as in the *DUVOL* estimation.

*EDF*
_{
it
}: Proxy for default risk for firm *i* in year *t* and estimated as the expected default frequency following the procedures in Vassalou and Xing (2004).

*VOL_ROA*
_{
it
}: Proxy for earnings volatility for firm *i* at fiscal year-end *t* and calculated as the standard deviation of the residuals estimated from our earnings expectation model using three to 5 years’ (as available) data.

### 3.5 Earnings attribute measures

*Acc_Q*
_{
it
}: Proxy for accrual quality for firm *i* at fiscal year-end *t* (following Dechow and Dichev 2002), calculated as the percentile ranking of standard deviation of residuals estimated from the accrual expectation model over a 10-year rolling window.

*Persist*
_{
it
}: Proxy for earnings persistence for firm *i* at fiscal year-end *t* and calculated as the percentile ranking of negative one times the slope coefficient from an AR(1) model for the ratio of earnings to total assets (Compustat: NI/AT) over a 10-year rolling window.

*Predict*
_{
it
}: Proxy for predictability for firm *i* at fiscal year-end *t* and calculated as the percentile ranking of the square root of the error variance estimated from an AR(1) model for the ratio of earnings to total assets (Compustat: NI/AT) over a 10-year rolling window.

*Relevance*
_{
it
}: Proxy for value relevance for firm *i* at fiscal year-end *t* and calculated as the percentile ranking of negative one times the R^{2} from the OLS regression of 12-month returns on the level and change in earnings scaled by market value of equity [Compustat: NI/(PRCC_F*CSHO)], estimated over a 10-year rolling window.

*Smooth*
_{
it
}: Proxy for earnings smoothing for firm *i* at fiscal year-end *t* and calculated as the percentile ranking of the ratio of standard deviation of net income divided by total assets (Compustat: NI/AT) to that of OCF divided by total assets. Standard deviations are calculated over a 10-year rolling window.

*Timely*
_{
it
}: Proxy for timeliness for firm *i* at fiscal year-end *t* and calculated as the percentile ranking of negative one times the R^{2} from the reverse earnings-returns model in Basu (1997), estimated over a 10-year rolling window.

*Conserv*
_{
it
}: Proxy for conservatism for firm *i* at fiscal year-end *t* and calculated as the percentile ranking of the ratio of the coefficient of negative returns to that of positive returns from the reverse earnings-returns coefficient model in Basu (1997), estimated over a 10-year rolling window.

### 3.6 Control variables for validity tests

*BM*
_{
it
}: Book-to-market ratio [Compustat: SEQ/(PRCC_F*CSHO)] for stock *i* measured at fiscal year-end *t*.

*MVE*
_{
it
}: Market value of equity (Compustat: PRCC_F*CSHO) for stock *i* at fiscal year-end *t*.

*CASH*
_{
it
}: The ratio of cash holdings and cash equivalents to total assets (Compustat: CHE/AT) for firm *i* at fiscal year-end *t*.

*ΔCASH*
_{
it
}: The ratio of changes in cash holdings and cash equivalents to total assets (Compustat: CHCHE/AT) for firm *i* at fiscal year-end *t*.

*Invest_CAPX*
_{
it
}: The ratio of capital expenditures to total assets (Compustat: CAPX/AT) for firm *i* at fiscal year-end *t*.

*Invest_RD*
_{
it
}: The ratio of R&D expenditures to total assets (Compustat: XRD/AT) for firm *i* at fiscal year-end *t*.

*LEVERAGE*
_{
it
}: The ratio of the sum of interest-bearing long-term and short-term debts to total assets (Compustat: (DLTT + DLC)/AT) of firm *i* at fiscal year-end *t*.

*OO*
_{
it
}: The ratio of property, plant, and equipment to total assets (Compustat: PPEGT/AT) for firm *i* at fiscal year-end *t*.

*ROA*
_{
it
}: The ratio of income before extraordinary items to total assets (Compustat: IB/AT) of firm *i* at fiscal year-end *t*.

*SIGMA*
_{
it
}: Standard deviation of daily stock returns for firm *i* in fiscal year *t*.

*SLACK*
_{
it
}: The mean of industry-adjusted ratio of inventory to total revenues (Compustat: INVT/SALE), industry-adjusted ratio of accounts receivable to total revenues (Compustat: RECT/SALE), and industry-adjusted ratio of selling, general, and administrative expenses to total revenues (Compustat: XSGA/SALE) for firm *i* at fiscal year-end *t*.

*SLACK_emp*
_{
it
}: Industry-adjusted ratio of the number of employees to total revenues (Compustat: EMP/SALE) for firm *i* at fiscal year-end *t*.

### 3.7 Cost of capital and control variables used in asset pricing tests

*RET*
_{
it+1} *−* *RF*
_{
t+1}: Proxy for the cost of equity capital of firm *i* in month *t* + 1 and measured as the firm’s raw return *RET*
_{
it+1} minus risk-free rate *RF*
_{
t+1} approximated by the US 1-month T-bill rate.

*MOM*
_{
it
}: Previous buy-and-hold return of stock *i* and calculated as the return over the 11-month period ending 1-month prior to month *t*, following Carhart (1997).

*MKTbeta*
_{
it
}: Sensitivity of stock *i*’s return to CRSP value-weighted market return that we estimate based on monthly data over the past 60 months ending in month *t*.

*SMBbeta*
_{
it
}: Sensitivity of stock *i*’s return to the size factor of Fama and French (1993) that we estimate based on monthly data over the past 60 months ending in month *t*.

*HMLbeta*
_{
it
}: Sensitivity of stock *i*’s return to the book-to-market factor of Fama and French (1993) that we estimate based on monthly data over the past 60 months ending in month *t*.

*UMDbeta*
_{
it
}: Sensitivity of stock *i*’s return to the momentum factor of Carhart (1997) that we estimate based on monthly data over the past 60 months ending in month *t*.

*TCA*
_{
it
}: Total accruals scaled by total assets (Compustat: TA) for firm *i* at fiscal year-end *t*. Total accruals are estimated as (Δ*CA*
_{
it
} − Δ*CL*
_{
it
} − Δ*Cash*
_{
it
} + Δ*STDEBT*
_{
it
} + *ΔTP*
_{
it
} − *DP*
_{
it
}), where Δ*CA*
_{
it
}, Δ*CL*
_{
it
}, Δ*Cash*
_{
it
}, Δ*STDEBT*
_{
it
}, and *ΔTP*
_{
it
} are 1-year changes in current assets (Compustat: ACT), current liabilities (Compustat: LCT), cash and short-term investments (Compustat: CHE), short-term debt (Compustat: DLC), and income tax payable (Compustat: TXP), respectively, for firm *i* in fiscal year *t*. *DP*
_{
it
} is depreciation expense (Compustat: DP) for firm *i* in fiscal year *t*.

*SUE*
_{
it
}: Proxy for earnings surprises, estimated as unexpected earnings [*ROA* of fiscal year *t* minus expected *ROA* from Eq. (2)] scaled by the standard deviation of the unexpected earnings.

*BETA_ROA*
_{
it
}: The sensitivity of earnings scaled by market value of equity [Compustat: IB/(PRCC_F*CSHO)] to the value-weighted aggregate earnings scaled by market value of equity, calculated over a 10-year rolling window, following prior research (e.g., Beaver et al. 1970).

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Konchitchki, Y., Luo, Y., Ma, M.L.Z. *et al.* Accounting-based downside risk, cost of capital, and the macroeconomy.
*Rev Account Stud* **21**, 1–36 (2016). https://doi.org/10.1007/s11142-015-9338-7

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DOI: https://doi.org/10.1007/s11142-015-9338-7