Measurements of the study's variables, sample and data collection, and statistics are explained next.

### Variables measurement

The variables for this study are classified into three categories: dependent, independent and control.

#### Measurement of the dependent variables

The dependent variable is the company's stock return volatility. The company's stock return volatility is measured by idiosyncratic volatility since it explains the central portion of stock return variation related to a firm's specific information [42, 50]. The idiosyncratic volatility is considered a good measure of its stock return volatility since it can be used in a better or inferior environment [61]. Cohen [10] and Wang et al. [58] showed that idiosyncratic volatility could be measured with the standard capital asset pricing model (CAPM) as in Eq. (1).

$$R_{i,t} = \alpha + \beta Rm_{t} + \mu_{i,t}$$

(1)

where *R*_{i,t} is the monthly return for firm *i* in the month *t*; *Rm*_{t} is the market return for the month *t.* The value weight market return is used as market return [35, 58]. The idiosyncratic volatility (IDIO) for the stock *i* is the variance of the error term (\(IDIO = \sigma^{2} (\mu_{i,t} )\)). Equation (1) is estimated each year and for each firm in the sample using the monthly market and return data. The analysis is conducted with the natural logarithm of IDIO.

#### Measuring the independent variables

The independent variables consist of five measures of earnings quality, including accrual quality, conservatism earnings persistence, predictability and smoothness.

##### Accrual quality

Accrual quality is estimated using the modified Dechow and Dichev [12] model widely used to measure accrual quality [13] (Shi and Zhou 2012). The model estimates the accrual quality in terms of the accrual and cash flow components of earnings, variation in sale and property plant and equipment, as in Eq. (2).

$$\Delta WC_{i,t} = \beta_{0} + \beta_{1} CFO_{i,t - 1} + \beta_{2} CFO_{i,t} + \beta_{3} CFO_{i,t + 1} + \beta_{4} \Delta SALES_{i,t} + \beta_{5} PPE_{i,t} + \mu_{t}$$

(2)

where Δ*WC*_{t} is the change in the working capital in the year *t*; *CFO*_{t} is the cash flow from the operation in the year *t*; Δ*SALES*_{t} is the change in sales in year *t*; *PPE*_{t} is the property, plant and equipment in year *t*; *μ* the prediction error; *i*, *t* the firm and year, respectively, and *β* is obtained from the regression model. All variables are scaled by total assets at the beginning of year *t*. AQ is computed as the standard deviation of the residual, calculated over 5 years (\(AQ_{i,t} = \sigma (\mu )_{i,t}\)).

##### Conservatism

Two types of conservatisms are distinguished, including conditional and unconditional conservatism. The Basu [5] model is used to measure conditional conservatism (CONSER1) due to its popularity [58]. The Basu [5] model is provided in Eq. (3).

$$EPS_{i,t} /P_{i,t - 1} = \alpha_{0} + \alpha_{1} D_{{}} + \beta_{0} R_{i,t} + \beta_{1} DR_{i,t} + \mu_{i,t}$$

(3)

where *EPS*_{i,t} is the earnings per share of firm *i* in the period *t; D* the indicator variable which is equal to 1 if *R*_{i,t} is negative (*R*_{i,t} < 0) and 0 otherwise; *R*_{i,t} is the stock return of firm *i* in the period *t*. From Eq. (3), CONSER1 is estimated with the formula: \((\beta_{0} + \beta_{1} )/\beta_{0}\).

The unconditional conservatism (CONSER 2) is measured using the book-to-market ratio, computed as a company's book value divided by its market value [49].

##### Persistence and predictability

Persistence and predictability are time-series measures of earnings. Earnings persistence (PERSIST) is measured as the slope coefficient obtained from the regression of current earnings on past earnings [13], as in Eq. (4).

$$Earnings_{i,t} = \beta_{0} + \beta_{1} Earnings_{i,t - 1} + \mu_{i,t}$$

(4)

Earnings predictability (PREDICT) is measured as the error variance from the earnings persistence model [23, 48] as in Eq. (5).

$$PREDICT_{i,t} = \sqrt {\sigma^{2} } (\mu_{i,t} )$$

(5)

##### Smoothness

Earnings smoothness (SMOOTH) is estimated as the standard deviation of operating income divided by the standard deviation of cash flow from operations [38, 48] as in Eq. (6).

$$SMOOTH_{i,t} = \sigma OI_{i,t} /\sigma CFO_{i,t}$$

(6)

The standard deviation is calculated for each firm over a rolling five-year window. A high value of SMOOTH, indicates less earnings smoothness, and a low value implies smoother earnings.

#### Measurement of the control variables

The control variables for the stock return volatility include the firm's size, leverage, growth (book to market), cash flow volatility, operating performance and stock return performance. These variables may lead to an increase or decrease in the stock return volatility [18, 31, 51, 58]. Therefore, these variables were included in the regression model in this study. The firm's size was measured as the natural logarithm of total assets. Leverage was calculated as the ratio of the total debts to total assets. Growth was computed as the market value of equity divided by the book value of equity. Cash flow volatility was calculated over a rolling five-year window as the cash flow variance from operation scaled by total assets. Before extraordinary items were scaled by total assets, earnings were used to measure the operating performance. Lastly, the annual buy and hold returns measured stock return performance.

### Sample and data

The sample included all non-financial companies listed in the JSE during 2009–2018. As in related studies [18], the financial companies were unnamed as they are a part of well-regulated industries. Furthermore, their accounting rules differ from that of other sectors, and the assessment of their earnings quality is likely to differ from that of different sectors. The final sample included companies that satisfied the following criteria: (1) availability of financial statements for the sample period with relevant information for measuring the variables, (2) the company had data for the past 5 consecutive years from the beginning of the sample period since the computation of accrual quality is based on the standard deviation of residual calculated over a 5-year rolling period [17]. After eliminating all companies with missing information, the final sample consisted of 800 observations obtained from 80 companies. The final sample represented 36% of the initial sample.

The IRESS Research Domain database extracted the companies' annual financial statements. The annual financial statements were analysed to retrieve relevant data to compute the study's variables. SPSS software version 27 was employed to analyse the MLR model's data. MLR is a more powerful estimating technique for analysing panel data than traditional estimating models such as ordinary least squares [22]. MLR addresses the shortcomings of conventional estimating methods and offers more benefits, such as greater flexibility in analysing panel data; it handles data well, using the maximum likelihood and restricted maximum likelihood estimations [25].

Before analysing the data, several tests were performed to ensure that the assumptions of linear regression were met. These tests included normality, multicollinearity, heteroscedasticity and autocorrelation. The results of these tests are provided in Appendix 1 and discussed below.

#### Normality test

The normality was checked using the histogram of standardised residual of the dependent variables and the P–P plot of standardised residual against the predicted values as advised by Field [22]. As illustrated in Fig. 1a of “Normality test” section in Appendix 1, the histogram has a bell shape and is symmetrically distributed around the mean. The points in the P–P plot in Fig. 1b of “Normality test” section in Appendix 1 are close to the diagonal line. Therefore, Fig. 1a and Fig. 1b of “Normality test” section in Appendix 1 show that data are normally distributed for the regression with the dependent variable idiosyncratic volatility.

#### Multicollinearity test

To test for multicollinearity in the independent variables, the variance inflation factor (VIF) test was used in this study as advised by Field [22]. VIF values obtained are provided in “Multicollinearity test” section in Appendix 1. “Multicollinearity test” section in Appendix 1 shows that all VIF values are below 10; therefore, multicollinearity is not a problem in the regression analysis in this study. This is further substantiated by the correlation results obtained in “Descriptive statistics and correlation analysis” section, where it is found that none of the correlation coefficients between the independent and control variables is above 0.80; this indicates that there is no multicollinearity problem [29].

#### Heteroscedasticity test

All variables of the study were winsorized to the 1^{st} and 99^{th} percentile to control for outliers.

After winsorizing, the Glejser test was performed to test the heteroscedasticity. The results are displayed in “Heteroscedasticity test” section in Appendix 1. There is no heteroskedasticity problem as the *p* values are above 0.05.

#### Autocorrelation test

The Durbin–Watson (DW) test was used to check for autocorrelation in the data. The regression with the dependent variable stock return volatility produced a DW values between 1.29 and 1.950. The DW values were below 2, indicating a serial autocorrelation problem. To address this problem, the MLR [22] was used to analyse the data. The MLR controls the serial correlation in the data or does not require the assumption of no autocorrelation to be met [22, 32].

### Descriptive statistics and correlation analysis

The descriptive statistic on the main variables of the study is provided in Appendix 2. The Pearson correlation matrix among the stock return volatility, measures of earnings quality and control variables is provided in Appendix 4. As shown in Appendix 4, IDIO is negatively correlated with AQ (*r* = −0.138), persistence (*r* = −0.173), predictability (*r* = −0.140), size (*r* = −0.073), leverage (*r* = −0.063), OPF (*r* = −0.352) and SRP (*r* = −0.228); all are significant except for leverage. In addition, IDIO displays a positive correlation with conservatism 1 (*r* = 0.015), conservatism 2 (*r* = 0.176), smoothness (*r* = 0.098), BTM (*r* = 0.174) and CFV (*r* = 0.095); all are significant except for conservatism 1.