Accounting information and left-tail risk

Abstract

Several recent studies attribute stock price crashes to firms withholding bad news from financial disclosures before a stock price crash. Contrary to this notion, we find evidence of a robust link between information in a firm’s financial disclosures and potential left-tail risk. We document that the sophisticated equity options traders incorporate information derived from financial statements about left-tail risk into prices of out-of-the-money put options on a firm’s equity, implying that a firm’s financial disclosures contain significant information relevant to pricing expected crash risk. However, we find that stock market investors at large appear to overlook this link and fail to incorporate information in financial disclosures about left-tail risk into stock prices in a timely fashion, potentially contributing to the severity of the eventual crash. These findings contradict the notion that managers can fully conceal information pertinent to left-tail risks and highlight the role of potential errors by investors in processing accounting information pertinent to left-tail risks. Our study is amongst the first to link financial statement analysis to expected crash risk.

Appendix

1.1 Variable Definitions

• $ATM\_IV_{i,t}$ – is the daily open interest-weighted implied volatility of at the money (ATM) call options, computed as the average over the fiscal year.

• $Beta_{i,t}$ – is the market beta estimated from the CAPM using daily stock and market returns over the fiscal year (used in Table 6).

• $BidAskSpread_{i,t}$ – is the mean daily relative bid-ask spread over the year, where relative bid-ask spread as the absolute difference in daily ending bid and ask divided by the average of daily ending bid and ask.

• $Cashflow\_Vol_{i,t}$ – is the standard deviation of operating cash flow (OANCF) (scaled by lagged total assets) over the past five years.

• $CRASH_{i,t,t + 12}$ – an indicator variable that takes on a value of 1 if firm i experiences a negative one-year stock return of -50% or worse (in other models we use -70% or worse) during year t,t + 12, and 0 otherwise. Year t,t + 12 is defined as the 12 months starting with four months after the most recent fiscal year-end. For generalized logit models, a value of -1 is assigned to firms with a one-year positive stock return of + 50% or greater (in other models + 70% or greater).

• $Earnings\_Vol_{i,t}$ – is the standard deviation of income before extraordinary items (IB) (scaled by lagged total assets) over the prior five years.

• $HHI_{i,t}$ – is the Herfindahl–Hirschman Index measured within each three-digit SIC industry-year.

• $Idosy\_Vol_{i,t}$ – is the standard deviation of weekly firm-specific returns over the fiscal year.

• $Illiquidity_{i,t} -$ is the median daily price impact over the year where price impact equals the daily absolute price change in percent divided by US$ trading volume (measured in thousands) from Amihud (2002). We omit zero return days to avoid misclassifying low trading activity days as highly liquid and multiply Illiquidity by 1,000. Smaller values indicate greater liquidity.

• $IV\_SKEW_{i,t}$ – a proxy for expected crash risk calculated as the average daily implied volatility skew over either the three months ($IV\_SKEW3_{i,t}$) or 12 months ($IV\_SKEW12_{i,t}$) beginning in the fourth month following the fiscal year-end.

• $Ln\left( {Mktval} \right)_{i,t}$ – the natural log of the market value of firm i's equity calculated as the shares outstanding (CSHO) times the stock price (PRCC_F) as of the fiscal year-end t.

• $Ln\left( \frac{B}{M} \right)_{i,t}$ – the natural log of the ratio of firm i’s book-value of equity (CEQ) to its market value as of fiscal year-end t.

• $Ln\left( {Leverage} \right)_{i,t}$ – the natural log of the ratio of firm i’s long-term total debt to its balance sheet value of assets as of fiscal year-end t.

• $Ln\left( {Ret} \right)_{i,t}$ – the natural log of one plus the one-year stock return during fiscal year t.

• $Ln\left( {Vol} \right)_{i,t}$ – the natural log of the ratio of firm i’s stock return volatility is measured as the standard deviation of its monthly stock returns ending over a 36-month period ending at fiscal year-end t.

• $MktBeta_{i,t}$ – the beta of a firm estimated using its past 36 monthly returns regressed against the value-weighted market index as of the end of fiscal year-end t.

• $\left( \frac{M}{B} \right)_{i,t}$ – is the ratio of the market value of equity to the book value of equity at the end of the year.

• $NEG\_SKEW_{i,t}$ – is the negative skewness of weekly stock returns over the fiscal year.

• $Sales\_Vol_{i,t}$ – is the standard deviation of sales revenue (scaled by lagged total assets) over the prior five years.

• $Stock\_Turn_{i,t}$ – is the average monthly share turnover over the fiscal year.

• $Strategy_{i,t}$ – is the business strategy composite measure of Bentley et al. (2013), scaled by 100.

• $Total\_Vol_{i,t}$ – is the standard deviation of weekly stock returns over the fiscal year.

• $WeakFund_{i,t}$ – defined as (9 – F-score)/9; ranges from 0 to 1, with larger values implying weaker fundamentals. (construction described in Sect. 3.2).

1.2 Calculation of the F-score

Following Piotroski and So (2012), the F-score is calculated for each firm using nine signals derived from its annual financial statements:

$$ \begin{aligned} F - Score \, & = \, I\_ROA + I\_CFO + I\_ACC + I\_DROA + I\_DLEV \\ & \quad + I\_LIQ + I\_SSTK + I\_DM + I\_DTURN. \\ \end{aligned} $$

(A.1)

Variable definitions follow; COMPUSTAT variables are in parentheses:

• ROA_i,t – income before extraordinary items (IB) divided by the beginning of the year total assets (AT_i,t-1). The indicator variable I_ROA_i,t equals 1 if ROA_i,t > 0 and 0 otherwise.

• CFO_i,t – measured as the cash flow from operations (OANCF_i,t, measured as funds from operations when OANCF is not available) scaled by the beginning of year total assets (AT_i,t-1). The indicator variable I_CFO_i,t equals 1 if OANCF_i,t > 0 and 0 otherwise.

• ACCRUAL_i,t – measured as the difference between income before extraordinary items (IB_i,t) scaled by the beginning of year total assets (AT_i,t-1) and cash flow from operations as described above. The indicator variable I_ACC equals 1 if ACCRUAL_i,t < 0 and 0 otherwise.

• DROA_i,t – measured as the difference between the current year’s ROA_i,t, and the previous year’s ROA_i,t-1. The indicator variable I_DROA equals 1 if DROA_i,t > 0 and 0 otherwise.

• DLEVER_i,t – measured as the difference between the current year’s debt-to-assets ratio and the previous year’s debt-to-assets ratio. The debt-to-assets ratio is measured as long-term debt (DLTT_i,t) divided by total assets (AT_i,t). The indicator variable I_DLEV equals 1 if DLEVER_i,t < 0 and 0 otherwise.

• DLIQUID_i,t – measured as the difference between the current year’s current ratio and the previous year’s ratio. The current ratio is measured as current assets (ACT_i,t) divided by current liabilities (CLT_i,t). The indicator variable I_DLIQ equals 1 if DLIQUID_i,t > 0 and 0 otherwise.

• ISSUANCE_i,t – measured as the amount of stock issued by a firm in a given year (SSTK_i,t). The indicator variable I_SSTK equals 1 if SSTK_i,t <  = 0 and 0 otherwise.

• DMARGIN_i,t – measured as the difference between the current year’s gross margin ratio and the previous year’s ratio. The gross margin ratio is measured as one minus the ratio of cost of goods sold (COGS_i,t) and net sales (SALE_i,t). The indicator variable I_DM equals 1 if DMARGIN_i,t > 0 and 0 otherwise.

• DTURN_i,t – measured as the difference between the current year’s asset turnover ratio and the previous year’s turnover ratio. The asset turnover ratio is measured as net sales (SALE_i,t) divided by total assets (AT_i,t). The indicator variable I_DTURN equals 1 if DTURN_i,t > 0 and 0 otherwise.