The informativeness of pro forma and street earnings: an examination of information asymmetry around earnings announcements

Abstract

Using adverse-selection cost as a proxy for information asymmetry, we find evidence that non-GAAP earnings numbers issued by management (pro forma earnings) and analysts (street earnings) improve price discovery. First, information asymmetry before an earnings announcement is positively associated with the probability of a non-GAAP earnings number at the forthcoming earnings announcement. Second, the post-announcement reduction in information asymmetry is greater when managers or analysts issue non-GAAP earnings at the earnings announcement and when the magnitude of the non-GAAP earnings adjustment is larger. Our results suggest that earnings adjustments by analysts and managers increase the amount and precision of earnings information and help to narrow information asymmetry between informed and uninformed traders following earnings announcements. Alternatively, the findings may be attributable to characteristics of non-GAAP firms and overall better reporting quality for those firms rather than non-GAAP earnings disclosure per se.

Appendices

Appendix 1: Lin et al. (1995) Model

Lin et al.’s (1995) and Masson’s (1993) models show how quote revisions following stock trades can be used to estimate the adverse-selection component of the bid-ask spread. In response to a sell (buy) order that reveals possible private information, the market maker adjusts the bid-ask midpoint downward (upward). In the Lin et al.’s model,¹³ bid-quote and ask-quote revisions (B _k+1 − B _k , and A _k+1 − A _k, respectively) for a trade at time k are related to adverse selection expressed as a proportion (λ_k) of the signed one-half effective spread (Z _k ), as shown in (5), (6), and (7).

$$ B_{k + 1} {-} \, B_{k} = \, \lambda_{k} Z_{k} $$

(5)

$$ A_{k + 1} {-}A_{k} = \, \lambda_{k} Z_{k} $$

(6)

$$ Z_{k} = \left( {P_{k} {-}MP_{k} } \right) $$

(7)

where B is the bid quote, A is the ask quote, P is the transaction price, MP is the quote midpoint, Z is the signed one-half effective spread that takes a negative value for sell orders and a positive value for buy orders, and λ is the adverse-selection component as a fraction of Z, where 0 < λ < 1. In this model, the midpoint revision and the effective spread¹⁴ relate to the adverse-selection component λ as follows:

$$ MP_{k + 1} {-}MP_{k} = \, \lambda_{k} Z_{k} $$

(8)

We begin by estimating the adverse-selection component (λ) of the effective spread on a daily basis using all N trades for a firm i during day j. We use ordinary least squares regression to estimate λ_ij as follows:

$$ ln\left( {MP_{ijn}^{k + 1} } \right){-}ln(MP_{ijn}^{k} ) = ADV_{ij} lnZ_{ijn} + \, \varepsilon_{ijn} , $$

(9)

where ln(MP) is the natural log of the quoted midpoint of the bid-ask spread, calculated as (bid + ask)/2; ADV is the regression estimate of λ, lnZ is the effective half spread, calculated as the natural log of price minus the natural log of quoted midpoint; and ε is the normally distributed random error term. From an economic perspective, ADV _ij is the adverse-selection cost as a proportion of the effective spread for firm i for day j.

We find the daily adverse-selection cost (cents per share) as ASC _ij  = ADV _ij  × ESPREAD _ij  × 100, where ESPREAD _ij is the average effective spread over all N trades for firm i in day j. Specifically, $ESPREAD_{ij} = \mathop \sum \limits_{n = 1}^{N} \left( {|PRICE_{nij} - \, MIDPOINT_{nij} | \times 2} \right)/N_{ij}$. For each earnings announcement, the pre- and post-announcement estimates of adverse-selection cost, ASCpre _it and ASCpost _it, are daily adverse-selection cost averaged over the respective 10-day pre- and post-announcement windows for quarter t.

Appendix 2: Barron et al. (1998) model

To control for the uncertainty of a firm’s information environment, we rely on the Barron et al. (1998) model. In this model, the uncertainty in analyst k’s forecast for firm i in quarter t (V _itk ) has two components: information uncertainty that is unique to analyst k’s private information set with respect to firm i’s earnings (D _itk or idiosyncratic uncertainty) and information uncertainty that is inherent to shared public information about firm i (C _it or common uncertainty). V _itk is an ex ante concept that represents analyst k’s assessment of the expected variance of EPS _it , conditional on the uncertainty of public information (an expectation shared by all analysts) and the uncertainty of private information (an expectation unique to analyst k).

On an ex post basis, we derive unbiased estimates of the expected values for D, C, and V for firm i in quarter t from three observable variables: analyst earnings per share forecasts (F _ikt ), actual earnings per share (EPS _it ), and the number of forecasts (N _it ). The estimating equations are:

$$ D_{it} = \mathop \sum \limits_{k = 1}^{{N_{it} }} \left[ {\left( {F_{itk} - \overline{{F_{it} }} } \right)^{2} /\left( {N_{it} - 1} \right)} \right] $$

(10)

$$ C_{it} = \left( {EPS_{it} - \overline{{F_{it} }} } \right)^{2} - (D_{it} /N_{it} ) $$

(11)

$$ V_{it} = D_{it} + C_{it} = \mathop \sum \limits_{k = 1}^{{N_{it} }} \left( {EPS_{it} - F_{itk} } \right)^{2} /N_{it} $$

(12)

where D _it is the dispersion in forecasts that depends on analysts’ reliance on noisy private information, C _it is the common forecast error that depends on analysts’ reliance on noisy public information, and V _it is the total information uncertainty about earnings. V _it represents private and public information uncertainty averaged across all N _it analysts. V _it is distinct from, although clearly related to, uncertainty about the intrinsic value of firm i conditional on investors’ information set. The inverse of V _it represents the precision of earnings information.

Appendix 3: Variable definitions

Variable used in pre- or post-announcement OLS models or treatment-effect outcome modelsa
ASCb	Adverse-selection cost in cents per share, found as ADV ×  ESPREAD × 100.
ESPREADb	Mean daily effective spread measured as the absolute difference between quoted midpoint and transaction prices.
ADV b	Mean daily adverse-selection component of the bid-ask spread, using the model in Lin et al. (1995).
STREETt	An indicator variable equal to 1 when I/B/E/S reports street earnings and 0 otherwise. Street earnings is indicated when I/B/E/S actual EPS (VALUE) differs from GAAP EPS. For analysts, GAAP EPS is diluted EPS (epsfxq) or basic EPS (epspxq), consistent with the I/B/E/S variable FDI. We obtain I/B/E/S data from its unadjusted earnings per share files to avoid potential problems that stem from rounding effects that compromise the accuracy of the I/B/E/S split-adjusted EPS files (Payne and Thomas 2003; Philbrick and Ricks 1991). We correct I/B/E/S unadjusted data when a stock-split date occurs after the date of a forecast and before earnings are released (Glushkov and Robinson 2006), such that I/B/E/S EPS data (forecast and actual) reflect the actual number of shares outstanding as of the end of the fiscal quarter, consistent with Compustat.
PROFORMAt	An indicator variable equal to 1 when the firm reports pro forma earnings and 0 otherwise. Pro forma earnings is indicated when management reports an earnings number that differs from GAAP EPS. For the manager, GAAP EPS is Compustat’s diluted EPS (epsfxq).
NonGAAPt	An indicator variable equal to STREETt for the analysis of analysts’ reporting choices and PROFORMAt for managers’ reporting choices.
ProbNonGAAPt	Probability of street earnings for analysts (ProbSTREETt) and the probability of pro forma earnings for managers (ProbPROFORMAt), estimated separately for analysts and managers, using a logistic regression model with the covariates discussed in Sect. 4.5.1.
Dt	Dispersion in analyst earnings forecasts, representing the uncertainty in analysts’ private information in the Barron et al. (1998) model. Forecast dispersion is estimated using the last earnings forecast for quarter t by each of N analysts as reported in the I/B/E/S detailed earnings forecast database. We require at least three analysts for firm i in quarter t.
Ct	Forecast error, representing the uncertainty in public information about earnings in the Barron et al. (1998) model. Ct uses the same earnings forecasts as Dt and the corresponding I/B/E/S actual EPS. We require at least three analysts for firm i in quarter t.
Vt	Total forecast uncertainty over all N analysts, representing private and public uncertainty with respect to earnings information in the Barron et al. (1998) model.
MIDPOINTb	Average daily midpoint of bid-ask spread.
TradeSizeb	Average trade size (number of shares) per transaction.
TradeFreqb	Average number of daily transactions.
MV	Market value of equity (prccq × cshoq) at the end of quarter t.
ANALYSTS	Number of analysts providing earnings forecasts (I/B/E/S item, NUMEST).
BTM	Book-to-market ratio (ceqq/MV) at the end of quarter t.
MBE	An indicator variable equal to 1 if I/B/E/S (manager) actual EPS met or exceed analysts’ median forecast and 0 otherwise.
BEAT	An indicator variable equal to 1 if I/B/E/S (manager) FE is positive and 0 otherwise.
MISS	An indicator variable equal to 1 if I/B/E/S (manager) FE is negative and 0 otherwise.
MBECQ ct−1	The number of consecutive quarters a firm met or beat (failed to meet) analysts’ median estimate based on I/B/E/S actual EPS (VALUE) less the median estimate (MEDEST). See footnote to this table for details.
LOSS	Indicator variable equal to 1 if I/B/E/S median earnings estimate is negative.
DEC	Indicator variable equal to 0 for any quarter when the earnings announcement date (rdq) occurred before the midpoint (March 31, 2001) of the March 21 to April 9, 2001, phase-in of decimalization of NASDAQ quotes and 1 otherwise.
REGFD	Indicator variable equal to 0 for any quarter where the earnings announcement date (rdq) occurred before the compliance date (October 24, 2000) of Regulation FD and 1 otherwise.
REGG	Indicator variable equal to 0 for any quarter when the earnings announcement date (rdq) occurred before the compliance date (March 29, 2003) of Regulation G and 1 otherwise.

Variables used exclusively in post-announcement OLS models or treatment-effect outcome models
EX	Street (pro forma) EPS for the analysts (managers) minus GAAP EPS. EX is in dollars per share and is equal to 0 when STREET (PROFORMA) is equal to 0.
absFE	The absolute value of FE.
absFEs	absFE as a percentage of end-of-quarter share price; absFEs = (absFE/prccq) × 100.
LOSS2	An indicator variable equal to 1 if actual earnings reported by I/B/E/S (manager) is negative for analysts (managers).
absEX	The absolute value of EX.
absEXs	absEX as a percentage of end of quarter share price (prccq); absEXs = (absEX/prccq) × 100.
RANKabsEXs	Ranked values of absEXs. Firms are grouped into percentiles to form rankings from 0 to 99, separately for the analysts and managers.
FE	The forecast error is found as I/B/E/S actual EPS less the median estimate (FE = VALUE − MEDEST) for analysts and managers, unless PROFORMA = 1. Then, for managers only, FE = manager reported pro forma earnings – MEDEST.
FE_FLIPS	An indicator variable equal to 1 if the FE > 0 and FE − EX < 0 and zero otherwise. FE_FLIPS is found separately for analysts and managers. FE_FLIPS is equal to 1 when income-increasing exclusions flipped the sign of the forecast error from miss to meet or beat analysts’ median estimate.

Variable used exclusively in probit/selection modelsa
SALESGROWTHe	Sales growth for quarter t, found as (saleq t /saleq t−4) − 1.
STDDEVROAe	Standard deviation of return on assets (roa = niq/atq) over the previous eight quarters.
SPECITEMS	Indicator variable equal to 1 if firm reports a nonzero special item (spiq) and 0 otherwise.
lnTA	Log of total assets (at) at the end of quarter t.
SOX	Indicator variable equal to 1 for all calendar quarters ending after the second calendar quarter of 2002 and 0 otherwise.
NQ dt	The number of consecutive quarters that I/B/E/S reported an earnings number that differs from GAAP earnings.
GQ dt	The number of consecutive quarters that I/B/E/S reported an earnings that is the same as GAAP earnings.
INTANGIBLESe	End-of-quarter intangible assets (intanoq) divided by total assets (atq).
MTBe	End-of-quarter market value (prccq × cshoq) divided by book value of common equity (ceqq).
LEVERAGEe	End-of-quarter total liabilities (ltq) divided by total common equity (ceqq).
negOPFE	Indicator variable equal to1 if operating EPS (oepsxq) is less than the median I/B/E/S forecast and 0 otherwise.
OPLOSS	Indicator variable equal to 1 if firm has an operating loss (oepsxq < 0) and 0 otherwise.

1. ^aI/B/E/S (Compustat) mnemonics are displayed in upper (lower) case and italicized
2. ^bThese variables are measured over the three intervals—the pre-announcement window (−12,−3), the earnings announcement window (−2,+2), and the post-announcement window (+3,+12). When necessary to prevent ambiguity, the variables have a suffix indicating whether the variable is the average over the pre-announcement window (pre), earnings announcement window (ern), or post-announcement window (post). For example, ASCpre is the average daily ASC over the (−12,−3) window. Changes in these variables are denoted with the prefix “chg.” Changes are expressed as post-announcement window averages less pre-announcement window averages. For example, chgASC = ASCpost − ASCpre. A variable expressed in natural logarithm form has the prefix “ln.” For example, lnTradeSize is the natural log of TradeSize
3. ^cFollowing Brown et al. (2009), we let I/B/E/S MBE _it equal to 1 when I/B/E/S actual EPS is greater than or equal to I/B/E/S median forecast EPS for quarter t and 0 otherwise. If, over 12 quarters, firm i had the series MBE _it = (0,0,0,1,1,1,0,0,1,1,0,0), then the corresponding values of MBECQ _it = (−1,−2,−3,+1,+2,+3,−1,−2,+1,+2,−1,−2)
4. ^dTo illustrate our sequence variables, let the indicator variable STREET _t be equal to 1 (0) if I/B/E/S earnings and GAAP earnings differ (the same) for quarter t. Then, if a (newly listed) firm has the STREET _t series (0,0,0,1,1,1,0,0) over its first eight quarters, the corresponding values of NQ _t would be (0,0,0,1,2,3,0,0), and the corresponding values of GQ _t would be (1,2,3,0,0,0,1,2). Thus GQ _it and NQ _it are the number of consecutive quarters that I/B/E/S reported GAAP and non-GAAP earnings, respectively, for firm i as of the end of quarter t. We restrict the range of these variables to no more than +8. Note that we measure NQ _t and GQ _t using the full history of I/B/E/S earnings starting with the first calendar quarter of 1995 and ending with quarter t. Before 1995 I/B/E/S actual EPS is unreliable. We thank Ted Christensen for bringing this point to our attention
5. ^eWe use the same definitions as Lougee and Marquardt (2004) for intangible intensity, sales growth, market-to-book, leverage, and earnings variability