Analysts’ use of dividends in earnings forecasts

Abstract

This paper investigates the association between current dividends and analysts’ subsequent earnings forecast errors. This investigation is motivated by the evidence on analyst optimism and Ohlson’s (1991, 1995) fundamental valuation theory that dividends displace future permanent earnings. For the sample period 1985–2016, we document that current dividends are positively correlated with analysts’ future forecast errors, suggesting that analysts potentially ignore the displacement effect of dividends on future earnings. Consistent with theory, this association persists in settings with stable dividends, (i.e., where dividends have limited or no signaling implications) and varies predictably with dividend payouts and cost of capital. We also find that this empirical regularity that analysts do not fully incorporate the effect of dividends on future earnings provides opportunities for arbitrage. More interestingly, we find that the strength of the association between dividends and analysts’ forecast errors has declined over the sample period; this decline appears to correspond with the underlying change in the discount rate over time. The finding that analysts’ do not fully incorporate the implications of current dividends on future earnings is consistent with previously documented inefficiencies in analysts’ use of publicly available information. However, such a systematic association with dividends also suggests that it may be a source of the persistence in analysts’ optimistic bias and thus offers new insights into analyst behavior.

Appendices

Appendix I Characterization of Analysts’ Forecast Error

If earnings can be characterized by a normal growth process, where the future earnings reflect growth at the cost of capital (r) over current earnings, the permanent earnings process can be modelled for the dividend displacement effect as follows.

$${x}_{t+1}=\left(1+r\right){x}_t-r{d}_t,$$

(A1a)

where x_t + 1, x_t, d_t, and r stand for one-year ahead earnings, current earnings, current dividends, and cost of capital (risk-free rate adjusted for equity premium), respectively. Further, an additional earnings growth process (denoted by α) will make the earnings dynamics to be as follows.

$${x}_{t+1}=\left(1+r+\alpha \right){x}_t-r{d}_t.$$

(A1b)

Next we model the forecasting process. The growth rate α is part of the private knowledge of the manager that is subject to signaling. Assume that the (positive) signaling effect is also interpreted by the market (analysts), making the earnings growth (over and above the normal increase due to cost of capital) an increasing function of current dividend (d_t), such that the growth α (d_t) is the additional effect on earnings.³³ Adding the signaling effect to the displacement effect and assuming that the cost of capital r is part of the common knowledge, the forecasted earnings corresponding to (A1b) becomes:

$${x}_t^{t+1}=\left(1+r+\alpha \left({d}_t\right)\right){x}_t-r{d}_t.$$

(A2)

As shown in Eq. (A2), the growth and the signaling effect will at least partly offset the dividend displacement effect through earnings growth. Earnings may be affected by other factors such as macroeconomic changes. To allow for these factors, we modify Eq. (A1b) to derive Eq. (A3), where η represents n other factors (with a coefficient γ; firm subscripts omitted) that could influence earnings, and ε_t + 1 denotes a (random) transitory component.

$${x}_t^{t+1}=\left(1+r+\alpha \right){x}_t-r{d}_t+\sum\nolimits_{i=1}^n{\gamma}_i{\eta}_i+{\varepsilon}_{t+1}.$$

(A3)

Besides the inferred growth from the signal, analysts’ earnings forecasts are likely to be based on the other information available that may be common to management and analysts. However, analysts’ forecasts may only include a subset of the other macroeconomic factors, say, p factors out of n where p < n. If we allow for the possibility that the parameter r, which represents the interest rate, is part of common knowledge and is not misestimated by analysts, then we can represent analysts’ forecast errors as follows.

$${ERR}_{t+1}={x}_t^{t+1}-{x}_{t+1}=\left(\alpha \left({d}_t\right)-\alpha \right){x}_t+\sum\nolimits_{i=p}^n{\gamma}_i{\eta}_i+{\varepsilon}_{t+1},$$

(A4a)

where ${x}_t^{t+1}$ is the forecast of earnings x_t + 1 at time t. Note that the ERR variable in Eq. (A4a) is independent of any earnings displacement. In fact, for efficient signaling to work, the recipient of the signal, in this case the analysts, must be able to correctly read the signal. Otherwise a signaling equilibrium cannot exist. Therefore α(d_t) must be equal to α. If so, ERR_t + 1 must be based on the transitory (random) component and the effects of other missing variables, or

$${ERR}_{t+1}={x}_t^{t+1}-{x}_{t+1}=\sum_{i=p}^n{\gamma}_i{\eta}_i+{\varepsilon}_{t+1}.$$

(A4b)

But suppose the analyst forecast process is not fully efficient in that a) it does not fully capture the effect of dividends and instead makes an adjustment equal to r’d, where r’d is the adjustment rate assumed by the analysts and b) does not completely account for the growth signaled, then the ERR would be as follows.

$${ERR}_{t+1}={x}_t^{t+1}-{x}_{t+1}=\kern0.5em \left(\alpha \left({d}_t\right)-\alpha \right){x}_t-\left({r}^{\prime }-r\right)\beta {d}_t+\sum_{i=1}^n{\gamma}_i{\eta}_i+{\varepsilon}_{t+1}.$$

(A4c)

Hence the following specification,

$${ERR}_{t+1}={x}_t^{t+1}-{x}_{t+1}=\kern0.5em \alpha {x}_t+\beta {d}_t+\sum_{i=1}^n{\gamma}_i{\eta}_i+{\varepsilon}_{t+1},$$

(A4d)

captures the separate effects of signaling and dividend displacement. The signaling effect will be captured in α, the coefficient on earnings, whereby a positive sign will reflect optimistic bias (overreaction to signal) and a negative sign will reflect a pessimistic bias (underreaction to signal), with zero coefficient reflecting an efficient reaction. Similarly, a positive sign on β will indicate analysts’ underreaction to the dividend displacement effect and a negative sign would indicate an overreaction to the dividend displacement effect, with a zero-coefficient indicating a proper accounting of dividend effect in their forecasts.

The factors represented by η are the control variables that may help explain the magnitude of the analyst forecast errors. The use of forecast error as the dependent variable in our tests using Eq. (A4d) also allows us to examine a proxy for permanent earnings that we expect the analysts to issue. Finally, since we do not focus on signaling, we refrain from any analysis of α.

Appendix II: Theil-Sen Estimation

Theil-Sen estimation is a method for robust linear regression that chooses the median slope among all lines of groups through n-dimensional sample points (where n is the number of parameters estimated). Ohlson and Kim (2015) examined the implications of using the Theil-Sen estimation and show that it is a robust alternative to OLS for applications in accounting and finance.³⁴ They also compared the results with traditional OLS estimators and concluded that the “TS estimator ought to be viewed as a competitive alternative to OLS approaches.”

The estimation process consists of randomly selecting subsamples with replacement and then estimating regression parameters (slope and intercept) from these subsamples. The Theil-Sen estimate of each parameter is the median of a finite number of subsamples (e.g., 5000). The estimation uses the sampling procedure to estimate the coefficients and intercepts and hence uses the entire dataset without being affected by any outlier problem. Thus the standard errors and confidence intervals for the Theil-Sen estimator are obtained through a sampling process akin to bootstrapping.³⁵ Further, Theil-Sen estimation, being nonparametric, does not require any underlying distributional assumptions. It competes well against nonrobust least squares, even for normally distributed data in terms of statistical power. Theil-Sen has been shown to have the properties of robust estimation and details its asymptotic and unbiased properties are discussed by Wilcox (2010) and Peng et al. (2008).

To empirically implement the Theil-Sen estimation approach, we use the procedure outlined by Ohlson and Kim (2015).³⁶ Within each year, we first randomly draw 5000 subsamples with N observations (where N is the number of regression parameters estimated). Next we regress the dependent variable Y_i,t on the N-1 independent variables. Specifically, we run 5000 such regressions for each of the 32 sample years. For each of these 5000 regressions, we get N regression parameters (i.e., intercept and the β and γ coefficients). Third, within each year, we take the median of each regression parameter from the 5000 estimated parameters, yielding N regression parameter medians for each year. These N regression parameter medians represent one set of parameter estimates for each sample year.

Finally, to test whether the regression parameters are statistically different from zero, we follow an approach similar to that of Fama and MacBeth (1973). Specifically, for each of the N parameter estimates in a given year, we use the distribution of the 32 annual medians to calculate time-series averages, conduct t-tests, and determine the reported p values. Since each regression is estimated by year, a given firm can show up once or not at all in a single regression. Hence it is not necessary, nor possible, to include firm or year fixed effects in the Theil-Sen approach.

Appendix III: Variable Definitions

ATit	Total Assets (in millions of dollars).
BETAit	The firm-year specific year-end Beta estimates (BETAV) from the Center for Research in Security Prices (CRSP).
DPSit	Annual dividend per share from Compustat (DVPSX_C / ADJEX_C).
ΔDPSit	DPSit – DPSit-1 (in $).
ERRit + 1	FEPSit + 1 – EPSit + 1.
EPSit + 1	Actual EPS from IBES for fiscal period t + 1 (in $).
ΔEPSit	EPSit – EPSit-1 (in $).
FEPSit + 1	Consensus forecast of EPSt + 1, calculated as the average of the forecasts issued shortly (~90 days) after the Earnings Announcement Date of EPSt. from the IBES detail file.
FDPSit + 1	Consensus forecast of DPSt + 1, calculated as the average of the forecasts issued shortly (~90 days) after the Earnings Announcement Date of EPSt. from the IBES detail file.
FDPSit + 2	Consensus forecast of DPSt + 2, calculated as the average of the forecasts issued shortly (~90 days) after the Earnings Announcement Date of EPSt. from the IBES detail file.
IOSit	A firm-year specific measure of investment opportunities estimated as the first principal component, similar to Baber et al. (1996) and Kumar and Krishnan (2008), from a factor analysis of growth in market value (MVGROW), the market-to-book ratio of total assets (MBASS), and the ratio of research and development expense to total assets (RDASS). These variables are calculated as follows (Compustat variables in italics)37.
MVGROWit	MVALit/MVALit-1, where MVAL = AT – CEQ + PRCC_F *CSHO
MBASSit	MVALit / ATit
RDASSit	XRDit / ATit
NESTit	Number of analysts following firm i in year t-1.
PEGit	The cost of capital for firm i in year t, estimated following Botosan and Plumlee (2005):
${PEG}_{it-1}=\sqrt{\frac{FEPS_{it+1}-{FEPS}_{it}}{PRICE_{t-1}}}$
REPOit	Share repurchases, calculated as the difference between Purchase of Common and Preferred Stock (PRSTKC) and Preferred Stock Redemption Value (PSTKRV), as in.
TDPSit	Total Dividends per Share (TDPS) is a more comprehensive measure of dividends, which includes share repurchases (REPO). We follow Grullon and Michaely (2002) in how we measure TDPS.
σNIQit	Earnings variability, measured as the standard deviation of quarterly earnings estimated over the previous eight quarters, where missing values are omitted.