Do analysts’ target prices stabilize the stock market?

Abstract

If target prices reflect the true values of stocks, they should direct prices towards intrinsic values. But analysts’ optimism and use of less sophisticated valuation methods have been found to impede target price informativeness. Contrary to conventional belief, we propose that, due to analysts’ optimism, target prices are closer to intrinsic values, and hence more informative, when investor sentiment is low. Accordingly, we find that the association of target prices with future returns is highest when investor sentiment is low and target prices are inferred to be based on sophisticated valuation methods. When investor sentiment is high, however, we find that the association of target prices with future returns approaches zero, suggesting that analyst optimism drives target prices away from intrinsic values, irrespective of the implied valuation method. Further, investors’ reactions to target price revisions are strongly positive and seemingly irrational with high investor sentiment—which potentially destabilizes markets.

Appendices

Appendix 1

1.1 Valuation model description

1.1.1 Models classified as sophisticated valuation methods (V _RIP,V _RIF and V _DDM)

Residual Income Valuation with Perpetuity AssumptionV_RIP:

$$V_{RIP,t} = BVPS_{t} + \mathop \sum \limits_{\tau = 1}^{5} \frac{{E_{t} \left[ {RI_{t + \tau } } \right]}}{{\left( {1 + r} \right)^{\tau } }} + \frac{{E_{t} \left[ {RI_{t + 5} } \right]}}{{r\left( {1 + r} \right)^{5} }}$$

where V_RIP,t is the pseudo-target price at time t, BVPS is the equity book value per share, E[RI] is residual income (EPS_t+τ-r*BVPS_t+τ-1), EPS is analyst’s earnings per share forecast, r is the equity cost of capital, and τ is a time index (Bradshaw 2004). The time index is simplified for illustration. In fact, the residual income is discounted to the first day of the target price release month. Analyst and firm subscripts are omitted for brevity. Contemporaneously issued one- and two-year-ahead EPS forecasts are required to be available. Unavailable EPS forecasts from three up to five years are extrapolated by analyst’s long-term EPS growth forecast (Bradshaw 2004). Missing long-term EPS growth forecasts are replaced by the median consensus long-term EPS growth forecasts. In the first three months of a fiscal year, the equity book value per share is approximated by the clean surplus relation (BVPS_t = BVPS_t-1 + EPS_t-DPS_t where DPS is the dividend per share, we require that the EPS forecasts are not older than 90 days on the fiscal year end), afterwards the most recent equity book value per share (COMPUSTAT item #60 divided by item #25) is used. Future equity book values per share are also determined by the clean surplus relation. It is assumed that firms maintain their historical dividend payout ratio (Bradshaw 2004). The dividend payout ratio to compute the dividends per share is defined as the payout ratio of the most recent fiscal year (item #21 divided by item #237) or the mean payout ratio over the previous three years if the prior year payout ratio is less than zero or greater than one (Bradshaw 2004). For loss-making firms, the payout ratio is computed as the most recent dividends divided by 6% (Frankel and Lee 1998) of firm’s total assets (item #6). Further, unreasonable payout ratios of less than zero or greater than one are set to zero or to one, respectively (Lee et al. 1999). The industry discount rate r is the 48 industry-specific risk premiums (Fama and French 1997) plus the risk-free rate (30-day U.S. treasury bill yield) using twenty-year rolling regressions in effect for the month prior to the target price release date (Bradshaw 2004). We apply twenty-year rolling regressions since five-year rolling regressions generate in part negative industry discount rates after the subprime crisis. Monthly industry discount rates are annualized by multiplying with 12.

1.1.2 Residual Income Valuation with a Fade-Rate Assumption V _RIF:

$$V_{RIF,t} = BVPS_{t} + \mathop \sum \limits_{\tau = 1}^{5} \frac{{E_{t} \left[ {RI_{t + \tau } } \right]}}{{\left( {1 + r} \right)^{\tau } }} + \frac{{\omega E_{t} \left[ {RI_{t + 5} } \right]}}{{\left( {1 + r - \omega } \right)\left( {1 + r} \right)^{5} }}$$

where V_RIF,t is the pseudo-target price at time t, BVPS is the equity book value per share, r is the equity cost of capital (see RIM with Perpetuity Assumption), E[RI] is the expected residual income, ω is the industry rate of reversion, and τ is a time index (Bradshaw 2004). The industry rate of reversion of residual income ω is estimated by the following regression for each of the 48 industries (Fama and French 1997) using all observations with book value, earnings before extraordinary items and market value on COMPUSTAT between 1998 and 2014 (Dechow et al. 1999; Bradshaw 2004): $R{I}_{t}=\eta +\omega R{I}_{t-1}+{\varepsilon }_{t}$, where RI is the residual income realized in period t and ω is the industry rate of reversion (fade rate). Residual income is the income before extraordinary items (item #18) cleansed of special items (item #17), taxed at a notional rate of 35% and less a capital charge based on the industry cost of capital (see above) times beginning equity book value (item #60) and finally scaled by the beginning market equity (item #25 multiplied by item #199). We winsorize RI at the top and bottom 0.5% levels (Dechow et al. 1999) and employ an outlier robust regression.

1.1.3 Dividend Discount Model V _DDM:

$$V_{DDM,t} = \mathop \sum \limits_{\tau = 1}^{5} \frac{{DPS_{0} \left( {1 + LTG} \right)^{\tau } }}{{\left( {1 + r} \right)^{\tau } }} + \frac{{NEPS_{1} \left( {1 + LTG} \right)^{5} }}{{r\left( {1 + r} \right)^{5} }}$$

where V_DDM,t is the pseudo-target price at time t, DPS₀ is the most current dividend per share, LTG is analyst’s long-term EPS growth forecast, r is the equity cost of capital (see RIM with Perpetuity Assumption) and NEPS₁ (= EPS₃/(1 + LTG)²) is the expected normalized one-year-ahead earnings per share (Gordon and Gordon 1997). Missing three-year ahead analysts’ EPS forecasts EPS₃ are extrapolated by analyst’s long-term EPS growth forecasts (see RIM with Perpetuity Assumption). Dividend per share DPS₀ is computed by COMPUSTAT item #21 divided by item #25 assuming that data is available three-month after the fiscal-year end.

1.1.4 Models classified as heuristic valuation methods (V _PE,V _PEG andV _PB)

Price-Earnings ModelV_PE:

$$V_{PE,t} = E_{t} \left[ {EPS_{t + 2} } \right]*PE$$

where V_PE,t is the pseudo-target price at time t, EPS_t+2 is analyst’s two-year-ahead EPS forecast and PE is the industry forward price-earnings ratio (Bradshaw 2002). First, we compute a monthly forward price-earnings ratio for every U.S. firm with non-missing data based on the mean consensus analysts’ EPS forecast with a two-year horizon. Second, we identify the monthly median price-earnings ratio PE for every 48 industries (Fama and French 1997) based on the positive firm price-earnings ratios. We use SIC-Codes provided by CRSP to match the firm price-earnings ratios and the 48 industries. The pseudo-target price is based on the industry price-earnings-ratio in effect for the month prior to the target price release date.

1.1.5 Price-earnings-growth model V _PEG:

$$V_{PEG,t} = E_{t} \left[ {EPS_{t + 2} } \right]*LTG*100$$

where V_PEG,t is the pseudo-target price at time t, EPS_t+2 is analyst’s two-year-ahead EPS forecast and LTG is analyst’s long-term EPS growth forecast (Bradshaw 2004).

1.1.6 Price-book model V _PB:

$$V_{PB,t} = E_{t} \left[ {BVPS_{t + 2} } \right]*PB$$

where V_PB,t is the pseudo-target price at time t, BVPS_t+2 is the extrapolated two-year-ahead book-value per share (see RIM with Perpetuity Assumption), and PB is the industry price-book ratio. Firstly, we compute a monthly price-book ratio for every U.S. firm with non-missing data in COMPUSTAT. To compute price-book ratios we use annual COMPUSTAT data (item #199/(item #60/item #25)) and hold the ratios constant over twelve months. We assume that data is available three months after a fiscal-year end. Second, we compute the monthly median price-book ratio PB for every 48 industries (Fama and French 1997) based on positive firm price-book ratios. We use SIC-Codes provided by COMPUSTAT to match the firm price-book ratios and the 48 industries. The pseudo-target price is based on the industry price-book ratio PB in effect for the month prior to the target price release date.

1.1.7 Model to approximate the ex post intrinsic value of a stock

Residual Income Valuation with Perpetuity Assumption V_int based on actual future data:

$$V_{int,t} = BVPS_{t} + \mathop \sum \limits_{\tau = 1}^{3} \frac{{E_{t} \left[ {RI_{t + \tau } } \right]}}{{\left( {1 + r} \right)^{\tau } }} + \frac{{\left( {1 + g} \right)E_{t} \left[ {RI_{t + 3} } \right]}}{{\left( {r - g} \right)\left( {1 + r} \right)^{3} }}$$

where V_int,t is the ex-post intrinsic value of a stock at time t, BVPS is the equity book value per share, E[RI] is residual income (AEPS_t+τ-r*BVPS_t+τ-1), AEPS is actual earnings per share (COMPUSTAT item #237 divided by item #25), r is the equity cost of capital, g is a growth rate, and τ is a time index. We use moderate growth rates g based on inflation. We replace missing intrinsic values or intrinsic values lower than the current BVPSs with the current BVPSs.

Appendix 2

2.1 Variable descriptions

Variable	Description
	Main variables
SOPHjit	Sophisticated valuation’ variable is a categorical variable set equal to 1 if analyst j’s target price for firm i at time t is inferred to be based on a sophisticated valuation model, and 0 otherwise (see Sect. 3)
SENTt	Investor sentiment is approximated by the monthly Baker and Wurgler (2006, 2007) investor sentiment index at the target price release month t
SENTl1t	One-month lagged investor sentiment is approximated by the monthly Baker and Wurgler (2006, 2007) investor sentiment index with a time lag of one month at the target price release month t
SENTt (Instr.)	Predicted investor sentiment by regressing SENTt on the instrumental variables MICHt and EMVt (2SLS approach)
BLFITjit	‘BL fit’ variable is a categorical variable set equal to 1 if the pseudo-target price based on the sophisticated valuation VSOPH results in a pseudo-target-to-share price (for analyst j’s target price for firm i at time t) closer to the firm’s long-term BL ratio than the pseudo-target price based on the heuristic valuation VHEUR, and 0 otherwise (see Sect. 3)
TPjit	Analyst j’s target price for firm i at time t scaled by the firm’s total assets per share
TPPjit	Ratio of analyst j’s target price for firm i at time t to the closing price of firm i on the trading day before the target price release date t
TPEXCjit	Target price excess, calculated as the difference between analyst j’s target price for firm i at time t minus the ex-post intrinsic value Vint,it scaled by the closing price of firm i on the trading day before the target price release date t (see Sect. 3)
TPERRjit	Target price error, calculated as the difference between the analyst j’s target price for firm i at time t minus the one-year-ahead share price (or the last available share price) scaled by the closing price of firm i on the trading day before the target price release date t
TPREVjit	Analyst j’s target price revisions for firm i on time t, calculated as analyst’s target price divided by analyst’s previous target price minus 1 (Asquith et al. 2005)
FRETjit	Firm i’s one-year future return, calculated as the cumulative 250-days ex-dividend stock return (or maximum available returns in the case of delisted firms) following the target price release date t of target price j (Clarkson et al. 2020)
ARETjit	Firm i’s short-term abnormal return, calculated as the difference between the firm’s buy-and-hold return and the buy-and-hold return on the NYSE/AMEX/Nasdaq value-weighted market index starting at the target price release date t of target price j and ending two days subsequent to the target price release date (Brav and Lehavy 2003)
	Instrumental variables (IVs) to estimate SENTt (Instr.)
MICHt	Index of Consumer Sentiment (University of Michigan Surveys of Consumers) with a time lag of 12 months at the target price release month t
EMVt	Newspaper-based U.S. Equity Market Volatility tracker (Baker et al. 2019) with a time lag of 6 months at the target price release month t
	Control variables
PostREGt	‘Post-regulation’ variable is set equal to 1 if the target price is announced after April 30, 2003, and 0 before (e.g., Barniv et al. 2009; Chen and Chen. 2009)
FEPSjit	Analyst j’s one-year-ahead EPS forecast for firm i at time t scaled by the closing price of firm i on the trading day before the EPS forecast release date t
FEPSAjit	Analyst j’s one-year-ahead EPS forecast for firm i at time t scaled by the total assets per share of firm i
EPSREVjit	Analyst j’s earnings forecast revision for firm i at time t is calculated as analyst j’s one-year-ahead EPS forecast for firm i at time t divided by analyst j’s previous one-year-ahead EPS forecast for firm i minus 1 (Asquith et al. 2005)
FDIFFjit	‘EPS forecasts difference’ is the difference between analyst j’s two- and one-year-ahead EPS forecast for firm i at time t scaled by the closing price of firm i on the trading day before the EPS forecast date t (Clarkson et al. 2020)
FDIFFAjit	‘EPS forecasts difference’ is the difference between analyst j’s two- and one-year-ahead EPS forecast for firm i at time t scaled by firm’s total assets per share
IncFLTGjit	Long-term EPS growth forecast indicator variable is set equal to 1 if the target price j for firm i at time t is accompanied by an individual long-term EPS growth forecast, and 0 otherwise
FLTGjit	Analyst j’s long-term EPS growth rate for firm i at time t. If there is no individual long-term EPS growth forecast (IncFLTG = 0), FLTG is replaced by the median consensus long-term EPS growth forecast
IncRECjit	Stock recommendation indicator variable is set equal to 1 if the target price j for firm i at time t is accompanied by a stock recommendation, and 0 otherwise
RECjit	Analyst j’s stock recommendations RECjit for firm i at time t (1 for a ‘sell’ recommendation, 2 for a ‘underperform’, 3 for a ‘hold’, 4 for a ‘buy’ and 5 for a ‘strong buy’), if there is no recommendation on the target price release date t, RECjit is replaced by the median consensus stock recommendation
RECREVjit	Analyst j’s stock recommendation revision for firm i at time t is calculated as analyst j’s stock recommendation (1 for a ‘sell’ recommendation, 2 for a ‘underperform’, 3 for a ‘hold’, 4 for a ‘buy’ and 5 for a ‘strong buy’) for firm i at time t minus analyst j’s previous stock recommendation for firm i multiplied by 1/4 (see Feldman et al. 2012; Ho et al. 2018). If there is no recommendation on the target price release date, RECREVjit is set to 0
CSDit	Firm i’s daily return volatility at time t calculated over the last 250-trading-day period ending one day before the target price release date t
CBETAit	Firm i’s CAPM beta (Sharpe 1964; Lintner 1965; Mossin 1966) at time t, estimated from a regression of firm i’s monthly returns minus the risk-free rate on monthly value-weighted market returns minus the risk-free rate over a period of 60 months (minimum 24 months) preceding the target price month
CBMit	Firm i’s book-to-market ratio at time t (e.g., Fama and French 1992; Lui et al. 2007) which is calculated as the book value of equity per share (item #60 divided by item #25) divided by the share price at the end of the most recent fiscal year
CSIZEit	firm i’s size at time t (e.g., Banz 1981; Fama and French 1992, 1993), calculated as the log of the market capitalization on the trading day before the target price release date t
CEXFit	Firm i’s external finance at time t, calculated as the change in firm i’s assets (item #6) minus the change in retained earnings (item #36) divided by total assets of the prior fiscal year. When the change in retained earnings is not available, we use net income (item #172) less common dividends (item #21) instead (Baker and Wurgler 2006)
CPRETit	Firm i’s past stock return at time t calculated as the cumulative return over the 250-trading day period ending on the day before the target price release date t
CWHit	Firm i’s 52-week high price is the highest stock price of firm i over the 52-week period preceding the target price release date t scaled by the closing price on the trading day before the target price release date (Clarkson et al. 2020)
AFEXPjit	Analyst j’s firm-specific experience AFEXPj,t is calculated as the number of years (divided by 100) in which the analyst has issued target prices for the firm i up to the target price release date t (Clement 1999)
ANFIRjt	Number of firms followed by the analyst is calculated as the number of firms (divided by 100) for which the analyst j supplied at least one EPS forecast in a given year (see Clement 1999)
ANINDjt	Number of industries followed by the analyst is measured as the number of the 48 Fama and French (1997) industries (divided by 100) for which the analyst j supplied at least one EPS forecast in a given year (Clement 1999)
ABSIZjt	Brokerage size measured as the number of analysts (divided by 100) associated with a particular broker in a given year
AROUNDjit	‘Rounding’ is a categorical variable set equal to 1 if the analyst j’s target price for firm i at time t is rounded to the nearest dollar, and 0 otherwise
IND	Is a vector of dummy variables indicating in which of the 12 Fama and French industries the firm was operating on the target price release date. The variable of the industry “Business Equipment” is omitted and hence the corresponding fixed effect is reflected by the constant of the equation