## 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.

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## Change history

### 20 May 2024

A Correction to this paper has been published: https://doi.org/10.1007/s11156-024-01275-3

## Notes

Investor sentiment can be defined as: “…a belief about future cash flows and investment risks that is not justified by the facts at hand.” (Baker and Wurgler 2007, 129). For brevity, we interchangeably use the terms “investor sentiment” and “sentiment”.

Valuation methods can be observed in analysts’ reports, but these reports are not available for all target prices. Also, analysts often use different methods in parallel, so that the reported target price is not based on a single valuation model but several (e.g., Imam et al. 2008; Imam, Chan, and Shah 2013). It is hence difficult to determine what valuation method was used from analysts’ reports where several methods are reported. Literature hence infers the method that most closely approximates the reported target price.

Prior literature that has analyzed the influence of more sophisticated valuation method use (Gleason et al. 2013) and sentiment (Clarkson et al. 2020) has not investigated the interrelation between these factors. To maintain a continuous level of target price optimism, however, the influence of valuation method use would depend on the level of sentiment.

Our results are robust to a battery of sensitivity tests and different specifications such as different deflators. All tests control for analysts’ earnings forecasts, stock recommendations, firm, and analyst characteristics.

This paper is also related to Loh and Stulz (2018) finding that analysts’ output is more useful for investors in periods of high macro uncertainty, such as crises. While related, macro uncertainty refers to the fundamental business- and information-environment, where sentiment refers to investors’ opinions driven by factors other than fundamentals (Baker and Wurgler 2007). The Baker and Wurgler (2006, 2007) investor sentiment index (

*SENT*) is orthogonalized to the NBER recession indicator. Also, the economic policy uncertainty index (Baker, Bloom, and Davis 2016) used in Loh and Stulz (2018) is uncorrelated with*SENT*over our sample period (-0.02,*p*> 0.10).For example, an analyst commented: “

*4–5 years ago, the DCF method was practicably useless, because the resulting values were much lower than the companies’ market prices at that time.”*(Glaum and Friedrich 2006, 170). Similarly, another analyst stated: “*We try to guess what the share price would be, not try to guess what the value of the company would be. Share price is a factor of two things: one is the stock market sentiment towards earnings and other is the earnings … it is tough to guess what the sentiment would be towards the earnings and what the earnings is going to be. Multiples are basically a guess of that. It is about what it should be if you feel confident and what it should be if you are not feeling confident. You try to guess what the market will do in 12 months’ time.”*(Imam et al. 2008, 522).*V*_{SOPH}is the pseudo-target price*V*_{RIP},*V*_{RIF}*,*or*V*_{DDM}that is closest to the actual target price*TP*, measured by the absolute difference. Analogously,*V*_{HEUR}is the pseudo-target price*V*_{PE},*V*_{PEG}*,*or*V*_{PB}which is closest to the actual target price*TP*.The monthly investor sentiment index is a composite index originally based on six variables and defined using annual data in Baker and Wurgler (2006), now the index is only based on five variables and it is also calculated using monthly data (http://people.stern.nyu.edu/jwurgler/). We employ the version orthogonalized to several macroeconomic conditions. Kaplanski and Levy (2017) conclude that sentiment is exogenous to the work of financial analysts, where analysts do not initiate sentiment.

The detailed survey description is available at: https://data.sca.isr.umich.edu/fetchdoc.php?docid=24774 (Surveys of Consumers, University of Michigan).

The sample period refers to the target price release dates. Data to calculate other variables deviates in part from this period (e.g., daily stock returns to compute the firms’ one-year future returns

*FRET*).There are, however, no multicollinearity problems in our regressions, the highest VIF is 1.5. We also perform additional tests that include the interactions

*TPP*PostREG*and*TPP*PostREG*SOPH*in Eq. (8). Our main conclusions are robust when adding these interactions.

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## Acknowledgements

We gratefully acknowledge helpful comments by Rashad Abdel-Khalik, Peter Clarkson, Jeff Coulton, Christi Gleason, Frank Heflin, Ole-Kristian hope, Alan Hodgson, Jesper Haga, Andrew Jackson, Andreea Moraru Arfire, Peter Pope, Marco Wilkens, Anne Wyatt, and participants at the American Accounting Association annual meeting in San Francisco 2019, European Accounting Association conference in Cyprus 2019, the EIASM workshop on accounting and regulation in Siena, workshops at University of Augsburg, UNSW Sydney, University of Queensland, Brisbane. The paper was previously circulated under the title “Target price optimism, investor sentiment, and the informativeness of target prices”.

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## 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 Assumption*V*_{RIP}:

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}:

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}:

where *V*_{DDM,t} is the pseudo-target price at time *t*, *DPS*_{0} 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 *NEPS*_{1} (= *EPS*_{3}/(1 + *LTG*)^{2}) is the expected normalized one-year-ahead earnings per share (Gordon and Gordon 1997). Missing three-year ahead analysts’ EPS forecasts *EPS*_{3} are extrapolated by analyst’s long-term EPS growth forecasts (see RIM with Perpetuity Assumption). Dividend per share *DPS*_{0} 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} and*V*
_{PB})

**Price-Earnings Model***V*_{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}:

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}:

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:

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 *BVPS*s with the current *BVPS*s.

### Appendix 2

### 2.1 Variable descriptions

Variable | Description |
---|---|

| |

| Sophisticated valuation’ variable is a categorical variable set equal to 1 if analyst |

| Investor sentiment is approximated by the monthly Baker and Wurgler (2006, 2007) investor sentiment index at the target price release month |

| 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 |

| Predicted investor sentiment by regressing (2SLS approach) |

| ‘BL fit’ variable is a categorical variable set equal to 1 if the pseudo-target price based on the sophisticated valuation |

| Analyst |

| Ratio of analyst |

| Target price excess, calculated as the difference between analyst |

| Target price error, calculated as the difference between the analyst |

| Analyst |

| Firm |

| Firm |

| |

| Index of Consumer Sentiment (University of Michigan Surveys of Consumers) with a time lag of 12 months at the target price release month |

| 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 |

| |

| ‘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) |

| Analyst |

| Analyst |

| Analyst |

| ‘EPS forecasts difference’ is the difference between analyst |

| ‘EPS forecasts difference’ is the difference between analyst |

| Long-term EPS growth forecast indicator variable is set equal to 1 if the target price |

| Analyst |

| Stock recommendation indicator variable is set equal to 1 if the target price |

| Analyst |

| Analyst |

| Firm |

| Firm |

| Firm |

| firm |

| Firm |

| Firm |

| Firm |

| Analyst |

| Number of firms followed by the analyst is calculated as the number of firms (divided by 100) for which the analyst |

| 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 |

| Brokerage size measured as the number of analysts (divided by 100) associated with a particular broker in a given year |

| ‘Rounding’ is a categorical variable set equal to 1 if the analyst |

| 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 |

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Buxbaum, M., Schultze, W. & Tiras, S.L. Do analysts’ target prices stabilize the stock market?.
*Rev Quant Finan Acc* **61**, 763–816 (2023). https://doi.org/10.1007/s11156-023-01164-1

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DOI: https://doi.org/10.1007/s11156-023-01164-1