Investor sentiment effects on share price deviations from their intrinsic values based on accounting fundamentals

Abstract

We investigate the existence of evidence of investor sentiment on share price deviations from their intrinsic values across two sentiment regimes of shares market: the low-to-normal and the excess one. We use the residual income valuation model to calculate the intrinsic values of shares based on accounting fundamentals and we suggest a panel data threshold model to capture the sentiment regimes of the market, using as threshold variable alternative investor sentiment indices. The suggested model enables us, first, to endogenously identify from the data the threshold value of a sentiment index triggering market sentiment regime shifts and, based on it, to examine if the effects of investor sentiment on share prices across the above two sentiment regimes are in accordance to the theory. Application of the model to UK data shows that investor sentiment influences positively share prices in the low-to-normal and negatively in the excess one. We also show that investor sentiment dominates risk premium effects on shares characterized by low book-to-market, and dividend- and earnings-to-price ratios. The above results are consistent with the predictions of the sentiment hypothesis.

Appendix 1

In this appendix, we firstly present the results of our panel data integration-cointegration analysis for share prices $P_{it}$ and their intrinsic values $P_{it}^{*}$. Secondly, we give the definitions of the economic variables used to construct the economic sentiment index ($SI_{t}$) based on principal component analysis.

1.1 Appendix 1.1: Panel data integration-cointegration analysis

1.1.1 Appendix 1.1.1: Unit root tests

Before testing if $P_{it}$ and $P_{it}^{*}$ are cointegrated series, we first need to establish that both of these series are integrated series of order one, denoted as I(1). To this end, we conduct a number of alternative panel data unit root testing procedures, suggested in the literature. These include the following test statistics: Im’s et al. (2003) (denoted as IPS), Levin’s et al. (2002) (denoted as LLC), Breitung’s and Das (2005) (denoted as B-t) and Harris’s and Tzavalis (1999) (denoted as HT).¹⁶ The last test has higher power than the three tests for panels whose time dimension is short (finite). The test of Breitung and Das (2005) is appropriate for large T panels and it is robust to cross-sectional correlation of the panel autoregression model error terms. All the above test statistics allow for linear trends in the auxiliary regression testing for unit roots, so as to treat symmetrically deterministic trends in series $P_{it}$ and $P_{it}^{*}$ under the null and alternative hypotheses.

The results of our panel data unit root analysis are reported in Table 10. The table presents values of the above statistics. Their p-values (error type I of rejecting the null hypothesis of a unit root) are reported in brackets. The results of the table clearly indicate that $P_{it}$ and $P_{it}^{*}$ constitute I(1) series, for all i. The values of all the test statistics reported in the table can not reject the null hypothesis of a unit root at 5%, or at lower levels. The p-values rejecting the above null hypothesis are all equal to one for all the test statistics, which mean that the probability of rejecting the null hypothesis of unit root falsely equals one.

Table 10 Panel unit root tests

1.1.2 Appendix 1.1.1: Cointegration analysis

Our cointegration analysis relies on recent developments of panel data econometrics. Compared to single time series cointegration analysis, panel data cointegration methods can provide more robust and powerful inference about cointegration between series $P_{it}$ and $P_{it}^{*}$, for all i, since they are based on disaggregated data. Using panel data sets, we can avoid smoothing out possible differences in the stochastic trends of individual series $P_{it}^{*}$, or $P_{it}$, which may be proved very important for erroneously accepting the null hypothesis of cointegration between these series. The results of this analysis are reported in Table 11. In particular, the table presents values of cointegration test statistics and estimates of the slope coefficient of the following panel data cointegrating regression:

$$\begin{aligned} P_{it}=a_{i}+bP_{it}^{*}+\zeta _{it},\text { for }i=1,2,3,\ldots ,N\text { and }t=1,2,\ldots ,T\text {,} \end{aligned}$$

(7)

where $\zeta _{it}$ denotes the error term. The slope coefficient estimates reported in the table are based on the fully modified least squares (FMLS) and dynamic least squares (DLS) panel data cointegration methods suggested by Pedroni (2001), allowing for heterogenous error terms $\eta _{it}$. The cointegration test statistics reported in the table are those of Pedroni (1999). They are defined as panel-$\rho$ and panel-t, and they are based on the residuals of regression (7).

Table 11 Cointegration results

The results of the table clearly indicate that share prices $P_{it}$ and their intrinsic values $P_{it}^{*}$ obtained through formula (3) constitute a pair of cointegrated series with a long-run coefficient $b=1$, implying a cointegrating vector between $P_{it}$ and $P_{it}^{*}$ given by (1,-1). None of the cointegration tests reported in the table can accept the null hypothesis of no cointegration between $P_{it}$ and $P_{it}^{*}$, while the null hypothesis $b=1$ can not be rejected by the Wald test statistic reported in the table, denoted as Wald(1). These results mean that price deviations $P_{it}-P_{it}^{*}$ constitute stationary series, for all i. We have found that the success of the RIM to provide share prices $P_{it}^{*}$ which closely follow the long-run movements of their market counterparts can be attributed to the fact that this model relies on book values $B_{it}$. In particular, we have found that movements in $B_{it}$ determine to a large extent those in market prices $P_{it}$ and their intrinsic values $P_{it}^{*}$. Share prices $P_{it}^{{}}$ are found to be also cointegrated with their book values $B_{it}$, for all i. These results are not reported for reasons of space.

1.2 Appendix 1.1: Economic sentiment variables

The definitions of the economic variables used to construct the economic sentiment index, $SI_{t}$, based on principal component analysis are as follows:

Market share turnover is expressed in terms of trading volume and trading values. Market share turnover, or more generally liquidity, can be viewed as an investor sentiment index. Higher turnover predict lower subsequent returns in both firm-level and aggregate data (see, e.g., Baker and Stein 2004; Scheinkman and Xiong 2003). Market turnover by value is the total value of trades over the month divided by the total capitalization of the London stock exchange (LSE). Market turnover by volume is the total volume of shares traded on LSE over the month divided by the number of shares listed on the stock exchange.

Numbers of IPOs within each month First-day return of IPOs is expressed as the difference between initial trading price and offer price divided by offer price of the IPO stock. The IPO market is often viewed to be sensitive to sentiment. More specifically, high first day return on IPOs is considered as a measure of investor enthusiasm while the low return of IPOs is often interpreted as a symptom of market timing (see Baker and Wurgler 2007).

Consumer confidence is a business survey data reported by the European Commission and the European Financial Affairs. UK respondents express their economic or financial expectations over the next 12 months in the following areas: the general economic situation, unemployment rate, personal household financial position and personal savings.

Closed-end fund discount is the difference between the net asset value of a fund’s security holdings and the fund’s market price. Many authors based on the closed-end fund discounts in order to measure individual investor sentiment considering that when the discount increases the retail investors are bearish (see Lee et al. 1991; Neal and Wheatley 1998).

Put-call trading volume ratio is a measure of market participants’ sentiment derived from options. It equals to the ratio of trading volume of put options by the trading volume of call options considering a bearish indicator in the stock market. More specifically, when the trading volume of put options becomes large relative to the trading volume of call options, the sentiment goes up, and vice versa.

Put-call interest ratio is the open interest of put options divided by the open interest of call options. This ratio could be considered as a preferred measure of sentiment offering a better predictive power for volatility in subsequent periods, as it may be argued that the open interest of options is the final picture of sentiment at the end of the day or the week.

The market volatility index measures the implied volatility of options and defines the investor’s certainty or uncertainty regarding the volatility. More specifically, the higher the market volatility index is the greater the fear of investors becomes.