MSc Finance Thesis
By T. Louwman
Value Relevance of Accounting Data in Equity Valuations:
Evidence from the U.S. Pharmaceuticals, Biotechnology,
and Life Sciences Industry
Supervisor: dr. ing. N. BruniaDate: 12-06-2019
Abstract
This thesis uses a residual income model for equity valuation developed by Ohlson (1995) to shape a fundamental investor view on individual company equity valuation in the Pharmaceutical, Biotechnology and Life Sciences industry group. The model is used to show the value relevance of academic research in a practical setting by estimating the difference between the estimated and actual market value of equity. Using the margin of safety as a benchmark to test how well the estimation of market value of equity via the Ohlson (1995) framework is. As this thesis shows, the relationship between earnings, options nature of investments, R&D expenditures and the return on the market index shows value relevance in equity valuation. For this 9,687 firm-quarterly observations in a period from 1988 to 2018 are used. Coming as close as 23% from the actual market value of equity. Furthermore, this thesis shows that adjusting for heterogeneity between firms compared to using industry averages adds additional value to an investors individual firm equity valuation.
Keywords: Equity Valuation, Accounting Numbers, Firm Performance JEL-code: G1, G2, I1
1
I. Introduction
Equity valuation based on accounting information is performed by fundamental investors to determine the fair value of a security. Fundamental investors use this method to determine whether the market value of equity is in line with the value of the underlying company. In order for a fundamental investor to invest in a company, the investor determines by which percentage the market value of equity deviates from the fundamental value of equity. The maximum acceptable deviation is called the margin of safety (Larrabee and Voss, 2012). The actual market value plus or minus the margin of safety determines whether a stock is priced right or whether there is possible mispricing. Determining the fair value is important for an investor since, as Koller et al. (2015) states, noise traders1 will not be able to push prices above the fair value for
prolonged periods. This implies, over longer periods mean reversion takes place.
On the topic of equity valuation, academic literature has looked at the value relevance of accounting information (Fama and French, 2000; Ou and Penman, 1989; Holthausen and Larcker, 1992). They show that the book value of equity, earnings, and dividends contain information about stock prices. Ou and Sepe (2002) show that accounting data, both current and past, is value relevant and that investors rely heavily on analyst forecast in investment decision making. However, Dechow et al. (1999), point out that analyst forecasts are fairly optimistic, causing mean reversion of stock prices to be underestimated. Fama and French (2000), point out that the rate of mean reversion over time is 38% per year, which indicates its importance in stock price valuation. This brings up that question, “what can practitioners learn from academic literature in equity valuation?”.
Various equity valuation models have been discussed throughout past literature. However, one method in particular captures the relationship between accounting information and the market value of equity namely, the Ohlson (1995) residual income valuation (RIV) model, hereafter Ohlson model. A model based on the dividend discount model, expressing the market value of equity in terms of the book value of equity and the present value of future earnings. Ohlson (1995) models, that current value is determined by future financial performance, future financial performance is related to present financial performance, so the current value is related
1 Noise traders are nonfundamental investors, who base their trade on speculative information. Mostly these traders
2 to current financial performance. This assumption allows the Ohlson model to be used empirically. By testing the Ohlson model in an empirical setting, various researchers have shown the value relevance of current and past book value of equity and earnings.
Next to book value of equity and earnings, Ohlson (1995) also incorporates a term referred to as ‘other value relevant information’. This term refers to information not already incorporated in earnings or book value of equity. Previous literature has tried to extend the Ohlson model to see what the implication are of adding other, possible value relevant, information to the model. Zhang (2000) extends Ohlson’s (1995) and includes non-linear terms of accounting measures of performance that capture the option nature of future investments. Biddle at al. (2001) find, in line with Burgstahler and Dichev (1999), empirical evidence of the non-linear relationship between equity values and accounting measures of performance. Furthermore, Asthana and Zhang (2006) build upon value relevance of research and development (R&D), as proven by Hirschey and Spencer (1992) and Sougiannis (1994), via the Ohlson (1995) framework and find that R&D expenditures have an effect on the persistence of abnormal earnings. They also find that in large firms this persistence is larger compared to small firms. Moreover, Shah et al. (2008) finds R&D being value relevant and concludes markets not to be myopic. Furthermore, Fama and French (2000) find firms earnings showing mean reversion to the market return, implying that the return on the market has value relevant information for the market valuation of equity.
3 Previous research is dominated by cross-sectional estimation methods to determine the empirical implications of Ohlson (1995). As cross-sectional analysis looks at the time-varying nature of variables, it does not take into account the heterogeneity between individuals. The latter may be circumvented by using a time-series analysis (Callen and Morel, 2005). So, a time series analysis will provide information about the effect of value relevant information on individual companies.
As the goal of this thesis is to show how results from academic literature can contribute to improve the valuation of individual companies, a time-series evaluation of the RIV model on the PBLS industry group is conducted. In all, this leads to the following main research question;
“Do results from accounting data research help fundamental investors improve the firm level valuation of equity in the Pharmaceutical, Biotechnological and Life Sciences industry?
This thesis uses quarterly accounting data ranging from 1988Q1 to 2018Q4 on U.S. listed PBLS firms and include, the firm level book value of equity, earnings, R&D expenditures and return on the market index.
The results of this thesis confirm the value relevance of accounting information for the market value of equity. Namely, earnings, option and R&D expenditures show a positive relationship with the market value of equity. Furthermore, it shows firm-specific estimates to be a better proxy to estimate firm level market equity compared to industry averages, having a median estimation error of 23% compared to 38%. Moreover, the difference in the impact of information differs along the size2 of the company. This is especially seen with possible options
which clearly manifest itself in small and medium cap companies but not in large cap companies.
To the best of my knowledge, previous research has not taken an investor perspective on individual company valuation via the Ohlson model in the PBLS industry. Therefore, this thesis sets a base on how academic literature can help investors to determine how much the
2 This thesis makes the split between small, medium and large market capitalization (cap) companies.
4 fundamental market value of equity deviates from the actual market value of equity. In addition, it helps them to evaluate whether to dive deeper into a certain company.
This thesis will proceed as follows, section II reviews the theoretical model and previous empirical research, section III explains the sample data and research methodology data, section IV provides the estimation results and section V discusses the main conclusions.
II. Literature Review
The following section discusses the background on which this thesis is built. First, equity valuation models in general are discussed. After which, the equity valuation model as proposed Ohlson (1995) is explained. Lastly, previous (empirical) literature relating accounting data to equity market valuation based on the Ohlson model is lined out. This includes various extensions, (dis)advantages using the model and problems which may arise empirically when using the model.
Equity Valuation models
Generally, there are three equity valuation models, the dividend discount model (DDM), the discounted cash flow (DCF) model and the residual income (RIV) model. In the DDM, the market value of a company is calculated as the present value of expected future dividends and can be mathematically shown as;
!"#= ∑ &(()*+)
(-./)+
0
12- (1)
where,
!"# Firm value at end of period t; 3# Dividends at the end of period t; r Firm’s cost of capital.
5 In corporate finance practice, the DCF model is most commonly used among equity valuation methods. However, in prior academic literature, the RIV model is pointed out to better reflect market prices of securities than the DCF model (Callen and Morel, 2005).
As can be seen in the mathematical form of the three models, forecasting is based on an infinite horizon. However, for practical use, an investor needs a finite forecasting period and a “continuing value” at the end of the forecasting period (Penman, 1998). As Penman (1998), points out, this “continuing value” is hard to substantiate and based on numerous assumptions. Fundamental equity valuation models, such as the RIV model proposed by Ohlson (1995) are developed to overcome the need for a “continuing value”.
The Ohlson (1995) model
The Ohlson model is an extension of the linear RIV model and useful for estimating the relationship between the market value and accounting information. The RIV model of Ohlson speaks of “abnormal earnings”, instead of “residual income”, which is the reason why this thesis also refers to this as “abnormal earnings”.
To get a better understanding of the Ohlson model, first, the assumptions which the model is based upon are explained. Three key assumptions underlie the Ohlson model. First, today’s market value is the present value of future dividends as denoted by equation 1.
Second, the underlying assumption of the Ohlson model is the clean surplus relationship (CSR) between book value and earnings. The CSR assumption implies that the change in book value is equal to earnings less dividends paid out, so that;
3# = 4#+ 6"#7-− 6"# (2) where,
6 In line with the dividends irrelevance theorem of Miller and Modigliani (1961), Ohlson (1995) uses this relationship to state that, future earning are related to abnormal earnings and book values;
9# = 4#− : ∗ 6"#7- (3)
where,
9# Abnormal earnings at the end of period t.
Abnormal earnings can therefore be seen as earnings made during period t minus the cost of using capital. Equation 3, allows the RIV to be rewritten as the market value of equity equal to the current book value of equity and the present value of abnormal earnings (Dechow et al., 1999);
!"#= 6"#+ ∑ &(<)*+)
(-./)+
0
12- (4)
The third assumption is referred to as the linear information dynamics (LID) assumption and relates the firm intrinsic value to market information via;
9#.- = =--9#+ =->?#+ @-,#.- (5) ?#.-= =>>?#+ @>,#.- (6) where,
9# Abnormal earnings (earning in excess of the cost of equity capital) in period t ;
?# Denotes other information not included in earnings and book value at the end of period
t;
@B,#.- Uncorrelated over time and zero-mean error terms ;
=-- Constant persistence parameter of abnormal earnings, taking on a value between zero and one
=>> Constant persistence parameter of other information, taking on a value between zero and one
7 and comes up with two determinants of the persistence of abnormal earnings over time namely dividends policy and industry characteristics. These two determinants lead to the bases for the mean reversion assumption, in markets increasing competition is observed when highly profitability rates are reached and decreasing competition is observed in low profitability markets.
So, the current market value of equity is equal to the current book value of equity and the present value of future abnormal earnings. Combining the concepts of equation 4 with equation 5 and 6, the valuation function becomes;
!"#= 6"#+ D-9#+ D>?# (7) where, D- = (- . /) 7 EEFF FF D> = (- . / 7 E -./ FF)(- . / 7 EGG)
To conclude, firm value is a function of the current firm book value of equity plus a multiple of current abnormal earnings plus a multiple of current other information. Via this model, Ohlson (1995) developed a framework which could be used in empirical accounting based analysis of the market value of equity.
Empirical studies on the Ohlson (1995) model
As the Ohlson model allows for the addition of information which is not captured by either book value of equity nor earnings, prior studies have tested the Ohlson model empirically in different markets and settings. Here, the focus is on the valuation link of the Ohlson model, the assessment of the fundamental value of the firm via equation 7.
8 One research in favour of the Ohlson model is conducted by Pennman and Sougiannis (1998). They compare the dividend cash flow and residual income approaches, finding evidence for the equity valuation models based on earnings, as the Ohlson model, to have higher explanatory power compared to the other two discussed approaches.
On the contrary, even though many researchers have argued in favour of using the Ohlson model in equity valuation, other researchers have found problems with the Ohlson model empirically. Dechow et al. (1999), exercise a cross-sectional analysis of the Ohlson model and reject the model. In addition, Myers (1999), also rejects the Ohlson model in a time-series analysis. Both Dechow et al. (1999) and Myers (1999) acknowledge the relevance of including other information since it yields more accurate results but find it almost impossible to implement the other information factor since it is not always event driven. As an example, Myers (1999) comes up with the idea that market sentiment is likely to have an impact as well. However, market sentiment is hard to measure via accounting information. This makes it difficult to propose a set of information characteristics to be used for consistent reflection of price drivers.
To conclude, a limitation of the model is not specifying the “other information” factor, causing various researchers, under whom Callen and Morel (2005), to drop this variable from the model and focus on the main components opted by Ohlson (1995). Other studies, do try to find value relevance accounting information (e.g. Biddle et al., 2001; Burgstahler and Dichev, 1997; Hirschey and Spencer, 1992).
The other information factor
As shown, the other information is indeed relevant in the Ohlson model. Therefore, various research has tried to find an explanation for this.
Option-style characteristic of earnings
9 such that earnings can be seen as an option-style variable in the valuation of the market value of equity.
In general, since a firm has the option of continuing current activities or use resources for an alternative purpose, a function of the assets in place, book value of equity, and earnings determines the market value of equity (Burgstahler and Dichev, 1997). The twofold in the use of resources is the reason for a firm to have an like structure in its earnings. This option-like structure represents a non-linear effect of earnings on the market value of equity. Burgstahler and Dichev (1997), develop a model in which they state that the effect of earnings on the market value of equity depends on the profitability of a company. In other words, they assume firms with higher earnings to book value will be more likely to use the earnings to increase future performance compared to low profitability companies since the benefits are higher. Their research finds, different levels of the book value of equity, earnings show different effect, which is a non-linear and convex valuation function. Concluding, the impact of earnings on the market value of equity increases with earnings to book value and this is inversely the effect of the book value of equity, showing this convex relationship between earnings, the book value of equity and the market value of equity.
More formally, Zhang (2000) comes up with a model to describe the option-like characteristics of earnings in a company. He states, that the level of profitability of a firm has an impact on the investment decisions they make. For steady-state firms, the options are less likely to be observed, since in the moderate climate they operate in no large investment opportunities or distress scenarios will take place. However, highly profitable companies will try to expand their business due to the arising investment opportunities high earnings bring. On the contrary, low profitable firms are more likely to discard their operations, due to the lack of investment opportunities and the lack of profits. For high profitability firms in this case, abnormal earnings are the main driver behind the market value of equity, whereas, for low profitability firms book value of equity is this driver.
10
Research and Development
The investors view on firm valuation goes beyond financial performance, another important factor is financial health (Koller et al., 2015). R&D expenditures can be viewed as investments in future performance, since it is exploring options for future growth opportunities. Furthermore, the reason for investing in future performance implies that a company is currently doing well and has room to invest in the future. The more invested in the future, the more certain a company might be that it will still be around in that period. Therefore, a company’s R&D expenses can be viewed as a measure of current financial health. And as pointed out by Cockburn and Long (2015), in the PBLS industry group R&D is more important compared to other industries.
In line with the importance of R&D in the valuation of equity, Hirschey and Spencer (1992) find, via a cross-sectional analysis, that R&D has value relevance in all size classes. Even though R&D is value relevant over all size classes, it is vitally for small market capitalization (cap) companies. That is, small cap companies use R&D investment more efficiently compared to their larger competitors.
Furthermore, a cross-sectional investigation of large U.S. companies by Sougiannis (1994) also find that R&D expenditures have a significant positive effect on the market value of equity. Sougiannis (1994) splits the explanation into two parts namely, an indirect and direct part. First, indirect via abnormal earnings it has a negative effect, due to the increase in expenses and therefore lowering abnormal earnings. Second, direct via R&D expenditures having an effect on the assumed future earnings, increase in R&D expenditures provides investors with information about potential future earnings and is therefore reflected by the “other information” variable (Z).
11 Asthana and Zhang (2006) combine the idea of Hirschey and Spencer (1992) and Sougiannis (1994), by looking into the size effect of R&D expenditures on the persistence on abnormal earnings. By conducting a panel analysis, they find that larger firms have a higher significant effect on the persistence of abnormal earnings than small firms.
A panel data analysis by Shah et al. (2008) finds that the market is not myopic since they find value relevance of R&D in market valuation of equity. Compared to Asthana and Zhang (2006) and Hirschey and Spencer (1992), Shah et al. (2008) do not find that large cap firms have a clear cut advantage over small cap firms in terms of R&D expenditures. Moreover, they also look into industry differences in which they find that, for the Pharmaceutical and Biotechnology industry, R&D shows a significant positive relationship between the market value of equity and R&D expenditures.
Return on the stock market index
As pointed out at the beginning of this section, Ohlson (1995) assumes mean reversion of profits via linear information dynamics, which is driven by the industry characteristics. Dechow et al. (1995) point out that profitability is related to industry-specific characteristics. Profitability is related to industry competition, the rate of mean reversion. Thus, there is an indirect relationship between industry-specific characteristics and market value of equity. Fama and French (2000) build upon this finding by showing mean reversion to the market return over time of more than one third. Moreover, they find that the market to book ratios can predict future earnings. They based this result on the observation that when the market return is increasing in year t, the return on assets increases in year t+1. This implies that the return on the market index can be seen as an indicator of future profitability.
III. Research Methods and data
12
Sample selection
The initial sample includes all firms from the PBLS Industry Group (Global Industry Classification Standard 3520) that have been listed on the New York Stock Exchange, the American Stock Exchange and NASDAQ-NMS Stock Market between 1988 and 2018. This resulted in 1,232 unique firms, being unbalanced panel due to mergers, acquisitions, IPOs, delisting, bankruptcies, etcetera.
The quarterly acting and market data are retrieved from Compustat3, using the same variable
codes as Biddle et al. (2001). Furthermore, return on the market index is retrieved from the Kenneth French data library4. The variable specification can be found in tables 2 and 3. This
results in 48,674 firm-quarter observations.
As explained by Hou et al. (2017), anomalies are largely caused by microcaps and should therefore be excluded from the sample. Therefore, in line with Fama and French (2006), years in which a firm has a book value of equity less than 12.5 million USD are excluded from the sample for that particular firm, this in order to account for undue influence of small firms. When considering the performance over the lifetime of firms in the industry group, figure III.1 shows, over half the sample is on average negatively performing over their lifetime (loss firms). Since Ohlson (1995) suggests book value of equity to be a proxy of expected future normal earnings. For loss firms this is even more the case, since current earnings aren’t informative about future earnings. As Collins et al. (1999), point out is that the relationship between the market value of equity and earnings is not homogenous across profit and loss firms. They find, loss firms to have a lower capitalization rate on earnings compared to profit firms. Implying that including both profit and loss firms in the same sample can give a biased estimation coefficient of earnings. Therefore, loss firms are excluded from the sample.
Moreover, as in line with Biddle et al. (2001) and Burgstahler and Dichev (1997), to account for unrepresentative the dataset is trimmed on the bottom and top 3% of earnings to book ratio and 3% of the market to book ratio.
13 In table III.1. one can see how the used sample is constructed. The raw data column displays the number of firm-quarterly observations and the number of firms in the raw data sample. Microcap, trimming and negative earnings display the total number of observations and the number of whole firms excluded from the sample. The reason for the number of firms in the sub-samples not to add up to the total number of firms is that some firms transfer from one group to another from year-to-year, so they are included in a category for the years they meet the criteria.
Table III.1. Sample development in number of observations (number of firms) Raw data Microcap Negative earnings Trimming Total sample
Industry Group 48,674 (1232) 11,894 (200) 26,115 (825) 978 (0) 9,687 (207) Small cap 4,242 (153) Medium cap 1,998 (96) Large Cap 3,447 (183)
When executing the exclusion of observations from the sample as described above, the final sample contains 207 unique firms with 9,687 firm-quarterly observations.
14 Figure III.1. Observations in the sample over time
Variables
As said, table III.2. displays the variable explanation both retrieved variables from Compustat database, Kenneth French Data Library and constructed variables. Table III.3. displays the description of the constructed variables used in the estimation models. Earnings used in this thesis are denoted as earnings before extraordinary items, even though the violation of the clean surplus accounting as mentioned by Lo and Lys (2000). However, earnings before extraordinary items is commonly used as variable in equity valuation for security analysis because it avoids one-time line items. Reason for avoiding one-time line items is that the long-term fundamental investor focuses on long horizons and in this one-time line items do not add value. Furthermore, the book value of equity only contains commonly issued equity, as preferred equity can be viewed as debt equivalent.
Table III.2. Description of retrieved variables Symbol used
in model Variable name Compustat code Additional notes 6"# Book value of equity CEQQ
4# Earnings IBQ Income before extraordinary items
H# Share Price PRCCQ Closing Share Price
I# Common Shares Outstanding CSHOQ J3# Research and Development Expenditures XRDQ JK# Return on the stock market
index Retrieved from the French Database
0 100 200 300 400 500 1988 2018
15 Table III.3. Description of constructed variables
Symbol used
in model Variable name
Method of
construction Additional notes !"B# Market value of equity HB#∗ IB# Common shares only !"B#L Scaled market value of equity
!"B# 6" B,#7-!"B#LL Scaled unrecorded goodwill
!"B#− 6"B# 6" B,#7-4B#L Scaled earnings
4B# 6" B,#7-(4B#L)> Scaled option term M 4B#
6"B,#7-N >
J3B#L Scaled R&D expenditures
J3B# 6" B,#7-JK#L Scaled return on the stock market index
JK# 6"
B,#7-Summary statistics
16 Table III.4. Summary statistics sample
P∗∗∗∗ mean median Std. Dev. min max
Panel A. Retrieved variables Compustat*
!" 8,109 16,190 1,698 38,616 0.01 370,732 6" 8,560 3,981 459.90 11,046 12.52 90,018
4 9,199 180.60 11.77 536.60 -6,273 12,274
J&3 4RSTIUVWX:TY∗ 7,834 193.20 13.51 480.80 -1.49 9,235
Panel B. Retrieved variable from Kenneth French Database**
JK 9,687 2.68 3.67 7.87 -23.24 20.40
Panel C. Constructed variables for estimation
!"B#LL 7,887 3.55 2.52 21.14 -459.20 1,719
4B#L 8,457 0.04 0.03 0.11 -3.51 4.19
(4B#L)> 8,457 0.01 0.00 0.29 0 17.54
J3B#L 7,384 0.05 0.04 0.10 -2.80 6.01
JKL 8,609 0.07 0.00 2.45 -25.31 182.70
Panel D. Constructed variables for data selection***
H 4 O 9,687 40.05 54.07 42.02 -60.77 96.00 !" 6" O 9,687 4.63 4.32 0.95 3.41 7.80 Number of firms 207
* Unscaled variables are displayed in millions of USD ** Return on the stock market index is measured in real terms
*** price-earnings and market-book ratio are displayed as median values **** Firm-quarterly observations
All variables except for JK and H 4O are skewed to the right. In small sample sizes, this implies that normality assumptions are not met, however, considering the number of observations, large sample theory applies and therefore this effect is neglected in this thesis. Summary statistics of the sample divided into small, medium and large cap firms can be found in appendix A. Moreover, all variables are scaled in order to avoid non-stationarity of the time-series. The results of the unit root tests are included in appendix B.
The scaling is based on the same method used by Burgstahler and Dichev (1997). Equation 7 is divided by the lagged book value of equity, resulting in;
17
Model specification
First of all, this thesis uses the Ohlson model in an empirical setting introduced by Biddle et al. (2001), using unrecorded goodwill as the depended variable. The unrecorded goodwill is, as can be seen in table III.3. the result of subtracting book value of equity from the market value of equity. Secondly, since examining the value of the cost of capital is beyond the scope of this thesis equation 8 is written in a way to eliminate the obligation to specify the value of the cost of capital. These two remarks lead to equation 9;
!"#L−6"#L= D1(4W− :6"W−1)L+ D 2?#L+@W (9) Where, !"#L−6"#L = !"#LL; D-(4#− :6"#7-)′= D-(&)7/^_)`F) ^_)`F = D-4W ′− D -/^_^_)`F )`F = D-4W ′− D -:.
Shows that −D-: becomes constant. So that;
!"#LL= D0+ D14#L+ D2?#L+ @W (10) As ?# represents all other value relevant information, the model used to estimate the theoretical market value of equity in this paper can be specified as;
!"#LL= D
0+ D14#L+ D21(4#L)2+ D22J3#L+ D23JK#L+ @W (11) Techniques to estimate the theoretical market value of equity are cross-sectional regression, time-series regression and panel fixed or random effects regression (Brooks, 2014). From an investors perspective, the goal is to estimate the most accurate individual firm market value of equity. The estimation of the market value of equity on a firm level perspective is, in this thesis, done via equation 11. To account for firm-specific characteristic the time-series model is used. Via the time-series approach firm-specific coefficient estimates are estimated. In order to account for outliers and negative values to compensate for positive values, leading to biased results, the median value instead of the mean value is being evaluated.
This technique pools together all available years for each company separately. This reasoning results in the following model specification;
!"B#LL= D0V+ D1V4B#L+ D21V(4B#L)2+ D
18 Here, accounting for firm heterogeneity seem most appropriate. After testing for heteroscedasticity and autocorrelation, of which results can be found in appendix B, the regression has been corrected with Newey West Standard Errors (Hill et al., 2011).
From section II, expectations concerning the direction of the effect of the various variables can be made. In general, the relationship between the variables and the market value of equity is expected to be positive. Furthermore, one would expect the effect of the constant displayed in equation 12 to be negative, due to DcB to be defined as −D-:. However, due to the linearization of the model by including the quadratic term, this constant become uninterpretable.
Determining the estimation Error
On a statistical base one will look at the (adjusted) R-squared to see how of the variability in the dependent variable is explained by the independent variables. However, an investor’s objective is not to explain the variation of independent variables versus the dependent variables. An investor has as objective to be as close to the actual market values of an individual company as possible. Therefore, one can determine how much the estimated market value of equity is off the actual market value of equity. To assess this error, one needs to transform the estimated scaled unrecorded goodwill, which can be calculated by;
!"dB#LL= De0V+ De1V4B#L+ De21V(4B#L)2+ De22VJ3B#L+ De23VJK#L (13)
To the estimated market value of equity is off of the true market value of equity, using the transformation seen from equation 9 to 10 coming to;
!"dB# = f!"dVW′′∗6"B,#7-g + 6"B# (14) To evaluate how the model runs on an industry level, the mean and median values of the errors are considered;
∑jikF(h_di)7h_i))
l (15)
19 Therefore, in addition, due to this evaluation method, consider the absolute errors, this in order to overcome the problem of overvalued companies compensating undervalued companies in the mean and median values of the errors;
∑jikF(|h_di)7h_i)|)
l (16)
Equation 16 is therefore used to overcome biased results.
As past performance is no guarantee for future results, an investor will try to determine a margin of safety. This margin of safety is a margin which is the maximum deviation the estimated market value can be off of the actual market value (Larrabee and Voss, 2012) and still be considered fair valued. This is under the assumption that the model used to estimate the market value of equity has the right specification. This deviation determines whether a security analyst gives a recommendation to buy, hold or sell. In this thesis, the margin of safety is used to determine whether, assuming the market values have on average the right price (Arbitrage Pricing Theory by Ross, 1976), the model is doing a reasonable job in predicting the market value of equity. The margin of safety is a subjective, and therefore arbitrary number, previous research has taken various thresholds to evaluate results. Ou and Penman (1982) and Holthausen and Larcker (1992), argue to use a cut-off percentage, giving a certain margin of safety, from the fundamental value in order to determine whether a security is over- or under-priced. Bradshaw (2004) argues that within a 30% deviation of the fundamental value a securities analyst should give a hold recommendation. This implies, when the market value of equity deviates 30% from the estimated market value of equity, the model is doing a reasonable job to determine the market value of equity of a firm. On the contrary, Koller et al. (2015), uses a 15% margin of safety to evaluate investment opportunities. The results will reflect on both these numbers and in general on the (absolute) estimation error.
Potential Size Effects
As pointed out, this thesis will make an analysis on firm level bases. In order to do that, the sample is divided into three size samples, small, medium and large market capitalization companies.
20 more on cash flows generated by current operations. As pointed out, both option-style term and R&D are some in a way connected to possibilities of opportunities. In line with Hirschey and Spencer (1992), this implies small firms, compared to their larger competitors, will have a larger impact on their market value of equity of options and R&D compared in comparison to the weight of book value of equity and therefore on the market value of equity. Therefore, implementing a shift between large, medium and small market capitalization gives an interesting insight into the effect of earnings, options, and R&D on the market value of equity.
Loss firms
As mentioned previously in this section, due to possible bias in the parameters, loss firms are excluded from the sample at first, implying over 80% of firms and observations are excluded. However, to assess the impact of including the loss firms, as found by Collins et al. (1999), the same time-series regression as on the main sample, is conducted on a sample pooling profit of loss firms together.
Firm-specific versus industry parameters
However, assumed is that firm-specific parameters give a more accurate estimation of the market value of equity. When estimating firm-specific risk, Koller et al. (2015) point out, that considering industry betas compared to firm-specific betas a better estimate can be derived assuming the correlation between estimation errors across companies is equal to zero. This might have implications for equity valuation as well. To verify that firm-specific parameters are adding value for individual company valuation, a panel model regression is conducted. The panel data regression is written in the form of;
!"B#LL= D0+ D14B#L+ D21(4B#L)2+ D
21
IV. Results
The results are presented below in tables IV.1. to IV.5. First, the overall firm-by-firm median time-series regression coefficients are presented in table IV.1. Since the interpretation of median t- and therefore p-values do not necessarily match the coefficient estimate’s median value, table IV.3. present the percentage of significant and insignificant values for the firm-by-firm regression estimates. As an investor is interested in how accurate a model predicts the true market value of a firm, tables IV.4. and IV.5. shows both the estimation and absolute estimation error of the true market value of equity compared to the estimated market value of equity. Thereafter, to see the impact of assumptions made in this thesis for the main sample and time-series regression on the estimation of the market value of equity, the effect of loss and profit firms, and the effect of industry versus individual parameters is shown.
Before going to the results, a couple of remarks should be made on the interpretation of the results. First, since the small cap companies represent approximately half of the sample, both company and observations wise, this might give a biased result in the overall results. However, to see how to PBLS industry group is doing in general, the overall results are discussed first before splitting the sample up between market capitalization sizes. Second, the results will be focussed on the effect of the independent variables on the market value of equity instead of on the unrecorded goodwill for two reasons. The first reason is that the reflection of results on previous research, since previous research has also reflected on the market value of equity and not on unrecorded goodwill. The second reason, because unrecorded goodwill is the reflection of the effect of the variables on the market value of equity which is not caused by the book value of equity.
Effect of accounting data and the size effect
22 parameters, implying no significant relationship between the depended variables and market value of equity.
Table IV.1. Time Series – Regression results (profit firms) Overall
Mean Median St. Dev. Min Max
DcB 1.14 1.00 2.32 -9.96 7.44 D-B 14.54 13.47 47.71 -153.04 260.63 D>-B 214.67 77.37 788.84 -1,509.29 5,610.74 D>>B 31.22 24.22 121.02 -659.84 1,000.03 D>nB 10.51 0.68 128.84 -388.96 1,102.34 n 49.43 41 29.7 12 119 N 138 Adj. R-sq. 0.43 0.39 0.31 -0.14 1.00
N. is the total number of firms
n is the number of time periods per firm-specific betas
As an investor looks to see how the dependent variables affect individual companies, table IV.2. shows the effect of accounting information along the three market capitalization groups, a firm-specific characteristic.
23 Table IV.2. Time Series – Regression results (profit firms)
Small Medium Large
Mean Median St. Dev. Min Max Mean Median St. Dev. Min Max Mean Median St. Dev. Min Max
!"# 0.76 0.72 3.47 -20.10 11.23 29.23 26.50 15.28 8 74 0.94 1.30 4.13 -10.00 8.46 !$# 27.72 11.51 119.33 -124.24 981.28 2.30 1.37 7.00 -8.55 45.01 31.15 32.68 84.40 -254.55 224.50 !%$# 19.27 48.73 1,633.69 -10,900 5,610.73 631.24 94.51 2,697.43 -963.21 19,324.81 16.39 -20.40 985.59 -1,825.73 4,397.61 !%%# 17.87 23.01 105.19 -640.95 349.52 77.41 30.25 188.41 -278.23 1,000.03 51.25 23.94 90.52 -44.94 410.77 !%&# 0.55 0.61 14.29 -110.88 51.59 5.43 5.00 54.31 -163.72 141.86 103.62 -0.12 332.70 -281.49 1,102.34 n 32.83 27 19.03 10 103 30.75 29 14.80 11 74 52 43.50 32.42 8 119 N 102 56 32 Adj. R sq. 0.46 0.45 0.33 -0.14 1.00 0.45 0.45 0.32 -0.22 0.99 0.33 0.35 0.36 -0.99 0.92
N. is the total number of firms
24 Table IV.3. Time Series – Percentage of firms with a certain sign (profit firms)
Overall Small Medium Large
Sign. + Sign. - Insign. Sign. + Sign. - Insign. Sign. + Sign. - Insign. Sign. + Sign. - Insign.
!"# 45% 9% 46% 35% 12% 53% 46% 7% 46% 41% 16% 44%
!$# 42% 12% 46% 41% 12% 47% 20% 16% 64% 44% 6% 50%
!%$# 32% 19% 49% 34% 18% 48% 34% 11% 55% 9% 16% 75%
!%%# 54% 7% 39% 48% 8% 44% 61% 7% 32% 53% 0% 47%
!%&# 23% 13% 64% 28% 13% 59% 18% 20% 63% 19% 13% 69%
25 Table IV.4. Time Series – Estimation Error Results (profit firms)
Overall
Mean Median St. Dev. Min Max Estimation Error -0.15 -0.06 0.50 -4.76 4.38 Abs. Estimation Error 0.34 0.23 0.39 0 4.76
N 6,289
N is the number of estimations
Table IV.5. Time Series – Estimation Error Results (profit firms)
Small Medium Large
Mean Median St. Dev.
Min Max Mean Median St.
Dev.
Min Max Mean Median St.
Dev.
Min Max Estimation Error -0.15 -0.05 0.54 -4.51 4.38 -0.076 -0.031 0.31 -2.47 0.88 -0.11 -0.05 0.36 -1.92 1.60
Abs. Estimation Error 0.36 0.23 0.43 0 4.51 0.22 0.16 0.23 0 2.47 0.28 0.20 0.26 0 1.92
N 2,981 1,461 1,531
26 As pointed out, confirming the findings by Shah et al. (2008), R&D expenditures are in all size classes clearly apparent, ranging from 23.01 for small cap companies to 30.25 for mid cap companies, implying that the market is not myopic. As Hirschey and Spenser (1992) argue, medium cap companies have a greater magnitude compared to large and small cap companies. In this sample however, small cap companies tend to have a comparable influence of the R&D expenditures on the market value of equity as large cap companies, 23.01 compared to 23.94. This is not in line with Hirschey and Spenser (1992), who find a clear advantage of small cap firms compared to large cap firms. Reason for this might be the nature of R&D in a company. As R&D can be both internal and acquired, not including acquired R&D might give biased results. Furthermore, small firms might be more reliant on patents compared to large firms (Hirschey and Spencer, 1992; Cockburn and Long, 2015). Thus, R&D can in addition be viewed as an option on future profits, the value relevance of R&D expenditures on the market value of equity is maybe partially already explained via the effect of the option-style term. Furthermore, in terms of significant coefficients for R&D expenditures, medium, 61%, and large, 53%, cap companies show the largest portion of significant expected sign pattern for all variables. A reason behind large cap companies to be outperformed by medium cap companies might be due to the fact that for example, major pharmaceutical firms acquire innovative, mostly small cap and start-ups, firms so they will not increase R&D expenditures but increase acquisition expenses in order to acquire R&D.
Only a small portion of the sample firms show a significant, either positive, ranging from 18% to 28%, or negative, ranging from 13% to 20%, relationship of the return on the market index and market value of equity. Since in the time-series regression the time component is seen as absorbed the current return on the market index on future periods might, via this approach, not completely represented in the market value of equity.
27 priced correctly. However, if Koller et al.’s (2015) 15% is considered as a margin of safety, less than 50% of the sample is rightly priced. As the margin of safety depends on the investor’s view, for some investors there will be more companies within the margin of safety and therefore to look further into compared to others.
The effect of loss firms
This thesis finds loss firms to have a deflating effect on the parameter the earnings of profit firms. As pointed out by, Collins et al. (1999), pooling both profit and loss firms together cause biased results due to the difference in capitalization rate of earnings. As in investor looks into firm-specific characteristics, the main sample of this thesis, as pointed out in section III, excluded loss firms. Excluding loss firm has a large impact on the sample size, namely over 80% of the sample is excluded from the regression. Results from the pooled sample are shown in tables IV.6. to IV.8.
Table IV.6. shows, in comparison with table IV.1., the estimated median earnings coefficient decreases from 13.47 to 3.28. Moreover, the option-style term showing the potential for highly profitable companies also decreases from 77.37 to 5.43. These results are in line with Collins et al. (1999) who find a deflation effect of combining loss firms with profit firms, due to the lower earnings parameter of loss firms. For results of the size effect on pooling profit and loss firms, see appendix C.
Table IV.6. Time Series – Regression results (profit and loss firms) Overall
Mean Median St. Dev. Min Max
!"# 1.12 0.86 2.73 -12.38 16.49 !$# 1.02 3.28 44.81 -359.57 271.19 !%$# 68.21 5.43 413.13 -1,509.29 5,613.24 !%%# 17.53 18.78 79.29 -659.84 1,000.03 !%&# 5.77 1.44 74.38 -309.12 1,137.53 n 37.23 29 23.657 14 120 N 558 Adj. R-sq. 0.55 0.57 0.32 -0.21 1
N. is the total number of firms
28 Table IV.7. Time Series – Percentage of firms with a certain sign (profit and loss firms)
Overall
Sign. + Sign. - Insign.
!"# 39% 11% 50%
!$# 38% 3% 59%
!%$# 36% 19% 45%
!%%# 50% 13% 37%
!%&# 32% 13% 55%
Sign. + The coefficient having a significant (minimum 10% significance level) and positive
Sign. – The coefficient having a significant (minimum 10% significance level) and negative effect
Insign. The coefficient having an insignificant effect
Furthermore, looking at table IV.8., the same conclusions can be drawn as in the main sample, the median absolute estimation error, 29%, is still within the margin of safety as suggested by Bradshaw (2004), and outside the margin of safety set by Koller et al. (2015), however the estimate has become worse not only overall but also over the size classes.
Table IV.8. Time Series – Estimation Error Results (profit and loss firms) Overall
Mean Median St. Dev. Min Max Estimation Error -0.24 -0.08 0.77 -8.88 11.13 Abs. Estimation Error 0.48 0.29 0.64 0 11.13
N 18,798
N is the number of estimations
To conclude, the bias in estimated earnings parameters and an increase in the estimation error in the market value of equity show just reason for investors to make a distinction between loss and profit firms.
Industry parameters versus firm-by-firm parameters
29 firm-specific characteristics, are especially important. This subsection compares firm-specific parameters to industry average parameters and their effectiveness in estimating the market value of equity. The results of the panel regression are displayed in table IV.9. and IV.10.
Table IV.9. Fixed effects model – regression results
Overall Small Medium Large
'()*. '()*. '()*. '()*. !"# 0.65 (0.42) 0.30 (0.33) -0.08 (0.37) 1.53*** (0.29) !$# 14.35 (9.07) 10.98 (10.76) 17.88*** (5.89) 23.74*** (4.63) !%$# -14.53*** (3.07) -13.68*** (3.35) -110.37 (77.57) 64.41 (48.89) !%%# 51.31*** (8.51) 50.82*** (9.47) 81.24*** (12.49) 25.94*** (4.37) !%&# 6.38*** (1.15) 6.48*** (1.17) 22.39 (22.72) 88.02 (75.03) n 166 134 83 51 N 6,960 3,497 1,746 1,717 Adj. R-squared 0.78 0.85 0.58 0.26
N. is the number of total observations n is the number of firms
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
When estimating industry average parameters for the various factors, a number of interesting results appear in the area of a bias towards small cap companies, the negative effect of options and the expected size effect through R&D expenditures.
30 of profitability and the market value of equity. This result seems economically unfeasible as in that case higher profitability is related to a lower market value of equity. Third, looking at R&D expenditures, medium cap companies still have a bigger magnitude compared to small and large cap, 81.24 compared to 50.82. In contrast to the time-series approach, the fixed effect regression does find, in line with Hirschey and Spenser (1992), evidence for small cap firms being more efficient with R&D expenditures compared to large cap competitors. Which can be observed via a significant positive magnitude of almost double compared to its large cap competitors, 50.82 compared 25.94. Fourth, considering time variation in the model causes the return on the market index to get a greater positive magnitude in all size classes. However, it still does not have any influence on the market value of equity with medium and large cap companies.
Table IV.10. Fixed effects model – Estimation Error Results Overall
Mean Median St. Dev. Min Max Estimation Error -0.31 -0.13 0.84 -9.32 3 Abs. Estimation Error 0.57 0.38 0.69 0 9.32
N 6,598
N is the number of estimations
Moreover, the statement made by Koller et al. (2015) on industry betas versus firm-specific betas, does not find support in this thesis. This implies that using a firm-specific model, such as the time-series firm-by-firm approach, is the right choice for individual firm valuation. This results from the absolute estimation error, calculated with the fixed effect estimates, to give worse prediction results compared to the firm-specific estimates. The absolute estimation error even falls outside the margin of safety assumed by Bradshaw (2004), where in the time series approach it wouldn’t.
31 Table IV.11. Fixed effects model – Estimation Error Results (profit firms)
Small Medium Large
Mean Median St. Dev. Min Max Mean Median St. Dev. Min Max Mean Median St. Dev. Min Max Estimation Error 33 -0.13 0.98 -8.98 3.31 -0.23 -0.06 0.81 -7.93 1.31 -0.24 -0.17 0.51 -3.07 0.70
Abs. Estimation Error 0.68 0.44 0.79 0 8.98 0.54 0.39 0.642 0 7.93 0.42 0.32 0.39 0 3.07
N 3,134 1,540 1,599
32
V. Conclusion
The aim of this thesis is to see how academic accounting research results can contribute to improve the equity valuation of an individual firm for a long-term fundamental investor. The equity valuation model, a residual income model, used in this thesis, is the framework developed by Ohlson (1995). The use of a firm-by-firm time series model makes the RIV model applicable on firm level bases independently from the availability of data from other firms. In general, the RIV model is seen as a comprehensive tool for an investor to determine a firm’s market value of equity in general. Applying the RIV model on firm level bases provides investors insight into how much the equity value on the market is off from the fundamental equity value. This thesis proves that firm-specific indicators such as size, earnings, and R&D expenditures contribute to the estimation of market equity values of individual firms compared to industry average parameters. Moreover, these factors can be used to determine whether a firm is worth looking into from an investor perspective.
To come to these implications, this thesis uses the Ohlson model to estimate the fundamental market value of equity. For this estimation quarterly accounting data on the common book value of equity, earnings, R&D expenditures and return on the market index is used. Via a firm-by-firm time-series regression, firm-by-firm-specific parameters are estimated for a sample containing 1,232 firms and 9,687 firm-quarterly observations of the period from 1988Q1 to 2018Q4. The sample contains, small, medium and large cap profit companies, in addition, loss firms and microcap firms are excluded from the sample. The exclusion of loss firms from the sample has caused over 80% of the firms and observations to be excluded from the retrieved data, making it an assumption which should be verified for validity. Next to magnitude, direction and significance of the individual parameters is value relevant information for an investor, the difference between the actual market value of equity and the estimated market value of equity is useful to see how well the accounting data explains the actual market value. This under the assumption that on average the value of equity is priced right in the market. To evaluate the accuracy of the estimated fundamental market value of equity against the actual market value of equity, the concept of a margin of safety is used.
33 market index was expected to have a positive effect on an individual stock, this thesis does not find support for this claim. Furthermore, evidence is found for the value relevance of firm-specific characteristics in accounting data, such as the evidence for using individual firm parameters versus industry parameters, presence of size effects and difference between profit and loss firms.
The evidence for differences between individual firms and the industry average is shown by the firm-by-firm parameters to give a better approximation of the market value of equity compared to industry parameters. The presence of size effects is observed since the error between the estimated market value of equity and the actual market value of equity of medium cap companies, compared to small and large cap companies, is the smallest. In addition, dividing the sample based on size shows that the value relevance of various accounting numbers is different depending on the firm size. Namely, options seems to be more important for small and medium cap firms, whereas, large cap firms seem to have a more linear relationship between the market value of equity and earnings. Moreover, R&D effect of medium cap firms seems to be the most important. Furthermore, the assumption of dividing the sample in loss and profit firms is justified due to the proof of earnings parameter deflation caused by loss firms. Namely, including loss firms deflate the earnings term compared to the sample including only profit firms.
This thesis sets a basis for the value relevance of academic accounting data research for a long-term fundamental investor in individual firm equity valuation. Previously, studies have looked into the investors perspective to use the Ohlson model as an indication of over- or undervaluation of a stock. However, the purpose of this thesis is to see whether individual firm characteristics, found value relevant by academic research, can be used by a long-term investor to see whether the actual equity value is within its margin of safety and therefore worth looking more closely into.
34 equity in the PBLS industry group, further research could look into the splitting of R&D expenses into internal and acquired R&D. By doing this the complete effect of R&D on the market value of equity might be captured. Lastly, only the effect of non-linearity and R&D expenditures on the market value of equity is examined in this thesis, however, previous research has pointed towards the creation of options on future earnings by investing in R&D. Therefore, future research might look into the interaction effect of R&D expenditures and the non-linearity effect of earnings.
VI. References
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Bradshaw, M., 2004. How do analysts use their earnings forecasts in generating stock recommendations?. The Accounting Review 79.1, 25-50.
Brooks, C., Introductory Econometrics for Finance. Cambridge University Press, New York. Burgstahler, D., Dichev, I., 1997. Earnings, adaptation and equity value. Accounting review 72.2, 187-215.
Callen, J., Morel, M., 2005. The valuation relevance of R&D expenditures: Time series evidence. International review of financial analysis 14.3, 304-325.
Cockburn, I., Long, G., 2015. The importance of patents to innovation: updated cross-industry comparisons with biopharmaceuticals. Expert Opinion on Therapeutic Patents 25.7, 739-742. Collins, D., Pincus, M., Xie H., 1999. Equity valuation and negative earnings: The role of book value of equity. The Accounting Review 74.1, 29-61.
Dechow, P., Hutton, A., Sloan, R., 1999. An empirical assessment of the residual income valuation model. Journal of Accounting and Economics 26.1-3, 1-34.
35 Hill, R., Griffiths, W., Lim, G., 2011. Using Stata for Principles of Econometrics. John Wiley & Sons, New Jersey.
Hirschey, M., Spencer, R., 1992. Size effects in the market valuation of fundamental factors. Financial Analysts Journal 48.2, 91-95.
Holthausen, R., Larcker, D., 1992. The prediction of stock returns using financial statement information. Journal of accounting and economics 15.2-3, 373-411.
Koller, T., Goedhart, M., Wessels, D., 2015. Valuation: Measuring and managing the value of companies. John Wiley & Sons, New Jersey.
Kumari, P., Mishra, C., 2017. A Literature Review on Ohlson (1995). Asian Journal of Finance & Accounting 9.2, 28-47.
Larrabee, D., Voss, J., 2012. Valuation techniques: Discounted cash flow, earnings quality, measures of value added, and real options. John Wiley & Sons, New Jersey.
Lo, K., Lys, T., 2000. The Ohlson model: contribution to valuation theory, limitations, and empirical applications. Journal of Accounting, Auditing & Finance 15.3, 337-367.
Miller, M., Modigliani, F. 1961. Dividend policy, growth, and the valuation of shares. Journal of Business 34.4, 411-433.
Myers, J., 1999. Implementing residual income valuation with linear information dynamics. The Accounting Review 74.1, 1-28.
Ohlson, J., 1995. Earnings, book values, and dividends in equity valuation. Contemporary Accounting Research 11.2, 661-687.
Ou, J., Penman, S., 1989. Financial statement analysis and the prediction of stock returns. Journal of accounting and economics 11.4, 295-329.
Ou, J., Sepe, J., 2002. Analysts earnings forecasts and the roles of earnings and book value in equity valuation. Journal of Business Finance & Accounting 29.3-4, 287-316.
Penman, S., 1998. A synthesis of equity valuation techniques and the terminal value calculation for the dividend discount model. Review of Accounting Studies 2.4, 303-323.
36 Rayburn, J., 1986. The association of operating cash flow and accruals with security returns. Journal of Accounting Research 24, 112-133.
Ross, S., 2013. The arbitrage theory of capital asset pricing. In: MacLean, L., Ziemba, W., Handbook of the fundamentals of financial decision making: Part I, Singapore. pp 11-30. Shah, Syed Zulfiqar Ali, Andrew W. Stark, and Saeed Akbar. "Firm size, sector and market valuation of R&D expenditures." Applied Financial Economics Letters 4.2 (2008): 87-91 Sougiannis, T., 1994. The accounting based valuation of corporate R&D. Accounting review 69.1, 44-68.
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Database sources
Compustat North America Fundamentals Quarterly. (2019. March 11). Retrieved from https://wrds-web.wharton.upenn.edu/wrds/query_forms/navigation.cfm?navId=60
37
Appendix A. Descriptive statistics of subsamples based on size
Table A.1. Summary statistics small cap companies (profit firms) "∗∗∗∗ mean median Std. Dev. min max
Panel A. Retrieved variables Compustat*
$% 4,242 563.10 353.40 525.70 0.013 1,999 &% 4,237 187.00 117.70 193.10 12.52 1,713
' 4,234 4.47 2.14 9.61 -75.13 78.26
(&* ',-./01234.5∗ 3,554 6.32 2.90 10.14 -1.50 206.90
Panel B. Retrieved variable from Kenneth French Database**
(6 4,242 2.80 3.67 8.01 -23.24 20.40
Panel C. Constructed variables for estimation
$%7899 4,152 3.04 1.82 28.86 -459.20 1,719
'789 4,146 0.02 0.03 0.12 -2.16 4.19
('789)< 4,146 0.02 0.001 0.35 0.00 17.54 (*789 3,500 0.04 0.03 0.13 -2.80 6.01
(69 4,154 0.10 0.02 2.91 -21.77 182.70
Panel D. Constructed variables for data selection***
= ' > 4,242 45.36 58.97 40.11 -60.77 95.97 $% &% > 4,242 4.65 4.32 0.99 3.410 7.80 Number of firms 153
* Unscaled variables are displayed in millions of USD ** Return on the stock market index is measured in percentages *** price-earnings and market-book ratio are displayed as median values
38 Table A.2. Summary statistics medium cap companies (profit firms)
"∗∗∗∗ mean median Std. Dev. min max
Panel A. Retrieved variables Compustat*
$% 1,998 4,648 4,095 2,117 2,000 9,996 &% 1,996 1,372 1,140 933.50 137.30 6,758 ' 1,997 47.07 36.70 55.28 -411.90 656.80 (&* ',-./01234.5∗ 1,767 53.30 32.93 80.63 -0.40 1,441
Panel B. Retrieved variable from Kenneth French Database**
(6 1,998 2.33 3.41 7.98 -23.24 20.40
Panel C. Constructed variables for estimation
$%7899 1,964 3.53 2.96 4.66 -118.60 38.07
'789 1,965 0.04 0.04 0.04 -0.30 0.42
('789)< 1,965 0.00 0.00 0.01 0 0.18 (*789 1,747 0.04 0.03 0.05 -0.87 0.45
(69 1,966 0.00 0.00 0.02 -0.27 0.16
Panel D. Constructed variables for data selection***
= ' > 1,998 31.31 47.57 42.68 -60.77 95.97 $% &% > 1,998 4.53 4.29 0.90 3.41 7.80 Number of firms 96
* Unscaled variables are displayed in millions of USD ** Return on the stock market index is measured in percentages *** price-earnings and market-book ratio are displayed as median values
39 Table A.3. Summary statistics large cap companies (profit firms)
"∗∗∗∗ mean median Std. Dev. min max
Panel A. Retrieved variables Compustat*
$% 1,869 63,994 44,752 59,023 10,008 370,732 &% 2,327 13,128 5,984 18,232 13.06 90,018
' 2,968 521.70 201 847.30 -6,273 12,274 (&* ',-./01234.5∗ 2,513 555.90 258.80 722.10 0 9,235
Panel B. Retrieved variable from Kenneth French Database**
(6 3,447 2.73 3.84 7.63 -23.24 20.40
Panel C. Constructed variables for estimation
$%7899 1,771 4.75 3.84 3.50 -29.57 23.45
'789 2,346 0.06 0.05 0.12 -3.51 2.18
('789)< 2,346 0.02 0.00 0.29 0.00 12.30
(*789 2,137 0.05 0.05 0.07 -1.00 1.46
(69 2,489 0.08 0.01 2.57 -25.31 118.10
Panel D. Constructed variables for data selection***
= ' > 3,447 38.58 54.07 42.96 -60.77 95.97 $% &% > 3,447 4.67 4.32 0.92 3.410 7.80 Number of firms 183
* Unscaled variables are displayed in millions of USD ** Return on the stock market index is measured in percentages *** price-earnings and market-book ratio are displayed as median values
40
Appendix B. Statistical tests
Unit Root Test for stationarity
To check for stationarity the Fisher-like Unit Root test has been conducted on the variables, results can be found in tables B.1., for non-normalized variables, and B.2., for the normalized variables.
Table B.1. Fisher-type Augmented Dicky-Fuller Unit Root Test non-normalized variables
&%78 '78 (&* ',-./01234.578 (68 $%78 P 384.46 1,025.01*** 482.10*** 3,285.38*** 455.66*** Z 12.58 -10.01*** 3.86 -42.74*** 4.94 L* 10.85 -13.83*** 2.18 -64.39*** 2.93 Pm 0.83 23.40*** 6.31*** 101.05*** 4.17*** #panels 197 198 178 207 190 *** p<0.01, ** p<0.05, * p<0.1
Table B.2. Fisher-type Augmented Dicky-Fuller Unit Root Test normalized variables
'789 ('789)< (*789 (689 $%789 P 1,961.48*** 2,668.47*** 4,491.02*** 3,565.77*** 900.85*** Z -26.75*** -33.93*** -49.34*** -45.77*** -10.37*** L* -38.46*** -53.77*** -97.62*** -73.58*** -14.31*** Pm 59.93*** 86.35*** 164.28*** 119.88*** 21.23*** #panels 194 194 174 205 185 *** p<0.01, ** p<0.05, * p<0.1
41 Table B.3. General model tests
Overall Small Medium Large
White test1 5,899.78*** 3,004.98*** 1,343.61*** 406.93*** Wooldridge test2 234.63*** (10) 164.04*** (9) 341.14*** (7) 579.91*** (7) 1 Test for heteroscedasticity
2 Test for autocorrelation (between parentheses the number of lags to be included in the Newey-West Standard Errors to adjust for autocorrelation and heteroscedasticity)
*** p<0.01, ** p<0.05, * p<0.1
Panel data model tests
Table B.4., show clear evidence for a fixed effects model since the Hausman test indicates on a 1% significance level that the null hypothesis of a random effect model to be the best fit should be rejected.
Table B.4. Hausman test
Overall Small Medium Large
Hausman 473.96*** 497.82*** 655.32*** 672.09***
*** p<0.01, ** p<0.05, * p<0.1
Table B.5. indicates also to include time-fixed effects in the fixed effect model.
Table B.5. Redundant fixed effects test
Overall Small Medium Large
Time-fixed effects 663.65*** 341.14*** 579.91*** 704.44***
42
Appendix C. Size effect of loss firms in the sample and estimation method
First a note has to be highlighted namely, the small cap companies still, as in the main results, seem to bias the estimation coefficients overall, like in the time-series regression, the weight of the firms is not value-weighted, one can see that the small cap companies represent over half the observations in the overall sample.
Size effect of loss firms
Table C1. Time Series – Regression results (profit and loss firms)
Small Medium Large
Mean Median St. Dev. Min Max Mean Median St. Dev. Min Max Mean Median St. Dev. Min Max
!"# 0.95 0.71 2.89 -17.37 13.37 2.81 1.70 6.54 -9.67 45.01 1.30 1.20 3.46 -10.88 9.36 !$# 1.33 0.89 52.85 -258.53 690.73 1.81 7.48 190.34 -1,605.24 699.05 14.97 17.85 70.89 -254.55 224.51 !%$# 39.41 5.13 600.54 -9,318.33 5,613.24 429.2 8 55.25 2,087.15 -963.21 19,324.81 103.94 37.81 885.48 -1,825.73 4,397.61 !%%# 14.01 16.12 65.56 -640.95 382.50 65.38 34.19 156.83 -278.23 1,000.03 61.21 30.71 91.84 -46.97 388.09 !%&# 2.59 1.44 8.94 -29.90 107.58 12.78 5.19 63.94 -180.47 229.37 128.07 4 0.79 367.92 -309.12 1,137.53 n 32.42 27 17.56 14 109 10.12 3.70 69.10 -180.47 229.37 92.04 -7.40 384.37 -761.03 1,137.53 N 492 96 38 Adj. R sq. 0.57 0.60 0.32 -0.21 1 0.46 0.48 0.35 -0.35 1 0.36 0.38 0.34 -0.99 0.87
N. is the total number of firms
