Beta Estimation

7 The detailed discussion is provided in Section 2.1.

8 In the following, two parts are needed to estimate betas for individual firm (denoted as βⁱ): the computation of ICOE (denoted as r) based on CAPM, and the computation of expected stock returns (E(Ri)) based on FF4.

Details are listed in Section 2.3 beta estimation.

Financial statement and accounting data for main variables such as EPS, book value of total assets, and number of shares are collected from COMPUSTAT and Global Vantage.

Stock return data are available and computed from CRSP. Risk-free rate and Fama and French factors (MKT, SMB, HML, and MOM) are collected from the Kenneth R. French Data Library in Dartmouth website.

All key variables are defined in Table 1.

Table 1 Definitions of Key Variables

This table displays the definition of all key variables. The full sample period is from 1994 to 2009.⁹

Indication Variables

Ri Annual stock return computed from CRSP

Annual Excess Return (1)

ER1 Annual stock return – Risk-free rate

= Sum of 12-month (Stock return – T-bill rate)

Annual Excess Return (2)

ER2 Annual stock return – Expected stock return derived from FF4¹¹

Measures of Valuations (V)

Actual EPS EPS (Income before extraordinary items－Preferred dividends) / Common shares outstanding

9 Most definition of our control variables follow Hahn and Lee (2009) and other reference we already mentioned in paper, including I, P, and G…,etc, whose original description can be referred to Hahn and Lee (2009) P.898-904 and Appendix P.919, and the detail is listed in our Table 1.

Definition of stock returns and EVA related variables mainly follow Fama, French ,1998-2008 and Yoo et al., 2004,2008, and there are some time adjustments concerning financial data publish in accounting system are considered here but omitted in time line description. The original description can be referred to their notations, and the detail is listed in our Table 1 as well.

10 In general discussion, extensive literature use stock returns (denoted as Ri), Tobin’s Q, and ROA as proxies for firm value or firm performance in solid and regular illustration in textbook of finance. Stock returns should to be considered of equity value because of the return in market value of holding a share of equity.

11 Two kinds of expected stock returns (denoted as E(Ri)) are considered in this paper: risk-free rate and expected return derived from FF4.

12We use actual earning at time t as the forecasted ahead earning of time t-1. The implication is that we use forecasts exactly equal to actual.

13 ICOE is derived from CAPM. Detail is listed in Section 2.3.

Proxy for

Financial constraints (FC)

Size ln(TA) The natural log of book value of total assets at fiscal year end.

Tangibility1 Tang1 Cash holdings + 0.715 × Receivables + 0.547 × Inventories + 0.535 × PPE) / book value of total assets¹⁴

Tangibility2 Tang2 Cash holdings + 0.715 × Receivables + 0.547 × Inventories + 0.535 × PPE － book value of total debt) / book value of total assets

Proxy for Profitability (P)

Profitability Profitability (P)

EBITDA/ Book value of total assets

Proxy for

= CAPEX / lagged PPE(lagged property, plant, and equipment)

Tobin’s Q Q Market value of total assets / Book value of total assets

= Book value of total assets + Market value of common shares － Book value of common shares + Deferred tax ) / Book value of total assets

Proxy for Solvency(S)

Current Ratio CR Current assets/ Current liability

Proxy for Debt Ratio(D)

Times Interest Earned

TIE Times Interest Earned (or Interest coverage )

= Operating income before depreciation / Interest expense

Debt Ratio DR Debt ratio (or Book leverage)

= (Book value of Short-term debt + Long-term debt ) / Book value of equity

Three stock return measures are used as dependent variables (Ri, ER1, ER2). They also represent the valuation made from market perspective. In the literature, stock returns are decomposed into expected (or normal) returns and excess (or abnormal) returns. However,

14 The weights of each item in tangibility follow those suggested by Almeida and Campello (2007) and Hahn and Lee (2009), and we do not re-estimate the weights. It might cause some biases in this measure.

in this paper, the first expected return is equal to risk-free rate and the second expected return is mostly constructed as benchmark for the four-factor model (hereafter, FF4) of Fama and French, which is adapted from the regression procedures of Fama and MacBeth (1973). Annual stock return is the proxy for total value, and two excess stock returns are the proxies for excess value. Because of this difference of meanings, we expect to observe distinct empirical results when different dependent variables are used.

Two earning-based valuation indicators are used as major independent variables (EPS and EVA). They also represent the valuation made from operating perspective composed of accounting numbers. EPS is commonly considered as the measure of total equity value, and reflects much more on absolute performance, indicating the absolute magnitude of profit per share. Therefore, we infer that EPS might be more associated with stock returns (Ri).

Meanwhile, EVA is equal to the remaining part of EPS minus the total opportunity cost of equity funds. That is, EVA should be considered as an excess equity value. Moreover, EVA originally reflects on relative performance, indicating excess profit earned comparing to the growth with cost, thus it should indicate excess returns (ER) more adequately.

EVA decomposes EPS into normal value and excess value, where normal value is concerned with ICOE, whereas excess value is simply EVA. Using the decomposition of EPS, we want to explore whether we can augment the goal of finance to a further step. That is, we can maximize firm value by maximizing shareholder wealth. Nevertheless, can we can maximize shareholder wealth by maximizing EVA because another part of EPS is only of normal value. If this value is true, maximization of firm value is then more reasonably related to the maximization of EVA.

Several firm characteristics are reported in this paper, including financial constraints, growth of investments, profitability, solvency, and debt ratio, are viewed as control variables. We attempt to develop the expected signs of coefficients of those variables in the following discussion, and we provide descriptive statistics for key variables in Table 2.

Table 2 Summary Statistics of Key Variables

This table displays the summary statistics of key variables reported as time-series averages of the

cross-sectional mean, median, and standard deviations over the period from 1994 to 2009. The number of total sample firm years (N) is 1760.

Variables Mean Median Std. Dev. Variables Mean Median Std. Dev.

Ri 0.149 0.154 0.358 Investment 0.219 0.185 0.147

EPS 1.554 1.350 1.898 Q 2.390 1.955 1.679

EVA 0.863 0.688 4.071 Profitability 17.244 16.770 6.829

ln(TA) 8.833 8.812 1.202 CR 1.796 1.532 1.285

Tang1 0.395 0.398 0.097 TIE 35.700 11.700 335.500

Tang2 -0.184 -0.191 0.204 DR 1.350 1.360 34.98

In Table 2, EVA is accounted for as 55.5% of EPS on average (0.863/1.554), but with larger variance (4.071 > 1.898). This indicates that a few firms earn abnormally. Although Ri, EPS, and EVA are positive in mean, they still present negative relation to Ri in some cases afterward. Two measures of asset tangibility have counter signs in mean due to definitions. Thus, the ratio of total debt to total assets of book value on average is approximately 57.9% [0.395-(-0.184)].

Before we proceed with our discussion regarding expected signs of coefficients of variables, we must point out that collinearityproblems¹⁵

15 In multivariate analysis, the existence of collinearity may cause noise on coefficients of variables. And for some variables here, high correlations exist between y and x, and x and x. General procedure to deal with collinearity, such as observing Pearson correlation table and setting up partition of variables suggested in literatures, are considered in this study. We also consider endogenous problem, which will be mentioned in Section 3.4 Robustness check.

exist in our model (such as Q to Ri, profitability (P) and investment (I), the correlation is approximately 30% and 50%, respectively). Based on our partition of variables, collinearityexists between stock returns, investments, Tobin’s Q, and profitability (P is the ratio of EBITDA to book value of total assets, and can be interpreted as cash-based ROA) (Aggarwal & Kyaw, 2006). ROA can also be used to measure profitability. Previous studies usually classify investment and Tobin’s Q under growth opportunity of investments, and state that growth is realized as

future profitability; thus, at times, profitability and investments are classified as categories of profitability as well (Hahn & Lee, 2009; Tim & Vidhan, 2008; Doukas & John, 1995).

However, stock returns, investments, Tobin’s Q, and ROA are all considered proxy variables for firm performance in a large body of literature (Klapper, 2004; Wright, Kroll, Mukherji, & Pettus, 2009; Bhagat & Bolton, 2008). We also attempt to make some adjustments in the following models by providing models without coexistence of stock returns, Tobin’s Q, and profitability; the results are mentioned, but are omitted from the final table to make the coefficients in empirical results more stable and reliable.

Expected signs of coefficients of variables

We use the natural log of a firm’s assets at the end of the year as the proxy of firm size (Gozzi et al., 2008)¹⁶

However, in some cases, asset size also serves as proxy for firm risk. When asset size is the proxy for firm risk, controversial results arise, as reflected in previous studies. Some studies claim that size has a positive effect on the risk taking of a firm due to the moral hazard associated with “too-big-to-fail” policy (Boyd, Jagannathan, & Kwak, 2009), whereas others suggest a negative correlation between firm size and risk (Fama & French, 1992). Thus, both positive and negative impacts on firm value caused by asset size seem plausible, if one views stock returns as risk premiums.

. Firm size is considered a determinant of financial constraints or capital market access (Titman & Wessels, 1988) that affects decisions of managers and firm value (Cho, 1998; Lee & Chuang, 2009). It is positively related to firm value (Opler &

Titman, 1994；Maury, 2006) because small firms are younger and less well known, and are therefore more likely to face financing constraints and vulnerable to capital market imperfections arising from information asymmetries and collateral constraints (Gertler &

Gilchrist, 1994).

16 Other proxy variables for firm size also exist, such as natural log of a firm’s total sale or market value of equity.

Asset tangibility is considered the expected asset liquidation value for a firm. A firm with greater expected asset liquidation value (or collateral assets) should have less financial constraints, and therefore have a higher firm value (Almeida & Campello, 2007; Hahn & Lee, 2009). Following all that, we expect that financial constraints are negatively related to stock returns (measures of financial constraints are all reverse indicators; when these measures are bigger, financial constraints are less, and stock returns are bigger). We also expect that measures of financial constraints are positively related to stock returns.

The discussion of financial constraints in some studies often involves issues of maturity stage and firm scale. Previous studies suggest that large firms tend to have low growth (maturity stage) and lower firm performance (Opler &Titman, 1994；Maury, 2006; Lee &

Chuang, 2009). If we attempt to restate the description above, we could say that large firms tend to earn normal stock returns and have lower firm value, whereas small firms tend to earn abnormal (or excess) stock returns and have higher firm value. Therefore, this theory suggests a negative relation of size to stock returns, and negative relation of size to excess stock returns.

In sum, after combining theories of size effect, firm risk, financial constraints, and maturity stage, both positive and negative impacts on firm value caused by asset size are still likely to appear, and the relation of asset tangibility to excess stock returns remains unknown as well.

Growth of investments and profitability both have positive contribution to firm value (Hahn & Lee, 2009, Fama & French, 1992), and naturally, we expect to observe a positive relation between investments, profitability, and stock returns. As Penman (2010) says,

“Don't pay too much for the growth.” After considering corresponding opportunity cost of equity funds, seeking for growth of investment and profitability may be harmful to a corporation. That is, when firms make inefficient investments with rate of returns lower

than ICOE, we infer that such may enhance stock returns, while simultaneously decrease excess stock returns.

Current ratio is expected to observe a positive relation with stock returns (Menon,1987;

Richards, 1980; Donaldson, 2000). Meanwhile, debt ratio (or book leverage) is expected to observe a negative relation with stock returns. Times interest earned is a quality measure for debt. Studies show controversial results on the relation between leverage and firm value;

some support a positive relation (Harris & Raviv, 1990; Stulz, 1990), whereas others support a negative relation (Opler & Titman, 1994; Majumdar & Chhibber, 1999; Weill, 2008). Studies also suggest that the relation is based on degrees of growth opportunities;

thus, debt financing will enhance firm value in low-growth firms, but reduce firm value in high-growth firms (McConnell & Servaes, 1995; Jung, Kim, & Stulz, 1996; Barclay, Marx,

& Smith, 2003). Often, high debt ratio can reduce the opportunities of managers to overinvest, and decrease agency cost in low-growth firms, thereby generating high free cash flow (Jensen, 1986; Stulz, 1990; Gul & Tsui, 1998). Based on the pecking order theory, firms that are more profitable can meet the funding requirements through internal earnings and less borrowing (Myers & Majluf, 1984).

2.2. Models and Hypotheses

Three kinds of model designs are presented in this paper: whole sample model, sub-period model, and causality model.

(1) Whole sample model

In the whole sample model, we take a full effective sample period (1994–2009) to conduct panel regression tests with fixed effect and no intercept model settings. Based on our partition of control variables mentioned above, we proceed to determine the valuation indicator, EPS or EVA, that has better explanatory power of stock returns in all eight model combinations.

(2) Sub-period model

According to Haugen (1999), EMH-based studies and behavior finance are rivals in new finance period¹⁷

Therefore, in sub-period model, we set the year 2002 (the year the Nobel prize is won by Kahneman, a scholar of behavior finance) as the cut-off point of the rising stage of behavioral finance; thus, we divide the whole sample period into two sub-periods (i.e., the former period, 1994–2001, and the latter period, 2002–2009. The year 2009 is used as year dummy to avoid the influence of financial crisis). We then proceed to apply the same panel regression tests to each sub-period to compare their explanatory power. Under EMH, the explanatory power after considering FF factors should increase (Former < Latter). However, we expect to observe the “behavior finance effect” as time goes on; thus, we infer that the explanatory power of sub-period models will decrease over time (Former > Latter).

. Under this competition, we investigate whether the rising perspective of behavior finance seriously impact the power of EMH-based studies on business valuation.

(3) Causality model

We attempt to investigate the interactions between valuations made from operating and market perspectives, and test for the “behavioral finance effect” by causality models. We can consider the operating perspective consisting of two levels. Based on the theory of finance on value generators, major operating decisions (investing, financing, and payout policies) contribute to the quality of performance of a firm, and the performance reflect on valuations made from operating perspective such as EPS and EVA. As a result, we prepare to carry out the causality tests by setting up a three-step

17 According to Haugen 1(999), the present finance progress could be divided into several segmentations:

accounting-related research dominates “Old Finance” period until 1960; economic theories and rational hypothesis influence “Modern Finance”period until 1980. After 1980, theories regarding inefficiency and psychology take over, thus to form the “New Finance” period.

analysis on causality as follows: (I) investigate the causality between financial constraints and earnings from operating perspective; (II) investigate the causality between earnings from operating perspective and returns from market perspective; and (III) investigate the causality between financial constraints (FC) and returns from market perspective (MP)

Following this logic, we are able to establish a natural causality loop under EMH for this three-step analysis: financial constraints (FC) belongs to parts of operating decisions as the literature stated (Hahn & Lee, 2009), asset size can be regarded as an index of financing policy, and tangibility can also be treated as the bridge index between financing and investing policies through the use of net operating assets or collateral assets. Thus, we conduct the first step of natural causality loop: (I) financial constraints affect valuations from operating perspective. Thus, if firms publish good valuations from operating perspective to the public, good informative announcement based on accounting analysis should bring up the market price of individual stock, or market stock returns of individual stock. Therefore, we conduct the second step of natural causality loop: (II) valuations from operating perspective affect valuations from market perspective. Finally, combining (I) and (II), we obtain the third step of natural causality loop: (III) financial constraints affect valuations from market perspective.

This is consistent with a number of studies documenting that corporate investment behavior arising from financial constraints are reflected in the stock returns (Hahn &

Lee, 2009; Forbes, 2007; Whited & Wu, 2006) because the inability to borrow externally causes many firms to bypass attractive investment opportunities; it

influences the firm value (Campello et al., 2010; Cleary, 1999) based on internal fund assumption (Fazzari et al., 1988).

We conduct the two-way Granger Causality and Wald tests¹⁸

Hypothesis 1: EVA is more informative due to lower information asymmetry.

to illustrate the causality or leadership between stock returns, financial constraints, and earning-based valuations. We expect to detect the behavior finance effect by reversing the directions of causality. We establish one hypothesis for each model design. A total of three hypotheses are listed below:

Hypothesis 2: The explanatory power of Fama and French’s market risk factors

reduces over time due to the rising perspective of behavior finance (psychological and other factors).

Hypothesis 3: There exists a reverse causality relationship (behavioral finance effect)

between stock returns (valuation from market perspective), earning-based valuation (valuation from operating perspective), and financial constraints.

2.3. Beta Estimation

In the present paper, two parts are needed to estimate betas for individual firms

(denoted as βⁱ): one is related to the computation of EVA, whereas the other is related to the computation of expected returns (risk-adjusted returns). The former follows CAPM,

whereas the latter follows the Fama and French four-factor model.

We follow the COMPUSTAT procedure for beta estimation of individual firms. The data is only traceable within five years of the present date. For data out of this range, we adapt the formula and steps set in the database using S&P 500 Index returns as market returns (Rm), risk-free rate (Rf), stock returns of each firms (Ri) in monthly data form, to estimate current individual beta (β_i). At least 24–60 previous observations are required to meet the regression requirements. We then substitute individual beta (βi) into CAPM to

18 The causality model requires the two preliminary tests (unit root test and co-integration test) to be conducted to check whether the variable is stationary and existing an economic equilibrium, and an optimal lag number in time series model be selected based on AIC or SIC. In this paper, the validity of these preliminary results is checked, but omitted in the final table, and we conduct those tests by SAS procedures (varmax). We must note that the causality test cannot identify the difference between causality and leadership in statistic.

obtain ICOE (ri) for individual firms¹⁹

In the following, we estimate the expected stock return by the procedures in (Hahn &

Lee, 2009): estimating the Fama and French factor loadings (β' ik) for individual stock i using monthly rolling regressions with a 60-month window every month requires at least 24 monthly return observations in a given window and substituting those betas into the model

E(R_i)= R_it− Rf t− Σ{k=1~4} β'ik×F_kt (3)

to obtain expected stock returns, where Rit is stock return of firm i at time t, Rft is the risk-free rate (T-bill rate) at time t, and F_kt denotes one of the Fama and French four-factor loading (MKT, SMB, HML, and MOM).

.